 Vsrednji sečen sem prišljena na GW, tako kratkovače z vseh GW vseh vseh. Vsrednji sečen sem prišljena na 3 teoretičnih vseh. Prvno je Andra Marini, če je vseh vseh vseh jambu kod, in vseh sečen. Vsrednji sečen sem prišljena na Alberto Vandalini, In ne znam, da je... Z Davio, z Davio... Ok. Ok, zato. Daj, Andrei. Tako. Znam, da je... Tako. Ok. So... Dobro, svoje. Tako, svoje. So, svoje. So, svoje. So, svoje. So, svoje. So, svoje. So, svoje. So, svoje. So, svoje. So, svoje. Nah love. So, svoje, ne jo? Tako, svoje ligi. Tako, svoje. Svoje. g. But given anemiltonian, which in terms of some fields, you can get an equation of motion by this technique, very simple, not very complicated. And then we will understand mathematically g. W, where does it come from? At that point we will split our analysis in a diagrammatic approach in a functional derivative approach. So three different ways to see the same problem. This is essential for you, as it is for me, because it gives me different ways to derive the same stuff. Having different perspectives also gives you an idea of the limitations of this method, because you see it appearing as the result of approximations that apparently they are different, but they are just different ways to see the same approximation. OK, then. What is the main problem we need to solve? Because, I mean, from a very elemental physical point of view, the problem is very clear and very simple. So you have this many-body problem. This is many-body emiltonian. And the many-body emiltonian is complicated because you have the one over rr prime. So if you have a charge at r, then another charge at r prime, there will be an interaction between those two charges. And this interaction is long range. So this is the problem. So you can imagine that everything will be simple if you remove this interaction and you describe your system as two independent particles. This will be just simple, because even simple intuition will tell you that the dynamics will be the dynamics of the two independent particles. But the problem is the interaction. So now you may wonder if I have a system of two bodies or many bodies interacting, what happens if I remove one of the two, if I try to get it out? Or, alternatively, if I try to get it down, to get it in? In the first case, in the first case, this is just for the mission. Yesterday we had a talk by the experimentalist, was exactly explaining from the experimental point of view what they see when the electron is removed from the system. In general, experimentally, if you look at the distribution in energy of those photo-ejected electrons, they are not centred at a single energy. In general, when you do Arpus, you see structures. So this is, I don't know, for the mission as a function of the energy. So you don't have a delta function, because if you had a delta function, then you would say, oh, they are not interacting, I'm just removing one electron. But instead you see structures. Because when you do for the mission, you are actually accessing the excited state of the material, connected to the states with different number of particles. Now, let's forget for a moment the super complicated many-body problem. Let's do a step back. And we take the problem for a completely different perspective. If you have a system and then you add a charge, and then you assume that this charge is tiny enough to be treated with impertubation theory, the question is how can you calculate the change in the global density of the system. So now the problem is completely different. We are talking about a single charge that is added to your system, and this charge is assumed to be a tiny perturbation of the entire system. In this case, you can actually use the so-called Kubo expression. Ryogo Kubo, that was a Japanese theoretician, derived the exact expression with linear response for the change in any observable up on application of a tiny perturbation. In this case, our perturbation is this additional charge. So in the case of Kubo, the problem is written explicitly in terms of an external potential. We will see in a minute what is the external potential. For the moment, let's just concentrate on this simple problem. So you have the emiltonian, that is the bare emiltonian that is as complicated as you like. You add a tiny perturbation and then you just apply perturbation theory on a certain observable. In our case, the observable is just the time-dependent density. So rho is the density operator and we calculate the time-dependent density of this total emiltonian assuming that external perturbation is weak. This is Kubo and is the basis of linear response. Is the same expression that you apply to get absorption. Exactly the same. I think that yesterday David mentioned it. So the point is that now the external potential is not the external electromagnetic field, but it is the potential connected somehow to an additional charge. OK, then if you do the mass, it is very simple. We can realize that the induced density, that is the density that is induced by this perturbation is proportional to the external stimulus with the proportionality given by the density-density response function. The density-density response function is defined here at the end of the slide. It's just a mathematical object. It's the average of the commutator t-ordred, sorry, casual, not t-ordred. And actually this is just describing a very simple physical concept within linear response in Kubo. If you apply the perturbation at t, anything happening will be at later times. I mean, it's just simple intuition. OK, so then the key point is that this induced density will be proportional to the external density with the response function. So you see that we made appearing the response function by following a completely different path. But we have the response function. The response function is the main actor in GW. So you will see it appearing in any form whatever path we will take to GW at a certain point we will have to introduce the response function. So now if the induced potential is like this, then we may wonder, OK, if I add a charge and then the system produces a change in the density, then I can calculate easily at least the back effect of this charge to the entire system through the solution of Poisson equation. You know very well that in electrostatics a charge produces a classical potential. This classical potential is solution of Poisson. And the solution of Poisson is just the convolution of the induced charge in this case with the column potential. So this is the induced potential that appears in the system additional discharge. So now we have to do a step forward and say, OK, if I want to describe the effect of the potential in the wall dynamics, I have just to amend my total Hamiltonian with an addition Hamiltonian that in addition to the external potential includes the induced potential. Now, if you do simple math, you realize that this new potential, this new piece that you are to the Hamiltonian has the form of density, density interaction mediated by this object v kaj v. We made it appearing without using any diagrams and whatever. I mean, just intuition and electric theory. Now, if you do this, you say, oh, but this means that the perturbation made appearing in the Hamiltonian of a term where two densities, that is the external densities, the external charges that I've added, actually, I'm not interacting through v. So this interaction that is v, you see, this is v. Now, if you do the electric approach and then you consider that when... So, you have just to review this picture. Imagine that now there is... the blackboard is completely empty and then I add one charge. That's fine. There are no other charges. I add another charge. And then my heuristic derivation demonstrated that those two charges will now interact through something different because all the other electrons will react to the addition of the charge. So you realize quickly that this interaction here is not v, is not v, but it's w that is proportional to v kaj v. So by using this simple argument, you should have understood that the lowest process we may imagine in an extended material where actually there are collective reactions is to replace the long range interaction with something different, this screening interaction. This screening interaction is just the interaction that takes into account the reaction of all electrons to the perturbation. I mean, this very realistic approach is actually the basis of even more complex theories. If you try to look inside the Landau Theorie or quasi-particles, it's very much based on the assumption, on the idea, on the picture that the particles at the lowest order they can be considered as dressed and interacting through a potential that is different from the bare potential. And you can really build up lots of physics on the simple picture. Of course, now we have the problem of building up theory on top of this simple picture. For the GW, we have not all the huge problems that the Landau had, but we can use a simple intuitive link. Because you know, in a completely different way that the lowest and most simple approximation to the many-body problem is actually FOC. This is something that we study in our university courses. And actually FOC can be also derived without using complex many-body things with a variational approach. So the actually FOC can be introduced in many-body what you do with DFT. You may ask what is the lowest energy state that corresponds to as later determinant and this lowest energy state is the one solution where the orbital is a solution of the Archifog equation. Of course, this is something you have to know. In Archifog, you actually get two potentials. One is the Archry, is the classical potential and this is very much similar of what we had derived before. In Archifog approximation, the Archipotential that is an object that is present even in the exact theory is there, period. Just saying that I'll always order if you are at the charge, there will be an electrostatic potential. This is Archry. But then you have an additional piece that is FOC. The FOC term is purely quantistic and is due to the antismatic properties of the determinant. This is because the when functional electrons are antisymmetric. Because of this consequence, because of this, actually you have the consequence that two electrons cannot sit in the same state because of Pauli exclusion principle and this actually induces an additional piece that is the FOC term. Now, the FOC term, the difference with the Archry term is very simple actually, very physically different. But from a mathematical point of view the Archipotential is a density. There is a density, as you see, X prime, X prime. In FOC instead there is X, X prime. But still mediated by the Bercolom interaction. Well now, my intuitive, my realistic derivation says that OK, this screening is a quantistic process because it's not present in the classical theory. Then I can amend the quantistic part of Archry FOC by replacing B with W. I mean, guys, this is a DCGW. It's exactly GW. GW is a screened FOC potential. It's no more than this. Then, OK, there are complications due to the frequency dependent but you will see that length and there will be even lectures about this. But from a very conceptual point of view if you have to explain the GW to a student that knows nothing about diagrams and blah, blah, blah, you can use this approach. Now this approach, even if it is very simple and not at all formally derived, it actually leads to an important observation. You can find written in the literature that the GW is a dielectric approach. Why is it said to be dielectric approach? Because it assumes that the main physical process that occurs in a many body system upon additional removal of an electron is the screening of the interaction. So is a response function. This is the key. So the response function is the most important and dominant process that occurs in your system. And this is dielectrics because the response function that appears in GW is exactly the same that gives absorption. So with the same object, the response function you can calculate the screen interaction and also the absorption. But the absorption is an object of the electric theory of solids. This is an important concept that you have to bring to keep in mind that even if you do derivation, we will do some formal derivation in the following. But this is actually the main conceptual continent of the GW approximation. Ok, now let's see of course, what is the pro of this derivation is that it is simple. You get it done in fuselites. What is the cons? The cons is that it is not formally derived. So I don't know under which limitation it has been derived. And I cannot judge the validity of the theory. This is very essential for you. Whatever theory you are going to use in your career, it is very important that you know it at the level of understanding under which limitations you can use the theory. I mean, there are some rules. You cannot use the theory for everything. And now let's see what is in the case of the GW. Now a step forward. And we use a more formal derivation that will be common in the first part to the diagrammatic and to the functional derivative approach. So we keep in mind, again it is important that you keep in mind your heuristic derivation because that's the physical content. This is at the end the physical message of your derivation. But then you have to find a way to derive it more clearly. So we can revise quickly the concept of many body. Ok, one important thing in many body is that if you don't remember it you need to review it is the second quantization. So whatever root many body has to go through second quantization. So the transition between the wave function representation to the quantum field operators. Is something that if you don't remember please review it, but in general it's like chapter one or any book about many body. Any book about many body chapter one has second quantization of review. So it's simple. The important thing is that this object, this electron will be described as the state of a quantum field. So this this hat is just to specify that it is an operator. So this as anti commutation or commutation rules and can define propagator is an operator. So actually an operator in the fox space of the states of electrons. So if you don't remember the things just they have to revise. But once you know that the electrons are described in terms of field operators then you can actually draw a parallel with this life of an electron moving. So you have your gram state system and then you add. So this c dagger is really the addition at point r is exactly what I drew on the blackboard at point r of an electron. And then the many body now will tell you yes, but how is this original particle at air moving in time and this is through the time dependent term evolution operator u. Is describing the evolution of the electron from time t when it was added to the system to time t prime and then when you are at time t prime you can project by annihilating the electron. So c will annihilate. C dagger will create c will annihilate. So this is second quantization just trust me. So once you have calculated this is process you can actually define transition probability. So you can say what is the probability that when I add an electron in a point I will find it at point r prime and t prime many body and quantum physics is statistical theory so you describe every in terms of probabilities and another important thing that makes things a little bit complicated and this is something I don't know if you read the quote I think it was of Freeman Dyson of the conjecture of Feynman of rewarding quantum physics thermal trajectories and Freeman Dyson will say I mean this guy is completely crazy you cannot write everything in terms of trajectories but actually he was right so in many body you transform complexity in trajectories so all the informations about the many body system are included in this time evolution between t and t prime if you manage to describe exactly this evolution you solve exactly the problem and then how do you do it in practice well in practice you define two probabilities one is to go from t prime and the other to go from t prime to t well this is needed because you cannot break the time reversal so you would see it by doing the math you see that you need to include both probabilities to go back and forward in time when you do it you can actually build the Green's function that is a t-order product again the need of this ordering you say wow how do you know that it is a t-order well it is just a matter of doing the math if you do the math of the single probability Psydagreb C you realize that at a certain point you do need to include an ordering otherwise you cannot close the equation because the point is that how do I calculate the equation of motion for this object oh sorry one important thing is that the Green's function actually is the most elemental brick of the theory in the heuristic approach the response function was the most elemental brick but if you go in many body and you go still deeper in the theory you realize that the Green's function is the most elemental brick in your theory because it produces several observables the density, the independent density it is just a contraction of the Green's function so when you calculate the Green's function in theory for the Green's function you have automatically a theory for the density automatically so you see for example for this identity a link with DFT so and then sometimes one says that many body actually includes more than DFT and it is actually due to this connection from many body the core object of density function of the density is just a contraction so with many body it is just part of the information I can get because if you leave the Green's function open you have access to many more information so from this point of view many body is more general than DFT and indeed if you do the expansion of the Green's function in exact n plus 1 n minus 1 states of the Miltonian you can have so-called Lehmann representation so you can easily realize this has been already introduced by Pedro that the poles of the Green's function are the excitation energy of the system so you have that the two terms of the Green's function have poles at the difference of excited energies of the system with n plus 1 minus n minus n minus 1 so Green's function is just when it is exact it gives access to the exact excitation energies this is something that maybe you I invite you to think about so D, many body in Miltonian is completely unsolvable, it is an horrible object so it is a term that has a sum of single particle single particle objects that has some of four body so I mean the leptinol interaction will span four bodies I mean it is completely unsolvable if not in super simple models the power of many body is evident because it allows you to access the real excitation energies of a monster in Miltonian by a single body Green's function so by just looking at the time evolution of one leptin in the full many body you have access to the excitation energy of the monster I mean this is very powerful very powerful extremely powerful and actually the many body concept with Green's function is one of the concepts that is most widely used in physics so you find it in high energy in quantum field theory so in the theories of particles of leptins and so on so for Green's functions you find it in the zero temperature many body the one we are doing now if you increase the temperature again you have Green's function if you go on the Keldisch contour you have Green's functions so Green's functions are really the most elemental bricks of I would say theoretical physics ok then we need say if that's important we need to find a way for Green's functions and then now I just briefly show you a method to get equation of motions for any object appearing in miltonian in our miltonian our miltonian is just a functional of these field operators there are only electrons but you can you can do theories even more complicated where you have besides those field operators of electrons you can give me an miltonian as a functional photons whatever you want if you are able to give me a field that describes that particle and in a miltonian I can give you an equation of motion how? by using simple Isenberg relation so if you want shredding or rooting for operators so if you from you know that the time derivative of any operator appearing in a miltonian is given by the commutator of this object with a miltonian this is all we need this is also for any field appearing in a miltonian if it is a photon same whatever then if you have this relation you can now, given this miltonian you can calculate easily the derivative because you can apply the derivative to the Green's function why is this? this is simple conceptually simple then mathematically it can be not so simple but how do you do it? you know that e dT of C rT is the commutator of C rT the miltonian and then you know that the Green's function G rT r prime T prime is equal to minus I and then you have an average of the T product of C rT C dagger r prime T prime now to calculate this commutator you just need the commutation rules for the Psi you know that C rT sorry, anti commutator C dagger r prime rT prime minus r prime plus minus I I never remember T minus T prime so you know the basic commutation or anti commutation relations depending whether it is a fermion or boson this is also for the electron field operators for the boson field operator whatever so thanks to this you can calculate explicitly this commutator it is a long expression but can be calculated it's not super difficult actually because if it is a four body operator then whenever you do a commutation you reduce a one field operator this can be it's really a textbook exercise so once you are able to explicitly write this as a functional it would be a functional of what? of C and of the column interaction thanks to this function you can calculate the derivative of this object because if I do E dT of G on the right hand side I have to do minus I E dT of this average but then I have two terms two terms one is when it is inside so T of E dT psi psi dot gr r prime T prime and then I have another piece that is just the derivative of the theta function this is not essential it is a technical piece but I mean if you just no complicated math if you write on a piece of paper the definition of the Green's function the definition of the Miltonian anti commutation relations and you do everything in a couple of pages then you just get that to have the derivative of the Green's function you have to do the T product of the derivative of the field operator now this derivative can be obtained from the commutation from the commutator now if you do it Green well if you do it you find yourself with this expression that the derivative contains this delta function this delta function appears because of the derivative of the theta function the derivative of the theta function is a delta function so you can really see in practice how you get this is a very I mean an important step of the derivation this is the g w coming from so you have this delta function then you have this g multiplied by h and this also appears because of the commutator then you have this horrible thing this horrible thing is a two-body Green's function you see psidaga so at two parts it is Green's function ok, you say oh wow this is terrible now we have two choices actually and there is actually a branch of physics that connected to each you have actually three choices and there are branches of physics connected to each of these choice one is to continue with the hierarchy so if I now want to calculate equation motion for l2 I need to do a c4 I need to calculate the derivative with respect to t1 this is g2 and then you realize that this will induce a g3 with three bodies and then you have four bodies and so on and so forth and this is the hierarchy it does also name it now I don't remember hierarchy and there are ways of reduce this hierarchy but there are also other ways ok so we have two different methods to calculate this two-part Green's function and to connect to this mass operator so this is a key step of the theory let's go back so now you have edtg proportional to g minus i this horrible thing what is the goal of your theory is to work to rewrite the right hand side this l2 in terms of g so even if you want to pay the price of an integral differential equation that eventually you can solve you need to rewrite everything in terms of no objects so the goal of both the Schwinger approach and the grammatica approach is to rewrite everything in terms of g everything in terms of g even if it is a complicated form it must be written in terms of g and Freemand Eisen actually is the father of this expression where you rewrite this complex object as the convolution of two objects this is the self-energy the self-energy is what remains out of the collision term in the question of most of the Green's function when you express explicitly the Green's function it is a way to re-sum to rewrite everything as a functional of the Green's function so the formal derivation of the self-energy is by this identity if you want at this level I can assume that there exists a form of the equation such that the two-body Green's function can be written by m by g and now there are two ways to do this because I mean I don't have any other choice that work out this L2 and there are two ways one is the Schringer approach and the other is the grammatica approach the Schringer approach is a way to rewrite exactly everything but it's very similar to DFT in the concept in the sense that in DFT at some point you do the theory very nice, you have a number of theorems and then you have this exchange correlation function that you don't know then you derive kanasham this functional produces a potential that you don't know and you actually push what you don't know more and more further in the theory so you say I have actually what is the remaining as the xc but do you know xc? No, I don't know xc so you actually rewrite everything exactly in terms of an unknown quantity the Schringer approach does the same the rule played by the vxc in many bodies played by the vertex function it is an object that is formally defined but that you don't know so you have to do approximations the grammatica approach is much more dirty and elemental because actually the aim is not to write everything exactly absolutely not but to understand what are the leading terms in this L2 what are the leading terms so from a point indeed historically the first one to be introduced was the Dagrammatic approach so immediately after the theories of many bodies by Vick, Feynman and so on and Bruckener, Loh the Gelman and Loh theorem and so on and so forth the GW was introduced along with the T-magics approximation using the Dagrammatic approach and this is why I would like to introduce it to you to give you an idea also to have a different perspective so let's take for the moment we can actually slow down for a second do you have questions are you lost or did you get at least the basic concept about this just to take 2 minutes then we actually it's a bit late did you get at least the physics of this so a question that could do you very simple question if now I tell you apply GW on H2 molecule what would you say on a molecule composed by 5 atoms so a colleague of you say wow I am applying GW I am applying Yambo on H2 molecule would you say yes good choice yes that's the point yes because when you are convinced that even if you don't know many body theory you don't know all this complicated stuff you know that the main ingredient of GW is the dielectric function if you have an isolated system there is no screening I mean come on it would better say to your colleague I mean don't spend time in computer resources to run GW use archifog so this is important I mean also to understand the limitations and potential applications of the method don't just apply the method because all the people is applying the method because there is a very nice Yambo code the developers are very nice persons and the school was very interesting we had good dinner at the same time if you are in a system even if it is extended sorry Andrea, I am Daniele yes I don't want to be polemic but just to say that there are hundreds of paper on GW on molecules there are benchmarks about the recycle of GW for molecules what is your perspective what is your thought about oh yes, but I said H2 molecule H2 of course if the molecule has a number of electrons such to create plasma waves of collective waves then that is it this is important I heard 5 atoms totally agree about 5 atoms is enough to have collective excitations so 2 atoms the point is that my message was just to get a physical intuition the main ingredients of the theory that actually defines also the limits of the theory at the same time if you want to study a system where the main physical process is not driven by screaming but by other kind of processes I don't know, short range interactions well in that case the most proper self energy is not the GW but it's something else I mean for example at the same time that GW was proposed Galitski proposed the so called thematic approximation is proven to be exact when you have a short range interaction so GW is really based on a dielectric concept ok so in the last few minutes if I have to decide between Feynman and Schwinger I prefer Feynman because I like Dagm I prefer Feynman rather than Schwinger also because Schwinger is a single road I mean you don't have any other choice and you get a point I mean it's an exact way of providing a problem and my feeling is that it actually makes appear more complicated instead with the diagrammatic approach you can use still elemental concepts so how is the story with the diagrammatic approach actually again the main actor is the response function and then with this we conclude maybe I jump to the end to the last remarks about GW so with the diagrammatic approach actually you really use a sort of lego approach that you can even do with your kids I mean it's just a lego it's a way to connect stuff in order to create objects so the response function that is again the most elemental ingredient in the GW approximation is a density dense response function now you realize something that is actually at the basis of the I mean it is the reason why the Schwinger approach is so complicated and why the diagrammatic approach also has to be done with care now the quantum interaction yes you see this object down here this object down here this is the beast problem of all the the source of all problems the quantum interaction is something that if you draw the diagrammatic is made like this you see you have Psi dagger Psi dagger so you have R R prime then you have in R you have Psi dagger Psi so you have Psi dagger Psi R in R prime Psi dagger Psi so you have Psi dagger Psi and here you have V now this process is the elemental diagrammatic object when you want to calculate the Green's function the one needed to derive the mass operator you actually have to do this very simple game so you have that your Green's function is of the kind Psi dagger Psi Psi Psi dagger so this means that Psi here and Psi dagger here Psi sorry Psi dagger so now you have to connect all the arrows in no possible ways in such a way to not leave any arrow free and also to not disconnect the diagram so I can do several things I can close like simply to not do like this and I can do this simple my kid could do the same and this is archery this is just archery this diagram, this closing is archery and the point is that this V actually appears not just once but an infinite number of times all the problem is due to this interaction actually in the dynamics appears an infinite number of times so if you write in terms of a sum so now the point is how do I choose the way if you have already two of this if you have already two of this you have already lots of possibilities to how to connect it I mean there are actually at the order two, there are two factorial so it is six terms there are different ways to connect it and if you go to i-orders you have more how do you select the diagrams well the diagrams are selected in the GW approximation if you go on many body textbooks about GW you see that the GW approximations for specific reason that is connected to the electric approximation you can realize easily that if you consider diagrams like this where you have you see where the connection here is done in such a way to just do this way this is the lowest order diagram of GW and as this form now the column interaction one over R minus prime as the problem that in the Fourier transformation it goes like one over q-square so the Fourier transform of V is 4 pi divided by q-square q-square it diverges so in homogeneous electron gas you can prove on a piece of paper that the lowest bubble diagram is divergent I'm almost done is divergent and the GW approximation is a way to cure this divergence and is the only way to re-sum diagrams in such a way that this divergence is regularized this is the GW approximation and then you can prove on a piece of paper that if you just consider all the diagrams of this form for the interaction so the V the bare interaction is replaced by one bubble two bubbles and so on and so forth you get that this interaction goes like this V of q instead of going one over q-square diverging it gets this difference Kai enters in the definition of W now this W of q is not divergent anymore so if you consider just the diagrams where you have an arbitrary number of bubbles it can be proved on a piece of paper that this series is regular in q so it does not diverge if you do this you get GW because GW is just the all possible diagrams where you have different bubbles there inside now you may wonder when is it exact can you tell me when is it exact surely it is the only way when you have long range interaction and you need this divergence on the other hand it can be proved that in the high density limit it gets exact when you have an homogeneous electron gas with high density of electrons then GW becomes the dominant diagram clearly all the real materials are in the middle they are not either with high density or low density but this gives you an idea of the physical content diagrams are sumed together and then you get oh and also I am going yes all the bubbles define actually the screen interaction and the screen interaction that is defined in this way should give you the oh sorry it is there so GW is just introduced as the sum of bubbles that cures the divergence of the long range column interaction so now you have different puzzles of the story so you know that GW is very much connected to the electric properties in addition when you have an homogeneous electron gas with the long range interaction this electric picture is the only one able to fix the divergence so it is the only physical one so in a way the GW is the leading term in a system with the electric properties and with a long range interaction is the leading term so of course what that problem introduced the Schwinger approach so the Schwinger approach actually rewrites everything exactly I mean this is a way of rewriting everything exactly introducing more terms behind the response function in GW you have also these vertex but it is just a way to push in something in some definition they are no part of the story so I just conclude with actually at the end of the story what is GW doing so the role of GW is to describe correlation and will just lead to an effect that in general is opposite to archifoc so the archifoc in GW will reduce the gap now a simple question but I want a quick answer as the GW is the screen archifoc do you expect that in modulus the archifoc correction to be larger or smaller than the GW correction I mean GW is the screen archifoc do you expect the GW correction to be larger or smaller than the archifoc gap correction yes smaller yes it is smaller and actually when you go to the beater effect gets even more tiny but physically the trend is to open archifoc close then in general GW that is archifoc plus correlation gives a reasonable agreement with the gaps then of course this is just a picture to close the talk because when it doesn't work we would open I would give you dubs while I don't have to give you dubs I have to give clear messages so in general it works but of course whenever you have systems where there is something that works against the electric properties then in those cases you may expect GW to be less efficient for example transition metals where we have localized orbitals that they produce in the material a combination of extended or localized properties so the different length scales in that case GW has problems or even lots of problems ok and then some references there are many that GW has been reviewed there are reviews about GW and we really found anywhere and after so many years that's been applied so many times that there is reasonably valid theory and thank you thank you Andrea and the session is open for questions if you have any too much and I didn't do winger I mean of course this is kind of things of course not in one hour so maybe I can start with a question so you have stressed a lot the importance of screening so one other aspect of GW is that it has a dynamical self energy so it's a dynamical screening can you comment about the dynamical part? yes so you will see in practice you will see you will see in practice in the end zone or did I remove it? yes so the frequency dependent of this self energy is a clear manifestation of the quantistic properties of the theory so you need an analogy you need an analogy so when you do wash you have your amyctonia that contains an independent particle plus an interaction part so amycton interaction now this complex thing in atrifok in atrifok is replaced by h plus h atrifok plus b atrifok so it is single particle this is two bodies this is one body this is all one body so the idea of atrifok is to replace the full interaction with a mean field potential when many body the picture is similar but contains a very drastic difference with many body approximately you can do the same trick where you have h but you have a frequency or a time dependent potential so many body revise everything in terms not of a static potential but a time dependent potential the reason is that there is retardation there is a very quantistic object so if you write everything in terms of dynamics of the electrons so consider that during the trajectory the electrons will see the time evolution of the system around so the density oscillation will see real the system oscillating in time and so on and so forth this time dependence is actually reflected in the solution of the problem in a picture like that so if you have imagine for the emission spectrum you have the energy in the independent particle picture let's call it this E0 within Archifork you have change of the energy still delta function well defined energy when introduce the surf energy actually this thing gets a shifted broadening and eventually structures this is of course magnified so physically the frequency dependent in the broadening of the line and also in the appearance of structures besides the main peak so this is the coherent and in coherent part of the Green's function so here you can have plasma replica or phonore replica so the frequency dependent physically is describing the fact that the the dressed electron so coherent with the Landau picture is not charge object but contains just a fraction of the charge and eventually also non coherent parts so the quasi particle picture is richer than the single particle picture in an emission approach like Archifork or DFT so we have one more question and then one from the audience online so my question is how do you quantify this screen ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?