 Can you hear me. Okay. So, good afternoon everybody. My name is Giovanni Marini and today, together with my colleague, we are more case here. We're going to present to introduce epic that is a code which is a 90 based. And first of all, let me take this opportunity to thank the organizers because they are giving us this great opportunity to present in such in front of such a great audience. And I'm really glad to have this, this occasion. So, I will start by just illustrating you the main contributors of this project. That's basically pretty old, actually, because it's started more than 10 years ago, and then it kind of become bigger and bigger, but never managed to get a collective effort in order to be published in this project. And so, basically, we are me and we have been building in the past months on top of the work of all these other researchers and professors, including Yelena's yagste, Matthew Galandra, Johnny profet and Francesco Maori but not leave them to that to them but just they are the main contributors. And they've been building a suite that we think we could be useful for the community in order to compute the electron for interaction based properties of materials. So, our talk is divided in three first three parts and the aim is to give you just an idea of what we can do and of course, if you may like some of these capabilities you are more than welcome to ask us for more explanation about them. So, what is epic epic is was born as a photo and based open source software for the calculation of the electron form based interaction properties from first principles, and it's the main ideas were laid in 12 years ago in this PRB by calendar and other authors, and basically the idea was to exploit the unitary linear representation in order to allow users to calculate with precision, some properties that are difficult to obtain ab initio and especially because they are difficult to converge on an ab initio framework. So, the typical workflow of a calculation one with epic is basically made by three steps. The first step is to prepare your calculation, and this include the linearization procedure of your system together with a calculation and linear response of some operator that you are interested in calculating. Then you proceed with your calculation. And this can be this will be illustrated in the next slides by Wilma. And you can analyze your results with some of the post processing that are included in the public release. Essentially, this is a, let's say this is a scheme of what we are proposing to you. That is, you have a generic DFT solver right now we just implemented for quantum espresso but our idea is that this can be extended to order to other ab initio softwares. And then you use the ability to one you know 90 to go to the real space and this smooth gauge together with the use of a linear, linear response solver that in these cases again quantum espresso but can be extended in order to compute a generic observable that in general can also be dependent on on the momentum at this moment this this operator that's known from ab initio on on a grid can be calculated on a much denser grid using the fast calculation that are possible only in the one year representation. So what we want to do is basically is to calculate this observable that in the most of the occasions that we will talk about today is the electron phonon matrix elements. And what we we we managed to do is to calculate them on a very dense grid. And in order to calculate it more precision, the, for example, the, the spectral function that you need or whatever. So now I will leave to Guillermo for some application this. Indeed. Okay, before that before going to the application I would like to, let's say expose some of the feature that we would like to share about this code. This is not merely, let's say that the code is working correctly, but we would like also to show you that we try to make the code accessible and really paralyzed and with a structure that is modular in such a way that is easier to implement a new feature. So this is creating the interpolation or routine that is common to all these factor calculation that are performed inside the code. And so, this is on the right of the slide you can see the main driver, the source code of the main driver sub routine and as you can see it's quite straightforward. And you have the first interpolation that I developed shouldn't care about because it's already, let's say implemented, and you found afterwards all the possible calculation that are already implemented. And each module is quite easy and I think it could be, it could look familiar to you because there are some allocation routine the allocation, the main driver of the calculation and the closing part of the module. It's just a way to show you that it's meant to be ascended this code and this structure is meant to be accessible to facilitate this procedure. And then let's go on to the capabilities are epic. And in particular to one of his best I think a feature that is the ability to catch to represent the resonances that are characterizing our system. And I think that is, you know, you are very familiar with this, the simplest resonance of all that is the case of a force. And this is an oscillator in which the, this is the simplest system in which the this characterized by his proper frequency, omega zero, and this force to move a sport to response to an external the perturbation that has its own frequency omega. And as you already know, maybe the feature that's come out and characterize this kind of response is really picked, and it's really difficult to be described in with a computation simulation. As a matter of fact, we are dealing with freestyle so the characteristic frequency that we are interested to a depends on the left side on the difference between the band structure value again values so that in order to get the right value of this character is frequency that is the problem is I would like to in probe with my perturbation and I need a very fine measure on on on both the K and Q space. And moreover, I need a really final resolution of the frequency because if I don't match exactly the characteristic frequency of my system I don't get the proper resonance teacher. So, an example of this come this feature that is really common in all the linear responses function. I show you the adiabatic form of frequencies and did the way. How we can compute inside the dynamical matrices and then retrieved the adiabatic form of frequencies just performing the. The square root of the values and as you can see this, the main challenging aspect of this computation is to compute this by a function. Something is happening inside my mind. Okay, sorry. And the most problematic part of this function is the denominator because since it diverges in just one point we have the most significant part of this function that is located in one point it's very difficult to be with a course mesh. And as a matter of fact, on the left side you have the comparison with the dots that are the experimental values. And, for example, in this point between the value of Q between gamma and this point here, you can see that if comparing the red line that is the interpolated line that we achieved with that it and if we really did the performance on a course read that we see that the this divergent and not a bad behavior is not captured by the course mesh so it's, it's very difficult to use the epic and the vanier deposition strategy in order to catch these features and indeed the. And it goes beyond this approximation was beyond the adiabatic approximation and can perform the calculation of these quantities in a really fast way also for different frequency. And as you can see here, we have also the problem of sampling the frequency in in a satisfying with a satisfying mesh, but the result is really significant so it is useful to actually in a very fast way. The interesting quantities that we compute inside epic and it's interesting to be shown here is that the, and then the one of double resonant Raman that it seems like quite a exotic response because it's a third order response. But since it's characterized by it's third order resonances, it's a factor in the really significant and are more significant, for example, of the resonant Raman and not the double that is the first I like to be in the. The Raman density intensity on the left. And so we have just some and here we have a double resonant problem. So as you can see, even if it's a higher order response, the effects are really visible. And indeed, we have the need to interpolate both the G that is the electron phonon operator and the coupling with the dipole moment that is the coupling with the external radiation. And it's interesting that to use this experimental measurement because it's, it is really sensitive, sensible to the different, for example, is taking in the graphene multi layer. Okay, so now I can. Yes, I will proceed with illustrating some other capabilities. Besides so this so called catching resonances part, there is also a full suite that we to calculate superconducting related properties was our base basically on the knowledge of the electron covering malice element from the knowledge of these, you can promptly calculate the final line with for example, which is the basic quantity that's really that's needed to calculate the Liashberg function. And the Liashberg function in general gives you access to all the way to calculate superconducting properties of your compound. So basically we're solving the island lines formalism or we're solving the isotropic Liashberg, and this is both, both of those, these possibilities are implemented in the, in the code, as well as a full an isotropic resolution of the Liashberg equation. So you solve this couple equation for the gap superconducting gap, and what you cannot obtain is something like for example the brilliance on resolved Fermi's after the result gap or superconductor as well as. For example, the tunneling conductance that you can compare with your experiments per se. And that said, I think he's also able to calculate, for example, excited electron lifetime, always thanks to the knowledge of electron phonon matrix elements and the possibility to interpolate them on a very fun mesh but for regarding q amp k points. What you can do is you can calculate the, the living of excitation for example in semiconductors. This is the case of value marks and I, for example, and the excitation in the old valley, and the time, how much it survives due to the electron phone scattering. And we obtained two pico seconds which is pretty good comparison to the experimental values ranging from 1.5 to 2.5 pico seconds. We also implemented the possibility to calculate this quantity in the presence of the divergence through and through the interaction for long range so small q vectors. This is because this is different from the from the general case just because you have this divergent term for very small q that you need to subtract before you perform the interpolation then you add it back in the so called the vocal form. We also implemented in epic so you are also able to calculate the, for example, a gamma gamma lifetime, let's say, small q lifetime, and I will leave to Yelma for the final remarks and some perspectives. I will wrap all the application that are already implemented we have both adiabatic and adiabatic foreign frequencies, the possibility to compute the imaginary part so the phone online with and the possibility to compute the double resonance. So as the superconductive parts of the resolution of the anaesthetic and make that a large burger system and also the computation of the excited electrons lifetime, but we are still working on other projects that I think we've come out. Now, I hope that is the quasi particle interference spectrum and the dynamical one effective charges and also the optical conductivity that I needed to compute the infrared spectrum in metals. And so, let's thank you all for your attention and we hope that you may find the more useful information on the side, the skewer code is just linked for the site website. And if you are more schooled we leave you our emails so please contact us say it would be beautiful if you would be. Yes, so if any of you has any idea on some feature that would like to see implemented the net because it feels like it's compatible with what we are doing we are more than happy to hear your idea and to help you implement it in an epic if you want to. Thank you very much. Okay, so thank you. Guilherme Giovanni for the very nice talk. Is there any questions here in three steps. Okay, there's more. In the meantime, if this is for the people connected on zoom if you have questions, you can start to think and maybe write it in the chat. Thank you for the top and you mentioned about the, we have been you have frequency dependent quantities use some trick differential strategy, or I remember quickly so could you explain what that is. Yes, that is. I think there is a bit difficult because it's, there is a bit of mathematics involved. I use a big as life. I imagine such a person did. And I try to explain it as, as easy as I manage but the all the results are in published indeed in the calendar prophet I'm already articles of 2010. The idea is, first of all, of representing a generic linear response function with a functional instead of a functional density. And with this recasting it's possible to prove that this is a variation around a stationary point that is the equilibrium point with the right density, use density point. And thanks to this variational recasting, it's possible to use. Let's say in exact induce density, come in certain in such a way of forming just an error that is quadratic on such density. In this way, we can just use, let's say, use an extra approximated density, and just leave the all the dependence on the frequency, not on the operator that depends on the density, but just on the denominator that is indeed describing all the resonances. In this way, we have a response that is depending on the frequency. Yes, but with approximation that is, and isn't it's quite cheap to achieve this approximation because you have just a double content is attractive. And once you have this variation of form, you find out that indeed, since all the dependencies is around this denominator, the if you implement a differential approach, the difference between these two. Counties related and localize only around the Fermi energy. So, in some other words, you have actually effective low energy and it's on and let's say, and that can be easily studied with a bunny without taking care of all the unoccupied fence. And this way you can achieve a really accurate differential and response function depending on the frequency in a really achieve and control approximation. If I may add to what we already said just to give you some perspective on why this is also important in the case why when you have no frequency dependence. And this is also important because when you have your your normal procedure for interpolating dynamical matrices in in the final in linear response. What you do is basically you are interpolating also long range. And those, in principle, are not good to interpolate with for interpolation. So what we do is basically we subtract the non analytic term, then we interpolate and then we read it using the fast algorithm that have been implemented. One quick question in this slide so it's omega zero is zero or you do you do finite frequency dfp team. Indeed, you can choose your starting frequency as well as you like so it's it's it's faster for you to use the omega zero is it's good, or you can shoot it for. Indeed, since the main problem of this computation are catching the, the requirement of having a very dense mesh, when there is a resonances maybe your best frequency is not zero because there is a resonance zero, for example, for a metal. You can choose another frequency that is a far away that the resonance and you are able to perform a correct calculation without using a dense mesh. So maybe it's not the best choice to use the zero frequency. Thank you. Other questions. I see one here. Just a quick question on this slide so the last thing is the electron forum metrics and are you using in this the screen squared. Sorry, I don't know if the microphone is on them but I maybe I understood the person, the question is yeah. This new study by. Where is the dressing, let's say the operator. Okay. Yes, this variation. This variation of formulation. Okay, let's start with the usual common standard linear response function in which only one of the two vertex is dressed. And indeed, this is correct, and that is also correct to dress both vertex, that is, and that subtracting a double counting there. And these are two correct formulation, but if you perform an approximation on the induced density. So if you use an exact in use density. One of the two formulation is better approach because the data the error that you introduce a in this using an exact induced density affect both the double counting and the, let's say double dressed term in such a way that these two can cancel out. So that, in the end, the error is quadratic instead of linear, and you will find that need the approximation is quite better. So yes, they are both vertices are best and there is an additional double counting. Other questions. Okay. Yeah. So, for the doubly resonant from a member from the paper by Maori and other. Maybe this slide or yes so you do only like one of the diagrams which is only one of these expressions but I think there's like 144 or something diagrams if you count all of them. Yes, and then knowing the first order, they're 12 and it's important if they go 12 otherwise you get the wrong answer. So is it did implement all of them are only this one. Unfortunately, all of them. Unfortunately. So, there's like, there's some part in the code where there's like this some with bunch of indices and then 144 variations of it to do all combinations of indices. Yes. Okay, that's impressive. Is there a way to automate that to automate it to automate generation of all those diagrams, because in the end, there's a lot of variables. There are ways to automate generation of all those diagrams, because you know experimentalist measured higher orders if you go to like Jim Scott from Bell Labs in like 70s. They went you know, fourth order or something. So there are ways to do those higher ones. And then you know who wants to count all those or maybe for some other thing. Yeah, let's do the machine do it. Yeah. Maybe we can think about. Yeah, I don't know. I don't know how to do it. If there are no other questions, I think we can thank Giovanni, and thank you. Yeah, sorry. Okay, so now we have another contributed talk. I just. Oh, no. Okay. See. Okay. I've seen your email address. Then I will receive. Just, no, just click on the button. And then you receive an email. One, two, two. Okay, so now we have a, another talk on a very similar topic. So it's, it's Phoebe. So it's Phoebe, a collection of phone on an electron Boltzmann equation solvers and the talk will be given by Jennifer counter and underage a lot from our university. Yeah, so I