Modern computational methods in physics part 1: Diagonalization

[@MrPSolver]

Very cool! I'd be interested in seeing the code to your "Tensor Renormalization Group" algorithm for the Ising Model. It seems to do an excellent job at reducing the "critical slowing down" you see in the regular metropolis algorithm.

[@JonathonRiddell]

I think I'll throw it into the next video in this series when I cover tensor type algorithms! Real space renormalization group methods are nice when you can get them working :).

[@eulefranz944]

James was really cool! I think he can explain things very well! It is always fascinating to me how people who know their stuff can put it into "simple words" but not lose the depth they try to achieve

[@JonathonRiddell]

That's great! I'll pass along your kind words. I think he will be a regular for the Sunday night chats for the foreseeable future.

[@albertliu2599]

Very nice video! I am currently a physics graduate student who is trying to get some knowledge of the computational methods. This subject is really intimidating at the early stage of learning. I really liked to hear different people describing them in they own way., which always give a me another perspective to see them. Hope I could get into my Phd in the future and help others like you did! Two questions, 1. at 18:12, is there should also be a exponential Lamda for |Emax> outside the bracket? 2. How could subtract a large enough C from the Hamiltonian helps to guarantee what we find is the ground state? Could you elaborate a little more?

[@cristiane.boghiu2941]

Very interesting! Thank you for making these videos.

[@QuanticSniperTGL]

In fact you can use Lanczos method to study out-of-equilibrium dynamics too ! You just need to replace the random initial state by the initial state of your dynamics🥳

[@peha7759]

I 'm very interested in using the MPO to calculate the OTOC in lager sysytem.Will there be an introduction of relevant content in the follow-up video？

[@JonathonRiddell]

The current plan for that video (which I think will be next weekend) is to do tensor renormalization group, matrix product states and then METTS (minimally entangled thermal states). Though I realize it was probably too restrictive to limit this series to 3, I might just ignore that lol. For example, I'll add Part 1.1 and talk perhaps show my large scale block diagonalization code. And maybe do OTOCs later. For MPO calculations of the OTOC, I don't think it will be directly applicable, but I will be doing a brief overview of itensor. If you haven't heard of itensor, coding up an algorithm like the OTOC might be significantly easier with the library. :).

[@peha7759]

@@JonathonRiddell Thank you for your reply and look forward to the next video

[@gabrielarey4125]

It is a never ending concept. Interesting take!

[@jcq7910]

I am looking forward to the Monte Carlo part!

[@JonathonRiddell]

Working in it :). Though the tensor network one is further along.