Solid State Upper division resources in CMT

[HoseinSqr]

Hi everyone.
I'll start my master's degree in physics next year. My plan is to continue my studies in theoretical condensed matter physics. So I've decided to increase my knowledge in this area. In my undergrad I took some courses like Intro. to QFT and Many-Body physics. Also I have studied those books by Altland and Simons and Kardar's Statistical Physics of Fields book. So I have at least a little knowledge about ideas like the RG , symmetry breaking, diagrammatic methods etc. Nevertheless I'm really confused about what should I do as the next step. Especially which books should I study now? I asked some Profs in my home university and some recommended me to study upper-division condensed matter books -like Philips' or Marder's- in order to gain a general knowledge about different areas of (hard) condensed matter physics. Some told me to study a bit about quantum computation and information.
But I want to do something a bit more purposeful. Something that can help me in my research in the future. For example I've been really interested in High T_c superconductors , but it seems that much of the essential problems in this field are solved -at least to some reasonable extend-. It seems that there are only fields like topological phases -though it seems that not much staffs have remained unexplored there- , FQHT (only one case is unsolved), and some problems like Ads/CMT, SYK models etc. which are not so much relevant to current experiments.
So after summarizing above facts, what would be your advice on the next textbooks I should study?

 

[soviet1100]

You're wrong in saying there isn't much to be explored in topological phases etc. There are SO many problems to study. I'm writing this assuming you're at the level where you have clearly understood the stuff in Altland & Simons (at least up to Chap 8 - RG group).

I would suggest starting to read research reviews and papers alongside textbooks. There are so many textbooks you can read and so much new stuff you can learn that you can exhaust your career in doing so. Look at what people are doing right now, and if any of the problems interest you, start thinking about it and reading books to learn ideas/methods that will aid you in solving the problem. Personally, I think focused reading like this is a lot more productive and effective.

1. If you're interested in CMT close to experiments, you could look at cold atom physics. There's a great review (many body physics with ultracold gases) by Bloch, Dalibard, Zwerger on rev.mod.phys.
2. You could look at low dimensional phases. e.g. 1D bosons - Cazalilla et al on rev.mod.phys.
3. there is so much to explore in non-equilibrium physics. you could read the keldysh formalism stuff from Altland & Simons. People have been looking at foundational stat.mech a lot recently - you could study thermalisation in different systems. For example, thermalisation (lack of) in many-body localised systems is a hot topic. You could look at developing and applying field theory methods to study non-equilibrium physics also (book by Kamenev - Field theory methods of non-eqm systems).
4. There's some interesting physics in the boundary of some topological phases - odd freq. superconductivity, emergent SUSY etc. (don't know much about this to point to a good reference except a famous paper by Grover et. al in Science).

In any case, if you want more advanced books to read, here's the list. Bear in mind that I haven't progressed much beyond the level of Altland & Simons myself, so I can't exactly speak to the quality of these books. This is some stuff I've been planning to read and is copy pasted from my own notes.

1. sections of Chetan Nayak's lecture notes on many-body theory
2. look at Fradkin - Field theories of CMP / Xiao Gang Wen - QFT of many-body systems
3. video lectures by F Schuller - geometric anatomy of theoretical physics (excellent)
4. QI from Nielsen & Chuang / Preskill's notes
5. find some resources for learning about tensor networks
6. read classic paper by Leinaas & Myrheim
7. Kamenev - Field theory methods of non-eqm systems

P.S. Much of what I've written is naturally in bias of my own current/future interests. CMP is a very wide field. There's soft CMP, biophysics, computational CMP etc. about which I know little to nothing.

tl;dr - look at reviews / papers, find problems you're interested in, read stuff that helps you solve the problem.