# Resources for entanglement entropy in condensed matter systems and black hole thermodynamics

Over the last month or so, I have set it upon myself to teach myself the AdS/CFT correspondence. In particular, I am interested in the connection between black hole entropy and entanglement entropy in condensed matter systems. However, I really need to learn more about the more finer details of entanglement entropy and black hole thermodynamics before I dive into AdS/CFT. Therefore, any resources on these two subjects would be greatly appreciated.

To be precise, I am looking at books/articles/websites (preferably some open-access pdf) which assumes an understanding of Sakurai-level quantum mechanics, some quantum field theory and special relativity. I am also familiar with condensed matter field theory and second quantization, so it's okay if it assumes some former knowledge in these topics. I would prefer pedagogical texts, as comprehensive as possible and with a lot of questions.

There are a lot of review articles and books on these topics. But most of them require some knowledge of basic General Relativity and QFT. For Black hole thermodynamics I found the reviews by Jacobson $$[1]$$ and Ross $$[2]$$ very useful.

On EE from condensed matter (QFT) point of view there are papers by Cardy and others. But for those you need CFT background. Here is a "non-technical" article $$[3]$$. You can look at the references therein, if you are interested.

For entanglement entropy of black holes probably the best article is this $$[4]$$. You can find most of the useful references, which you are looking for, there.

I could give you more references but not sure they will be useful at all.

$$[1]$$ T. Jacobson, "Introductory Lectures on Black Hole Thermodynamics".
$$[2]$$ S. F. Ross, "Black hole thermodynamics", arXiv:hep-th/0502195.
$$[3]$$ P. Calabrese and J. Cardy, "Entanglement entropy and quantum field theory: a non-technical introduction", Int. J. Quant. Inf. 4 (2006) 429.
$$[4]$$ S. N. Solodukhin, "Entanglement entropy of black holes", Living Rev. Relativity 14, (2011), 8.

• Please give me any references you have on the subject--I'm sure they will be useful. Thanks for the references you've already included. Jun 7, 2015 at 17:17