QFT topics for entanglement entropy

In summary, the QFT topics that you need to understand in order to better understand papers on entanglement entropy are: canonical quantization, free quantum field theory, entanglement entropy, and quantum field theory.
  • #1
shinobi20
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My goal is to study holographic entanglement entropy, but before that I need to study entanglement entropy in QFT first.
I want to know what are the QFT topics that I need to understand in order to proceed in reading papers on entanglement entropy such as,

Entanglement Entropy and Quantum Field Theory
Entanglement entropy in free quantum field theory
Entanglement entropy: holography and renormalization group

An example book could be QFT by Blundell, can anyone point which chapters/topics I need to study?

Contents of the book can be seen here:
Quantum Field Theory for the Gifted Amateur

I am only interested in studying QFT for the sake of understanding entanglement entropy. I have studied until canonical quantization but I still want to get some comments. Also, if anyone can give me extra advice on how to enhance my understanding in this area would be greatly appreciated!

I think I saw @ShayanJ discussed some topics on entanglement entropy so it would be great to also hear from him.
 
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^^^ i second this question! Would love some pointers. Information theory/stat mech maybe?
 
  • #3
Some good references:

Tom Hartman's lecture notes: http://www.hartmanhep.net/topics2015/

Dan Harlow's lecture notes: https://arxiv.org/abs/1409.1231

The last chapter of Eduardo Fradkin's textbook Field Theories of Condensed Matter Physics concerns entanglement in QFTs and gives an introduction to the Calabrese-Cardy approach.

I quite like the Casini-Huerta review linked in the first post. I have not watched these personally, but you can find video lectures by Horacio Casini given at Perimeter Institute here: http://pirsa.org/index.php?p=speaker&name=Horacio_Casini

I have done some research on entanglement in QFTs myself and would be happy to answer any questions you have.
 
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  • #4
king vitamin said:
Some good references:

Tom Hartman's lecture notes: http://www.hartmanhep.net/topics2015/

Dan Harlow's lecture notes: https://arxiv.org/abs/1409.1231

The last chapter of Eduardo Fradkin's textbook Field Theories of Condensed Matter Physics concerns entanglement in QFTs and gives an introduction to the Calabrese-Cardy approach.

I quite like the Casini-Huerta review linked in the first post. I have not watched these personally, but you can find video lectures by Horacio Casini given at Perimeter Institute here: http://pirsa.org/index.php?p=speaker&name=Horacio_Casini

I have done some research on entanglement in QFTs myself and would be happy to answer any questions you have.
OMG perfect thank you! :D
 

1. What is entanglement entropy in quantum field theory (QFT)?

Entanglement entropy is a measure of the amount of entanglement between two or more quantum systems. In the context of QFT, it is a measure of the amount of entanglement between different regions or subsystems of a quantum field theory.

2. How is entanglement entropy calculated in QFT?

Entanglement entropy is typically calculated by tracing out the degrees of freedom of one subsystem and then computing the von Neumann entropy of the remaining subsystem. This involves taking the logarithm of the reduced density matrix and multiplying it by the density matrix itself.

3. What is the physical significance of entanglement entropy in QFT?

Entanglement entropy is important in QFT because it provides a way to quantify the amount of entanglement between different regions of a quantum field theory. It also has implications for the behavior of quantum states under renormalization group transformations, and can be used to study phase transitions and other critical phenomena.

4. How does entanglement entropy relate to other measures of quantum entanglement?

Entanglement entropy is just one of many measures of quantum entanglement. It is closely related to other measures such as the entanglement entropy of formation, the relative entropy of entanglement, and the negativity. However, entanglement entropy is the most commonly used measure in the context of QFT.

5. Can entanglement entropy be experimentally measured in QFT?

Yes, entanglement entropy can be experimentally measured in QFT through various techniques such as quantum tomography and quantum state engineering. However, due to the complexity of QFT systems, it can be challenging to measure entanglement entropy directly and often requires indirect methods.

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