Questions tagged [topological-entropy]

11 questions
28
votes
4 answers

How to understand topological order at finite temperature?

I have heard that in 2+1D, there are no topological order in finite temperature. Topological entanglement entropy $\gamma$ is zero except in zero temperature. However, we still observe some features of topological order in fractional quantum Hall…
25
votes
1 answer

Quantum dimension in topological entanglement entropy

In 2D the entanglement entropy of a simply connected region goes like \begin{align} S_L \to \alpha L - \gamma + \cdots, \end{align} where $\gamma$ is the topological entanglement entropy. $\gamma$ is apparently \begin{align} \gamma = \log…
15
votes
0 answers

Topological entanglement entropy only defined for a system in the ground state?

What happens to the topological entanglement entropy of a system, when it is driven out of its groundstate by increasing the temperature?
6
votes
1 answer

A naive question about topologically ordered wavefunction?

Topological entanglement entropy (TEE, proposed by Levin, Wen, Kitaev, and Preskill) is a direct characterization of the topological order encoded in a wavefunction. Here I have some confusions, and let's take the spin-1/2 Kitaev model on the…
5
votes
0 answers

Types of entropy

As I understand, entropy was first introduced as a state function of a macroscopic system, based on observations such as those of Clausius and Kelvin, pertaining to the directionality of spontaneous processes. Then Boltzmann introduced the idea of…
5
votes
1 answer

Entropy of a polymer contained in a sphere with infinitely thin chords

Imagine that I have a polymer (approximated as a freely diffusing, freely jointed chain with some number of subunits 'N'), and I place this polymer into a sphere of some volume 'V'. Next, I proceed to add a series of infinitely thin, immobile chords…
MorningCoffee1998
4
votes
2 answers

topological entanglement entropy for a punctured torus and sphere

Topological entanglement entropy (http://arxiv.org/pdf/cond-mat/0510613.pdf, http://arxiv.org/abs/hep-th/0510092) is usually calculated for surfaces with boundary. How would it look like for compact surfaces and when these are punctured?
4
votes
1 answer

Topological phase

Can anybody tell me, if generically any system, which is solely described by a topological field theory, resides in a topological phase? I cant find any clear notion of topological phase. Only topological phase of matter, but I mean any kind of…
3
votes
2 answers

Knotted token-ring network

Suppose we have a rigid token-ring network. An observer at any node can seemingly determine the angular momentum of the network by measuring the time it takes for a packet to travel around the ring in each of the two directions. Is it possible by…
2
votes
3 answers

Statistical Entropy and Information theory

I am having trouble in understanding the following concepts : Pg 231 Appendix B of the link http://books.google.ca/books?id=lEu7CTGjdDkC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q=entropy&f=false which is of the book Chaos and…
1
vote
0 answers

Basic questions about fusion of two anyons

Suppose we have two anyons $a$ and $b$ on a manifold, and we use $|a\otimes b\rangle$ to label the corresponding wavefunction. Based on the fusion rule: $a\otimes b=\oplus_c N_{ab}^c c$, we may write the wavefunction $|a\otimes b\rangle$…