5
votes
2answers
192 views

Definition of short range entanglement

When studying Symmetry Protected Topological phases, one needs to define what a short range entangled (SRE) states means. But there appears to be different definitions that are not equivalent to each ...
2
votes
0answers
83 views

Construction of a spin chain Hamiltonian invariant under a finite subgroup of SO(3)

I would like to construct a 2-local Hamiltonian that acts on a 1D spin chain where each spin transforms as the 3D irrep of $A_4$ which is a subgroup of $SO(3)$. I know that an $SO(3)$ invariant ...
1
vote
0answers
24 views

Effective Theory of FQH Edge State

When I was learning Xiao-Gang Wen's paper about the edge theory of Fractional Quantum Hall(FQH) state, I had one question. The paper's link is as below:\ http://dao.mit.edu/~wen/pub/edgere.pdf As ...
4
votes
2answers
103 views

SPTs and systems with Topological Order

I am an undergrad interested in Condensed Matter Theory. Particularly topological phases and systems exhibiting topological order. A potential research advisor doing a lot of work in Symmetry ...
3
votes
0answers
72 views

Topolgical insulators order parameter

For topological insulators Is there any way to define order parameter for topological phase transitions?
2
votes
1answer
42 views

Locality in Condensed Matter Lattice Model

What is a proper definition of locality in condensed matter lattice model? I emphasize "condensed matter" because there is no Lorentz symmetry or "speed of light". I think it is quite important ...
1
vote
0answers
68 views

Interacting fermionic SPT phases in 2d with time-reversal symmetry

Interacting fermionic SPT phases in 1d and 3d with $\mathbb{Z}_2^T$ symmetry are classified by $\mathbb{Z}_8$ and $\mathbb{Z}_{16}$ respectively, as shown in the paper by Fidkowski and Kitaev ...
2
votes
0answers
127 views

Jordan Wigner Transformation in 1d Majorana chain

So, I was reading the paper by Fidkowski and Kitaev on 1d fermionic phase http://arxiv.org/abs/1008.4138. It explains the classification of 1d fermionic SPT phases with $\mathbb{Z}_2^T$ symmetry for ...
3
votes
1answer
74 views

Numerical Tools to find Braiding Statistics of Quasiparticles

While certain classes of systems that exhibit topological order can be solved exactly (such as the Toric Code, Abelian FQH Edges, etc.) there also exist systems (think of perturbed versions of the ...
5
votes
1answer
222 views

Degenerate perturbation theory applied to topological degeneracy?

Consider a quantum system described by a gapped Hamiltonian $H_0$ with degenerate ground states (GS), adding a perturbation term $V$ to $H_0$, then the low-energy physics can be described by an ...
4
votes
1answer
104 views

String-net models on non-trivalent lattices

I have just started reading about string net models. The following aspect wasn't entirely clear to me: String net models are most naturally defined on trivalent networks, that is to say networks ...
2
votes
1answer
113 views

Is there a wave function for anyons?

People talk about anyons a lot. But i have never seen an anyon wave function. I suspect that there is no such thing as a wave function for anyons. I mean, anyons are not generalizations of bosons ...
5
votes
1answer
159 views

What are qubits made of in Wen's string-net theory?

In Prof. Xiaogang Wen's theory, photons and electrons are described as quasi-particles appeared as a result of the existence of the string-net liquid, which is the topological order of the qubits that ...
3
votes
1answer
115 views

Chiral Spin Liquid(CSL), Chern number, and the ground state degeneracy(GSD)

Consider a 2D gapped CSL with a nonzero Chern number $m$, then is the GSD of the system on a torus directly related to the Chern number $m$? For example, see this article, in the last paragraph on ...
2
votes
0answers
84 views

Questions on the elementary excitations in the resonating-valence-bond(RVB) states?

It is known that the RVB states can support spin-charge separations and its elementary excitations are spinons and holons. But it seems that there are some different possibilities for the nature of ...
4
votes
0answers
84 views

Third-order topological quantum phase transition in p+ip superfluid

A two-dimensional spinless non-relativistic p+ip superfluid undergoes a quantum phase transition between the BCS (weakly-coupled) and BEC (strongly-coupled) regimes. This transition is driven by ...
2
votes
1answer
143 views

How many kinds of topological degeneracy are there?

Here I want to summarize the various kinds of topological ground-state degeneracy in condensed matter physics and want to know whether there exists any other kind of topological degeneracy. For ...
1
vote
1answer
141 views

What happens to chiral Majorana edge fermions near quantum phase transition in p+ip superconductors?

In the weakly-coupled BCS regime two-dimensional chiral (p+ip) spinless superconductors and superfluids posses a chiral gapless fermionic Majorana state localized near the boundary. This gapless edge ...
3
votes
0answers
100 views

Zumino's consistent and covariant anomalies - applied to quantum hall?

What is the `physical' meaning of consistent anomalies and covariant anomalies? Perhaps a good Reference is: Consistent and covariant anomalies in gauge and gravitational theories - William A. ...
0
votes
0answers
152 views

Topological disorder in condensed matter?

What is meant by topological disorder in condensed matter (both crystalline and amorphous)? For example, please see the following two papers from arxiv.org http://arxiv.org/pdf/0906.3848.pdf ...
3
votes
2answers
183 views

Dehn twists and topological order

I am trying to understand notion of a "Dehn twist" and how it relates to topological order. In particular refering to http://arxiv.org/abs/1208.4834 it is stated that Xiao Gang Wen's paper on ...
7
votes
1answer
519 views

What is parafermion in condensed matter physics?

Recently, parafermion becomes hot in condensed matter physics (1:Nature Communications, 4, 1348 (2013),[2]:Phys. Rev. X, 2, 041002 (2012), [3]:Phys. Rev. B, 86, 195126 (2012),[4]:Phys. Rev. B,87, ...
1
vote
1answer
127 views

Can spin liquids without spin-rotation and time-reversal symmetries possess nonzero Spin Density Wave (SDW) order parameters?

For those spin liquids with SU(2) spin-rotation symmetry or time-reversal(TR) symmetry , the Spin Density Wave (SDW) order parameters are always zero, say $\left \langle \mathbf{S}_i \right ...
4
votes
2answers
419 views

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 ...
4
votes
1answer
182 views

Fractionalization and the structure of spin rotation group?

As we know, the phenomena of fractionalizations in condensed matter physics is fantastic, like fractional spin, fractional charge , fractional statistics, .... And one key point is that the ...
5
votes
1answer
120 views

Can anyons emerge from momentum-space other than spatial dimensions?

So far in condensed matter physics, I only know anyons(abelian or nonabelian) can emerge as quasiparticles in 2D real-space. But is there any possibility to construct anyons in momentum-space ? And ...
4
votes
1answer
1k views

About Dirac cones

This nice image of Dirac cones (from this article), in a ($E,\vec k$ graph) will be an introduction for several questions, in the realm of topological insulators. 1) Does the Dirac cone appears ...
8
votes
1answer
707 views

Experimental signature of topological superconductor

I was wondering if someone can provides some clear experimental signatures of a topological superconductors ? I was thinking about that, because for topological insulator, one of the hallmarks is ...
11
votes
3answers
1k views

Reconciling topological insulators and topological order

We make an important distinction between the topological insulators (which are essentially uncorrelated band insulators, "with a twist") and topological order (which covers a variety of exotic ...
3
votes
1answer
809 views

Why we call the ground state of Kitaev model a Spin Liquid?

Now we always talk about the so-called Kitaev spin liquid. One important property of spin liquid is global spin rotation symmetry. Let $\Psi$ represents a spin ground state, if $\Psi$ has global spin ...
8
votes
1answer
214 views

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 ...
2
votes
0answers
94 views

Is it possible to have topological degeneracy in 1D ?

I mean to have q-fold degenerate ground states on a ring which could not be lifted by local perturbation. If the answer is no, then what is the physical (or mathematical) reason against having such ...
8
votes
1answer
366 views

Some questions about anyons?

(1) As we know, we have theories of second quantization for both bosons and fermions. That is, let $W_N$ be the $N$ identical particle Hilbert space of bosons or fermions, then the "many particle" ...
5
votes
1answer
307 views

A question on the doped Kitaev-Heisenberg model?

Recently, some groups have studied the effects of doping the Kitaev model on honeycomb lattice(e.g.,http://arxiv.org/abs/1109.6681 and http://arxiv.org/abs/1109.4155) and their calculations show the ...
19
votes
4answers
768 views

What observables are indicative of BCS Cooper pair condensation?

What observables are indicative of BCS Cooper pair condensation? "Thought" experiments and "numerical" experiments are allowed. This question is motivated by the question Has BCS Cooper pair ...
13
votes
2answers
2k views

Basic questions in Majorana fermions

Why any fermion can be written as a combination of two Majorana fermions? Is there any physical meaning in it? Why Majorana fermion can be used for topological quantum computation?
7
votes
0answers
324 views

Is the “particle number” of “electrons” well defined in Wen's string-net theory of elementary particles?

According to professor Wen's string-net theory, electrons can be viewed as the elementary excitations of string-net objects. Just like the phonons and magnons are the elementary excitations of ...
5
votes
2answers
456 views

Chiral edge state as topological properity of bulk state

As far as I know, quantum hall effect and quantum spin hall effect has chiral edge state. Chiral edge state is usually closely related with delocalization, since back scattering is forbidden. However, ...
11
votes
1answer
877 views

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 ...
10
votes
2answers
1k views

Why quantum hall effect has chiral edge state?

The most popular explaination may be the following: in magnetic field, electrons move in cycolotron orbits, such cycolotron orbits ensure electrons to move in one direction at the edge. That is why ...
4
votes
1answer
244 views

Notation in Spin Liquid

When construct spin liquid by projective symmetry group, we can classified spin liquids by the invariant group (IGG) of their mean field ansatze. For example, we can have Z2, U(1) and SU(2) spin ...
8
votes
1answer
237 views

Chiral coupling in string-nets

In Xiao-Gang Wen's review of topological order http://arxiv.org/abs/1210.1281 , he states in footnote 52 that string-nets are so far unable to produce the chiral coupling between the SU(2) gauge boson ...
5
votes
1answer
183 views

Measurement of topological spin

How do you measure the topological spin of an anyon? So how could an experimental setup look like? Is topological spin an observable at all?
6
votes
1answer
195 views

String-net condensation in 3D

In 2D and 3D quibit models, string-net condensation can happen. In 3D or higher models, is it possible for surfaces (instead of just strings) to condense?
6
votes
2answers
806 views

Why are Topological Superconductors hard to make?

Topological insulators (TI) have already been made in lab. Topological superconductors (TSC), being close cousins of TI, seem harder to make. Why is that? It seems that materials in connection with ...
7
votes
2answers
486 views

Realization of Witten-type topological quantum field theory in condensed matter physics

It is well-known that some exotic phases in condensed matter physics are described by Schwarz-type TQFTs, such as Chern-Simons theory of quantum Hall states. My question is whether there are condensed ...
1
vote
1answer
233 views

$Z_2 $ topological index in spin liquid

What is $Z_2 $ topological index in spin liquid system? How to understand its physical picture in condensed matter?
8
votes
1answer
510 views

What is topological degeneracy in condensed matter physics?

What is topological degeneracy in strongly correlated systems such as FQH? What is the difference between topological degeneracy and ordinary degeneracy? Why is topological degeneracy important for ...
7
votes
1answer
560 views

Topological Order and Entanglement

I have a question about entanglement in condensed matter physics. It seems that topological order origins from long range entanglement, but what is long range entanglement? It is the same as long ...
7
votes
1answer
769 views

Is resonating valence bond (RVB) states long-range entangled?

Quantum liquid is at the core of condensed matter theory study, examples include superfluid in Bose Hubbard model, quantum spin liquid around the RK point of a quantum dimer model, string-net ...