Topological order is a new kind of order in quantum matter, which corresponds to pattern of long-range quantum entanglement. See http://en.wikipedia.org/wiki/Topological_order

learn more… | top users | synonyms

64
votes
4answers
6k views

Gauge symmetry is not a symmetry?

I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate ...
6
votes
1answer
1k views

What is the relationship between string net theory and string / M-theory?

I've just learned from this one of Prof. Wen's answers that there exists a theory called string net theory. Since I've never heard about this before it picks my curiosity, so I`d like to ask some ...
19
votes
5answers
2k views

Simple models that exhibit topological phase transitions

There are a number of physical systems with phases described by topologically protected invariants (fractional quantum Hall, topological insulators) but what are the simplest mathematical models that ...
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 ...
18
votes
2answers
2k views

Topological Charge. What is it Physically?

I have seen the term topological charge defined in an abstract mathematical way as a essentially a labeling scheme for particles which follows certain rules. However I am left guessing when trying to ...
14
votes
2answers
2k views

What is a resonating valence bond (RVB) state?

There's something known as a "resonating valence bond" (RVB) state, which plays a role in at least some attempts to understand physics of high-$T_c$ superconductors. This, roughly, involves a state ...
3
votes
1answer
864 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 ...
17
votes
1answer
826 views

Zero modes ~ zero eigenvalue modes ~ zero energy modes?

There have been several Phys.SE questions on the topic of zero modes. Such as, e.g., zero-modes (What are zero modes?, Can massive fermions have zero modes?), majorana-zero-modes (Majorana zero ...
14
votes
3answers
2k views

How Non-abelian anyons arise in solid-state systems?

Recently it has been studied non-abelian anyons in some solid-state systems. These states are being studied for the creation and manipulation of qubits in quantum computing. But, how these ...
11
votes
5answers
2k views

Do Category Theory and/or Quantum Logic add value in physics?

I know they have their adherents, but do more or less esoteric branches of mathematics such as Category Theory and/or Quantum Logic provide powerful tools for new theory development or are they just ...
6
votes
1answer
279 views

Topological ground state degeneracy of SU(N), SO(N), Sp(N) Chern-Simons theory

We know that level-k Abelian 2+1D Chern-Simons theory on the $T^2$ spatial torus gives ground state degeneracy($GSD$): $$GSD=k$$ How about $GSD$ on $T^2$ spatial torus of: SU(N)$_k$ level-k ...
3
votes
2answers
306 views

Why is fractional statistics and non-Abelian common for fractional charges?

Why non integer spins obey Fermi statistics? Why is fractional statistics and non-Abelian common for fractional charges?
4
votes
1answer
473 views

A physical understanding of fractionalization

all! Is there a physical understanding of fractionalization in condensed matter physics? The textbook approach is theoretical, not physical. I'm thinking of spin-charge separation for electrons, the ...
2
votes
1answer
716 views

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 ...
16
votes
2answers
3k 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?
10
votes
2answers
348 views

Braiding statistics of anyons from a Non-Abelian Chern-Simon theory

Given a 2+1D Abelian K matrix Chern-Simon theory (with multiplet of internal gauge field $a_I$) partition function: $$ Z=\exp\left[i\int\big( \frac{1}{4\pi} K_{IJ} a_I \wedge d a_J + a \wedge * ...
17
votes
5answers
467 views

direct sum of anyons?

In the topological phase of a fractional quantum Hall fluid, the excitations of the ground state (quasiparticles) are anyons, at least conjecturally. There is then supposed to be a braided fusion ...
6
votes
3answers
367 views

Whis is the difference between charge fractionalization in 1D and 2D?

Both 1D Polyacetelene and 2D fractional quantum Hall state can support fractional excitations. But as I can see, there are some differences: the ground state of Polyacetelene breaks translational ...
9
votes
1answer
952 views

Topological order vs. Symmetry breaking: what does (non-)local order parameter mean?

Topological order are sometimes defined in opposition with the order parameter originating from a symmetry breaking. The latter one being possibly described by a Landau theory, with an order ...
8
votes
3answers
571 views

Why are some solitons formed from bosonic fields fermionic?

Some topological solitons formed from bosonic fields have fermionic statistics. Why?
8
votes
2answers
242 views

Wilson Loops as raising operators

Consider a U(1) Chern Simons theory on a torus $\mathbb{T}$: \begin{align} L &= \frac{k}{4\pi} \int_{\mathbb{T}} a \partial a \end{align} where a is some U(1) gauge field, $k\in\mathbb{Z}$ and we ...
7
votes
1answer
809 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 ...
11
votes
2answers
540 views

Is there a method for differentiating fractional quantum Hall states aside from finding Chern numbers?

The ground state for a quantum Hall system on a torus with fractional filling factor can be classified by the Chern number, which is why the Hall conductance is quantized. Is there another method or ...
6
votes
1answer
275 views

What's vison in Z2 resonating valence bond (RVB) state?

I have a problem on the "vison" exitation in the Z2 RVB state. The vison exitation is a topological exitation of the system like topological defect in nematic liquid , if I got it right. Because the ...
5
votes
2answers
495 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, ...
7
votes
1answer
599 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
0answers
328 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 ...
3
votes
1answer
133 views

Follow up question on “Wilson Loops as Raising Operators”

This is a follow-up question on the topic that I opened a few days ago, Wilson Loops as raising operators. The paper Topological Degeneracy of Quantum Hall Fluids. X.G. Wen, A. Zee. Phys. Rev. B ...
6
votes
2answers
284 views

Experimental evidence for non-abelian anyons?

Since non-abelian anyons have become quite fashionable from the point of view of theory. I would like to know, whether there has actually been experimental confirmation of such objects. If you could ...
4
votes
1answer
625 views

A simple model that exhibits emergent symmetry?

In a previous question Emergent symmetries I asked, Prof.LuboŇ° Motl said that emergent symmetries are never exact. But I wonder whether the following example is an counterexample that has exact ...
8
votes
1answer
386 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" ...
2
votes
1answer
120 views

FQH Edge Theory as decoupled chiral bosons

The action describing the edge theory of the Fractional Quantum Hall effect is given by \begin{equation} S = \frac{1}{4\pi} \int \mathrm{d}x \ \mathrm{d}t \left[ K_{IJ} \ \partial_{t}\phi_{RI} ...