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
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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 ...
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How to understand Modular transformation in topological order?
Topological order in (2+1)D is described by its ground state degeneracy and the braiding statistics and topological spins of excitations. People believe that these information is all encoded in ground ...
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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 ...
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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 ...
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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" ...
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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 ...
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What is the “BCS Cooper pair condensation” as a physical phenomenon in terms of experiments?
"Thought" experiments and "numerical" experiments are allowed.
This question is motivated by the question Has BCS Cooper pair condensate been observed in experiment? ,
and by our recent research on ...
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A simple model that exhibits emergent symmetry?
In a previous question Emergent symmetries I asked, Prof.Luboš Motl said that emergent symmetries are never exact. But I wonder whether the following example is an counterexample that has exact ...
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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 ...
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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?
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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 ...
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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, ...
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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 ...
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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 ...
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Questions about Thouless-Kohmoto-Nightingale-den Nijs (TKNN) paper
I am reading the famous and concise Thouless-Kohmoto-Nightingale-den Nijs (TKNN) paper Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Phys. Rev. Lett. 49, 405–408 (1982), where I ...
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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 ...
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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?
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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?
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Are Hall edge currents truly dissipationless?
Integer quantum Hall states has integer number of chiral edge current channels flowing around like supercurrent in a superconductor.
Are they truly dissipationless?
If so, what is the mechanism that ...
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What is the precise definition or list of prerequisites for an anyonic system?
I have been reading some reviews and looked into books on anyons and topological quantum computation and I found it a little difficult to make out a short list of parameters and a clear and short list ...
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Logic behind topological orders
Long-range entanglement (LRE) is the main feature of topological orders. The string-net condensation model was constructed to exhibit LRE.
But the many-body systems of such models do not look like ...
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What is the operator for the edge current of a fracional quantum Hall state?
The edge of a fractional quantum Hall state is a chiral conformal field theory. In the Laughlin case it corresponds to the chiral boson,
$$ S = \frac{1}{4\pi} \int dt dx ...
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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 ...
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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 ...
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Which theory is closest to Theory of Everything? [closed]
To present, Which theory is closest to Theory of Everything? In the future, it probably including into Theory of Everything.
Can you describe more detail or attach links that I can reading after?
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$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?
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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 ...
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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?
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Entanglement measure to classify topological ordered states
I know long-range entanglement is the essence of nontrivial topological ordered states. (Trivial refers to short range entangled and nontrivial refers to long range.) So, entanglement measure at large ...
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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 ...
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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?
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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 ...
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What is the code distance in quantum information theory?
What is the code distance in quantum information theory?
Code distance seems to be a very important concept in fault tolerant
quantum computation and topological quantum computation.
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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 ...
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Quasi 1D insulators with strong spin-orbital interaction
We know that the spin-1 chain realizes the Haldane phase which is an example of
symmetry protected topological (SPT) phases (ie short-range entangled phases with symmetry). The Haldane phase is ...
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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 ...
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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 ...
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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 ...
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Geometric Langlands as a partially defined topological field theory
I have heard from several physicists that the Kapustin-Witten topological twist of $N=4$ 4-dimensional Yang-Mills theory ("the Geometric Langlands twist") is not expected to give
rise to fully defined ...
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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 ...
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Group Cohomology and Topological Field Theories
I have a two-part question:
First and foremost: I have been going through the paper by Dijkgraaf and Witten "Group Cohomology and Topological Field Theories". Here they give a general definition for ...
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Quantum Hall effect for dummies
In the past few days I've become increasingly intrigued by the QHE, mainly thanks to very interesting questions and answers that have appeared here. Unfortunately, I am as of yet very confused by all ...
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Why are some solitons formed from bosonic fields fermionic?
Some topological solitons formed from bosonic fields have fermionic statistics. Why?
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
