Questions tagged [topological-phase]

The tag has no usage guidance, but it has a tag wiki.

Filter by
Sorted by
Tagged with
27
votes
2answers
2k views

Local explanation of the Aharonov-Bohm effect in terms of force fields

Here is an interesting paper for the Physics SE community: On the role of potentials in the Aharonov-Bohm effect. Lev Vaidman. Phys. Rev. A 86 no. 4, 040101 (R) (2012). arXiv:1110.6169 [quant-ph]. ...
16
votes
1answer
713 views

Are there topological non-trivial states in zero dimension?

The periodic table of topological insulators and superconductors suggests that there can be topological non-trivial phases in zero dimension in non-interacting system with certain symmetries. A 0D ...
15
votes
3answers
8k views

What does the Chern number physically represent?

In 2D the Chern number can be written as $$C_m=\frac 1{2\pi}\int_{BZ}\Omega_m(\mathbf k)\cdot d^2 \mathbf k$$ where we are integrating over the Brillouin zone. In 2D this is equivalent to finding ...
14
votes
2answers
855 views

1+1d TSC as $Z_2^f $ symmetry breaking topological order?

I have been struggling recently with a comprehensive problem on the relationship between topological superconductor and topological order. My question originates from reading a work conducted by Prof. ...
14
votes
4answers
9k views

Chern insulator vs topological insulator

What is the basic distinction between a Chern Insulator and a Topological Insulator? Right now I know that a Chern Insulator has "topologically non-trivial band structure" and that a Topological ...
14
votes
2answers
804 views

Why do lattice models of fermions need a spin structure?

It is well-known that in order to define a relavistic quantum-field theory containing fermions on a general manifold $M$, the manifold $M$ needs to be equipped with a spin structure. The spin ...
14
votes
2answers
620 views

Why is the phase picked up during identical particle exchange a topological invariant?

I've been wondering about the standard argument that the only possible identical particles in three dimensions are bosons or fermions. The argument goes like this: Consider exchanging the positions ...
13
votes
1answer
591 views

Has anyone experimentally shown the quantized thermal hall conductivity in Quantum Hall systems?

For background: In a $D=2+1$ state with edge modes described by a chiral $( c_L \neq c_R )$ CFT there is a predicted thermal Hall conductance associated with the gravitational anomaly at the edge. ...
12
votes
1answer
1k views

Has The Aharonov-Bohm Effect Been Experimentally Proven?

I have encountered two contradicting papers on the Aharonov-Bohm Effect: One supporting, The Aharonov-Bohm Effects: Variations on a Subtle Theme. H Batelaan and A Tonomura. Physics Today 62 pp. 38-...
12
votes
1answer
888 views

Aharonov-Bohm effect as a geometric phase-Adiabatic transfer not needed?

In his 1984 paper, Michael Berry proved that the Aharonov-Bohm effect is the same as a geometric phase. He did this by transferring a box containing charged particles around a solenoid. However, he ...
11
votes
1answer
982 views

Does the Kosterlitz–Thouless transition connect phases with different topological quantum numbers?

The Kosterlitz-Thouless transition is often described as a "topological phase transition." I understand why it isn't a conventional Landau-symmetry-breaking phase transition: there is no local ...
10
votes
1answer
2k views

What is so topological about topological phase transitions?

I am studying the KT-transition, which is called a topological phase transition. The phase transition is driven by vortices in a 2-D superfluid, where it is shown that at a critical temperature $T_c$ ...
9
votes
2answers
3k 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 ...
9
votes
2answers
6k views

Is band-inversion a 'necessary and sufficient' condition for Topological Insulators?

According to my naive understanding of topological insulators, an inverted band strucure in the bulk (inverted with respect to the vaccum/trivial insulator surrounding it) implies the existence of a ...
9
votes
1answer
2k 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 ...
9
votes
1answer
386 views

AKLT state and Nobel physics prize 2016

The AKLT Hamiltonian and the chain is described in Wikipedia, and also the page 17 of this year Nobel Prize advanced information I have questions concerning the info released by nobelprize.org, and ...
9
votes
1answer
260 views

Relation between a change in the topological invariant and the closure of the gap

I would like to understand the relation between a change of the topological invariant (e.g. when the Chern number changes from $1$ to $2$) and the closure of the gap of a condensed matter system. I ...
9
votes
0answers
217 views

Research: Mott insulator and topological order

I'm an experimentalist who is mainly focusing on strongly correlated electron systems (SCES), in particular Metal-insulator (Mott) transitions in the classical example $V_2 O_3$. Recently I decided to ...
8
votes
0answers
584 views

Physics uses of $SO(8)$ and Spin(8) triality [closed]

Triality is a relationship among three vector spaces. It describes those special features of the Dynkin diagram D4 and the associated Lie group Spin(8), the double cover of 8-dimensional rotation ...
7
votes
3answers
430 views

Small confusion about the Aharonov-Bohm effect

I am mostly aware of the Aharonov-Bohm effect's (AB effect) physical interpretation, as well as the corresponding mathematical/differential geometric interpretation. What does confuse me slightly ...
7
votes
1answer
648 views

Homotopy Theory for Topological Insulators

I'm trying to understand topological insulators in terms of homotopy invariants. I understand that in 2 spatial dimensions, we have Chern insulators since $$\pi_2(S^2) = \mathbb{Z}$$ One subtlety that ...
7
votes
1answer
2k views

What does it mean for a topological phase to be “symmetry protected”?

I have seen some very nice and enlightening awnsers to questions related to topological order and insulators, such as here, or here. However, I'm still puzzled by the concept of "symmetry protection" ...
7
votes
1answer
323 views

Meissner effect and topology

Is there any analogy between Quantum Hall Effect and Meissner Effect? In other words, can we relate the existence of edge currents in superconductors (of type 1) with edge modes in QHE (that yield ...
6
votes
2answers
2k views

Topological insulator vs. topological superconductors in any dimension

My question today is simple. What is the difference between a topological insulator and a topological superconductor? How that difference depends on the dimensionality of space(time)? What is the ...
6
votes
1answer
348 views

Why does a monopole operator break the global symmetry with topological current?

I am currently reading the paper "A Duality Web in 2+ 1 Dimensions and Condensed Matter Physics" by Seiberg et al, and on page 22 they add to the Lagrangian a monopole operator of the form $\phi^{\...
6
votes
1answer
779 views

Topological number of 1-D p-wave superconductor---Kitaev model/wire

After learning the Kitaev model, I tried to reformulate it and encounter some conceptual loopholes of my own. Here the setting: Given the 1-D chain Hamiltonian (differed from original form proposed ...
6
votes
1answer
1k views

Kane and Mele's argument on the existence of edge states in quantum spin Hall effect of graphene

Borrowing from Laughlin's argument on quantum Hall effect, Kane and Mele argued why there must be edge states in graphene with spin-orbit coupling in one paragraph, which is above the one with ...
6
votes
2answers
646 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 ...
6
votes
1answer
242 views

Topological Phase Transition v Quantum Phase Transition v Phase Transition

What are the main differences between this 3 type of phase transition? I understand the phase transitions of gas/liquid/solid as well as ferromagnet/paramagnet(Ising Model). All of which are between ...
6
votes
1answer
1k views

$Z_2$ topological insulator: odd vs. even number of edge state pairs

I am having trouble in understanding why in $Z_2$ topological insulators odd number of Kramers' pairs on one edge are protected by time reversal symmetry against elastic backscattering while even ...
6
votes
1answer
165 views

Formula for the topological invariant for each of the symmetry classes

Is there a reference that systematically derives the topological invariant/winding number for all the ten symmetry classes in Altland and Zirnbauer's periodic table? For example, in this answer, there ...
6
votes
0answers
70 views

Is there an AC version of the Quantum Hall Effect?

The quantum Hall effect has the well-known signature of plateaus in the Hall conductivity $\sigma_{xy}=n e^2/h$ for integer (or rational) n. This quantization is extremely precise, and can go up to ...
6
votes
0answers
956 views

What is a modular tensor category / functor?

I have reads several answers here about this notion, especially regarding topological order, see e.g. this answer, but this notion sounds completely new for me. Also, I found nothing really helpful on ...
5
votes
2answers
423 views

An exactly solvable model of 2D Majorana zero modes

The Kitaev's Majorana Model is an exactly solvable model of p-wave superconductor with localized Majorana zero modes in 1D quantum wire. For the 2D case, the general theory of Majorana zero modes near ...
5
votes
1answer
269 views

One dimensional phase transitions

Due to R. Peierls argument there is not phase transitions is one dimensional lattice systems. Argument in $d=1$ goes like that: flipping of one spin in system of N spins will lead to change of free ...
5
votes
1answer
256 views

Is topological surface state always tangential to bulk bands?

Think of a topologically nontrivial $D$-dimensional system. Its bulk bands form a $D+1$-dimensional manifold ($+1$ from energy). Its surface/edge bands form a $D$-dimensional one. Is the latter always ...
5
votes
1answer
103 views

Topological materials and fractionalized excitations

I've been told several times that topological materials (such topological insulators) must have "fractionalized" excitations. Equivalently, if a material does not have fractionalized excitations, it ...
5
votes
1answer
335 views

Relation between cobordism and unitary fusion category classification of TQFT/ SPT phase

In the introduction part of Gaiotto's paper (https://arxiv.org/pdf/1712.07950.pdf), he says "in the context of topological field theory, homotopy-theoretic ideas also lead to the classification of ...
5
votes
1answer
508 views

Goldstone mode as spin wave in 2D?

I'm trying to understand how Goldstone modes destroy long range order in 1D and 2D spin lattice. I started with a spin chain, using 1D XY-model, which has continuous symmetry. $H=- \sum_{<i j>} ...
5
votes
1answer
102 views

Gauging a symmetry-protected topological (SPT) phase

In this answer, it is said that gauging the symmetry which protects a symmetry-protected topological (trivial) phase gives something "morally very similar" to a phase with a topological order. What ...
5
votes
1answer
1k views

Relation of Berry phase and winding number

I am reading the following article dealing with the properties of Dirac fermion in condensed matter physics : https://arxiv.org/abs/1410.4098 In the page 5 of this article, the formula for the ...
5
votes
1answer
430 views

effective field theory of the projective semion model

The "projective semion" model was considered in http://arxiv.org/abs/1403.6491 (page 2). It is a symmetry enriched topological (SET) phase. There is one non-trivial anyon, a semion $s$ which induces a ...
5
votes
0answers
102 views

How is group cohomology in SPT's related to the 't Hooft anomaly on the boundary?

I understand that group cohomology description for symmetry protected topological phases (SPT) comes from discrete nonlinear sigma models. A tutorial on this can be found in the excellent lectures by ...
5
votes
0answers
142 views

What happens to topological insulators at finite temperature?

There is a similar question here, but I had a few things I wanted to ask. So basically pretty much all analysis/ theory of topological insulators is for pure wave-functions and conservative ...
5
votes
0answers
236 views

Different definitions of topological phases

When doing classification of topological phases, one need to formalize the problems mathematically. But, it seems that there are two not obviously equivalent ways to describe topological phases. In ...
5
votes
0answers
288 views

What is the different between topological order and Landau's order in a system

I have thought about topological order for a long time, but I am still confused it. Roughly speaking in my understanding, the topological state is the eigen-state of some special symmetry such time ...
5
votes
0answers
192 views

Topolgical insulators order parameter

For topological insulators Is there any way to define order parameter for topological phase transitions?
4
votes
1answer
291 views

Sources to learn about Berry phases and Adiabatic Theorem

I recently went through Griffiths' Quantum Mechanics text and there is a chapter called the Adiabatic Theorem that includes Berry phase and the Aharonov-Bohm effect. As I found them very ...
4
votes
1answer
1k views

Chiral anomaly in Weyl semimetal

In the presence of electromagnetic fields $E$ and $B$, four current is not conserved in a Weyl semimetal i.e. $\partial_{\mu} j^{\mu}\propto E\cdot B \neq 0$. There are some proofs in the literature ...
4
votes
2answers
633 views

String operators in the string-net model

In the string-net model http://arxiv.org/abs/cond-mat/0404617, quasiparticles are created by the string operators (defined in eq.(19)). An easier pictorial way to define string operators $W_{\alpha}(P)...

1
2 3 4 5