Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [topological-phase]

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

1
vote
0answers
27 views

Critical points of vector field with zeros in the magnitude

I am studying a vector field which has critical points (sources, sinks, saddle points and centers). The magnitude of the vector field goes to zero smoothly in these points, however. Contrast that to ...
2
votes
1answer
43 views

What are the applications of edge states in 1D topological systems?

In 2D, we get robust conducting edges. In 3D, we get robust conducting surfaces. These are interesting because we can possibly utilise this robustness for protected electron transport (or light ...
1
vote
0answers
23 views

BKT transition: nature of topological transition

BKT-transition is one of the most well-known topological transition in $O(2)$ model.But I misunderstand the physical interpratation of this transition. I started from the low-temperature expansion of ...
4
votes
0answers
62 views

Partial Transpose in Gapped Time-reversal Symmetric Spin Chains

Suppose you have a one-dimensional quantum spin system with on-site Hilbert spaces $\mathcal{S}$. Suppose there is an anti-unitary, anti-linear operator $C$ on $\mathcal{S}$ inducing an anti-linear, ...
0
votes
0answers
38 views

Does the polarized Kagome antiferromagnet contain Dirac or Weyl points?

I've been reading about frustrated quantum magnets lately and a prominent topic is the study of antiferromagnets on the Kagome lattice. A calculation of the spectrum for the sort of model I have in ...
1
vote
1answer
148 views

Basics of topological order and its relation to entanglement

What is a topological order that drives a topological phase transition? How is it different from say magnetic ordering or the superfluid ordering? What is its relation with entanglement? Please ...
1
vote
0answers
25 views

The surface states and Fermi arcs in Weyl semimetals

I'm confused about surface states in Weyl semimetals. Assume that we have a single pair of Weyl points and the Fermi level turned to this points. In this https://arxiv.org/abs/1301.0330 paper the ...
0
votes
1answer
83 views

How can I find edge states given a bulk Hamiltonian for a topologically ordered phase?

Suppose we have a momentum space tight binding Hamiltonian $H(\vec{k})$ that describes some topologically ordered system. It could be a Chern insulator in two dimensions, or a Weyl semimetal in three ...
1
vote
0answers
32 views

Lattice hopping at boundary in graphene lattice with magnetic field

Let's say I have a tight binding model for graphene, where I have a two-atom basis and three nearest neighbor vectors. I've applied a homogenous magnetic field $B$ in the z-axis, and can take the ...
0
votes
0answers
13 views

Are there any gapped systems that aren't invertible?

Assume the following definitions: A gapped phase of matter is a collection of (quantum-mechanical) systems with a unique ground state and an energy gap to all excitations in the limit of infinite ...
0
votes
1answer
61 views

Spin-1 Heisenberg model, the AKLT model, and their ground states

I am reading literature on quantum spin chains and matrix product states, and I notice similar arguments regarding the spin-1 antiferromagnetic Heisenberg model, $H_{H} = \sum_i S_i \cdot S_{i+1}$, ...
1
vote
1answer
39 views

Integer quantum Hall conductance and time-reversal symmetry

If we have a (2+1)-dimensional electronic gapped system with a unique ground state and it has a nonzero integer quantum Hall conductance, then the system (or its ground state) must break the time-...
1
vote
1answer
49 views

Do topological transitions only occur at Dirac points?

Topological phase transitions happen when the band gap closes. It is not true that all band crossings are topological. There are Dirac (linear) band crossings, quadratic band crossings, Dirac-like ...
1
vote
1answer
63 views

Aharonov-Casher effect vs Spin-Orbit coupling

The Aharonov-Casher phase is the electromagnetic dual of the Aharonov-Bohm phase. It arises when a neutral particle with a magnetic moment encircles, for example, a line charge, or moves on a closed ...
2
votes
0answers
46 views

The connection between symmetry and classifying spaces of a group

I recently read the following statement: "For any type of mathematical object, an object of that type with $G$ symmetry “is” a map from [its classifying space] $BG$ to the space of all objects ...
7
votes
1answer
524 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 $T_c$ ...
3
votes
0answers
56 views

Gapless modes at the boundary between topological insulator and normal insulator

I am currently learning about topology in condensed matter physics. I think I understand most of how topological indeces come about and differences between Z and Z2 indeces and the symmetries that ...
1
vote
1answer
59 views

Are fractional quantum hall effect system symetry enriched topological phases?

In the papers I review they first start to talk about topologically ordered phases of matter. Their standard example of it is FQHE. Than they give another set examples which are quantum spin liquids, ...
1
vote
1answer
60 views

Is the quantum Hall state a topological insulating state?

I am confused about the quantum Hall state and topological insulating states. Following are the points (according to my naive understanding of this field) which confuse me: Topological insulator has ...
1
vote
0answers
72 views

On string-like excitations in (3+1)d discrete gauge theory

(3+1)d discrete $G$-gauge theory (untwisted Dijkgraaf-Witten theory) has both point-like and loop-like excitations; Point-like excitation is an electric charge labeled by an irreducible ...
3
votes
0answers
67 views

Symmetry Protected Topological (SPT) phases of spin-1 chains

Let's consider this family of 1D spin-1 of hamiltonians: $$\sum_{i}[S^x_{i}S^{x}_{i+1}+S^y_{i}S^{y}_{i+1}+\lambda S^z_{i}S^{z}_{i+1} + D(S^{z}_{i})^2].$$ If I understand it right, these models have: ...
3
votes
1answer
56 views

Experimental confirmation of Majorana modes in Kitaev chain

I'm confused about majorana modes at the edge of Kitaev chain, what do we seek in experiment? When we first define this one we write the creation and annihilation operators as: $$a^{+}=\frac{1}{2}(\...
1
vote
1answer
42 views

In a class of parametrized symmetric Hamiltonians, should its symmetry operator be parametrized the same way?

I would like to ask the following in the context of symmetry-protected topological phase. Consider a class of Hamiltonians parametrized by $\{a_1,a_2,...\}$ denoted by $H(a_1,a_2,...)$. Suppose there ...
5
votes
1answer
74 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 ...
2
votes
0answers
51 views

Topological soliton objects in Minkowski v.s. Euclidean spacetime?

What makes the distinctions between the soliton objects in Minkowski or in Euclidean spacetime? It looks that usually, the Euclidean path integral is easier to be performed in many cases. In fact, ...
5
votes
3answers
258 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 ...
5
votes
1answer
184 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
195 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^{\...
0
votes
0answers
47 views

Classical statistical model based on group multiplication

For a (finite) group $G$, consider the following classical statistical model on a 2 dimensional lattice with oriented edges: Each edge carries a classical degree of freedom that can take values in ...
5
votes
1answer
88 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 ...
1
vote
0answers
16 views

Linking phase of flux lines and excitation energy of monopole

I am reading this paper and on the left-hand side of pp.10 it states the following relation between linking phase and excitation energy of monopole: Now the $\theta = \pi$ term in the bulk implies ...
0
votes
1answer
98 views

Winding number of SSH model 3

SSH model can be written as $$H=-\sum_n\big[Jc_n^\dagger d_n + J'd_n^\dagger c_{n+1}\big]+h.c.$$ in Fourier space $$H(k)= \begin{bmatrix} c_k^\dagger && d_{k}^\dagger \end{bmatrix} \begin{...
1
vote
2answers
267 views

Why does spin-orbit coupling lead to a nonzero Berry curvature?

Many theories consider spin orbit coupling to be a prerequisite for a nonzero Berry curvature, and therefore, for the classical anomalous Hall effect. Here, the spin orbit coupling is defined as: $$ ...
8
votes
3answers
2k 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 ...
2
votes
0answers
41 views

Relation of SPT phases with different boundary conditions

Using the definition that two SPT phases are distinct if they can't be connected by a symmetric finite depth local unitary, how does one relate systems with different boundary conditions? For example,...
1
vote
1answer
51 views

How do I understand different realizations of symmetry in the absence of fractionalization?

To use a simple example to ask my question, consider the two dimensional toric code with a $Z_2$ global symmetry acting in two ways: The most boring trivial way possible. By permuting the charge and ...
2
votes
1answer
102 views

Models for non-universal topological quantum computation

Anyon models do not lead in general to universal topological quantum computation (= existence of a universal set of quantum gates) when only the braiding is used for implementing gates. The Fibonacci ...
1
vote
0answers
131 views

Significance of topology in topologically ordered systems

The topology on which a lattice is placed plays an important role in topologically ordered systems, for example in toric code the degeneracy in the ground states is given by $4^{g}$ where $g$ is the ...
3
votes
1answer
90 views

Why is the flux quantized in 4D quantum Hall effect?

I am reading "Topological Field Theory of Time-Reversal Invariant Insulators" by Qi, Hughes, and Zhang (https://arxiv.org/abs/0802.3537). It argues that time reversal invariant (TRI) insulators in 2+1 ...
2
votes
2answers
71 views

How do you design an object that looks different after you spin 360 degrees?

According to quantum mechanics, after a 360 rotation electrons have the opposite phase. If you rotated yourself 360 degrees, your electrons would have the opposite phase to the electrons in the ...
0
votes
1answer
151 views

Does a gap closing mean an occurrence of a quantum phase transition?

If we have observed a closing of the excitation gap in the energy spectrum of a certain model, can we safely conclude that a quantum phase transition occurs?
1
vote
0answers
81 views

PT-symmetry in Energy Band of Crystals

According to this source, it is proved that, in absence of spin-orbit coupling, spatial inversion symmetry (as a part of point-group symmetry which operates as $\hat{S}\psi(\vec{r})=\psi(-\vec{r})$) ...
4
votes
1answer
247 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 ...
1
vote
1answer
88 views

Positive and negative winding number related by time-reversal symmetry

I am now reading some articles about Dirac fermions in condensed matter physics and the most famous example is graphene. I am now trying to understand page 5 in this article : https://arxiv.org/abs/...
4
votes
1answer
600 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 ...
2
votes
0answers
110 views

Is there a precise definition for a “parity”, “time-reversal” or “chiral” symmetry in general quantum spin systems?

By "quantum spin system" I mean a physical system with qu-$d$-its (called "spins", for possibly different $d$) distributed somehow over space and a Hamiltonian that is a sum of arbitrary local ...
2
votes
0answers
45 views

Qualitative understanding of Hamiltonian Terms for Quantum Phases

I have been reading up on topological order and quantum phases which are continually being discovered in condensed matter systems. (Here's a great article...https://www.quantamagazine.org/physicists-...
2
votes
0answers
59 views

Why is the seperation of a tight pair of vortices a Topological Phase Transition?

I have been doing some research on Topology in Physics and so I came across this picture Source is this link. Now the way I understood Topology so far is that you can classify specific ...
0
votes
1answer
25 views

Relative phase between neighbouring states in continous parameter space

The relative phase of two quantum states $|\psi_1\rangle,|\psi_2\rangle$ can be written, $$\gamma_{12}=-\text{arg}\langle\psi_1|\psi_2\rangle=-\text{arg}\big[|\langle\psi_1|\psi_2\rangle|e^{-i\gamma_{...
5
votes
1answer
143 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 ...