Questions tagged [topological-phase]
The topological-phase tag has no usage guidance, but it has a tag wiki.
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What is the critical temperature for a BKT transition in the 2D quantum XY model with $S=1$ (not $S=1/2$)?
What is the critical temperature for a BKT transition in the 2D quantum XY model with $S=1$ (not $S=1/2$)? For instance, the classical XY model has KTc/J = 0.898 and the quantum XY model with S=1/2 ...
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35 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 ...
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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 ...
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0answers
32 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 ...
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1answer
56 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 ...
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24 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 ...
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66 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, ...
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40 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 ...
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1answer
159 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 ...
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0answers
32 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 ...
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1answer
91 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 ...
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37 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 ...
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16 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 ...
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1answer
71 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,
$H_{H} = \sum_i S_i \cdot S_{i+1}$,
...
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1answer
47 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-...
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1answer
51 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 ...
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1answer
65 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 ...
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48 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 ...
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1answer
568 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 $T_c$ ...
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0answers
60 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 ...
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1answer
61 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, ...
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1answer
73 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 ...
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0answers
73 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 ...
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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:
...
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1answer
60 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}(\...
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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 ...
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1answer
76 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 ...
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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, ...
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3answers
278 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
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1answer
190 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
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1answer
201 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^{\...
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48 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 ...
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1answer
101 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 ...
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0answers
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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 ...
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1answer
105 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{...
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2answers
301 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:
$$
...
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3answers
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What does the Chern number physically represent?
In 2D the Chern number can be written as
$$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 ...
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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,...
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1answer
54 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
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1answer
104 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 ...
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0answers
132 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
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1answer
93 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 ...
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2answers
73 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 ...
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1answer
158 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?
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0answers
86 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 $\hat{S}\psi(\vec{r})=\psi(-\vec{r})$) ...
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1answer
260 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 ...
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1answer
90 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/...
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1answer
626 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 ...
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0answers
115 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 ...
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0answers
46 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-...
