# Questions tagged [topological-phase]

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165 questions
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### 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-...
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### 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 ...
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### Trivial phase in Kitaev chain, trivial phase in what sense?

I am reading 1D p-wave SC proposed by Kiteav---Kitaev chain recently. This paramedic model somehow bothers me with the word "trivial." In this SE post, the answer pointed out what we mean by "...
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### 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 ...
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### Chern number for the systems with open boundary conditions

For two-dimensional materials with periodic boundary conditions, we can solve the Bloch states and substitute them into the definition of Chern number, as shown in the picture: In the case of open ...
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572 views

### Chern number in one-dimensional system

As the title, could we define Chern number for condensed matter systems with one spatial dimension? E.g. the 1D Su-Schrieffer–Heeger (SSH) model.
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### Kosterlitz-Thouless in the XXZ chain: instanton condensation?

The anisotropic spin-$\frac{1}{2}$ Heisenberg chain $$H = \sum_n S^x_n S^x_{n+1} + S^y_n S^y_{n+1} + \Delta S^z_n S^z_{n+1}$$ is known to have the same physics as the two-dimensional classical XY ...
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### Equivalence between different definition of winding numbers

At the moment I am reading the paper by A. Schynder and S. Ryu arXiv: 1011.1438. The general setup is a superconductor with time-reversal symmetry. I can write my Bogoliubov - de Gennes in the ...
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### Can 1D SPT phase host non-Abelian topological defects?

People usually consider Kitaev chain as a topologically ordered phase in 1D, and the edge modes of Kitaev chain are Majorana zero modes (MZM), which are topological defects with non-Abelian mutual ...
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### Are Weyl and Dirac points topogical defects in nodal semimetals?

Recently, I heard the Weyl and Dirac points are topogical defects in nodal semimetals. I do not really get it. And the definition of topological defects is confusing to me. Are the topoligical ...
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179 views

### Transfer matrix approach to the topological phases

The transfer matrix contains all the information. i.e., information about the edges and bulk. What new insight does the transfer matrix approach provide in the study of the topological phases of ...
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### What is the difference between symmetry protected topological (SPT) order and topological order?

As far as I know, the SPT orders(or SPT phases) are all gapped and protected by symmetry. However they are short range entangled, and the topological order phases are all long range entangled. So the ...
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### Explain the characteristic features of long range entanglement

The long range entanglement (LRE) can exist in fermi liquids or lattice. The characteristic features of long range order entanglement could be the degeneracy, fractional excitation or the entanglement ...
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### why entanglement entropy is important in topological phases？

When mentioning interacting topological phases people always talk about entanglement entropy. why it is important? what is its physical meaning?
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796 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 ...
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### What are goldstone variables?

Pretty straightforward question (I hope). I am an experimentalist. I used to work in Nuclear Experiment (now I work in membrane biophysics). While reading about topological transitions in liquid ...
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357 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 ...
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776 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 ...
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### Is the topological index of a self-adjoint operator always zero?

By the Atiyah-Singer index theorem, the index of a self-adjoint opeartor D (e.g., Hamiltonian) is given by Index(D) = dim Ker(D) − dim Ker(D*), where D* is the adjoint operator of D. Since D is self-...
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343 views

### Have edge modes of the SSH model (or Kitaev Chain) been observed?

I am putting together a presentation on topological phase transitions in 1D tight binding models for a course in Solid State Physics, and while I have found many sources for theoretical descriptions I ...
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### Why do people always talk about continuous topological phase transition?

I have a question which puzzles me for a long time. Usually when people talk about topological phase transition, they usually have a gap-closing picture in their mind. Namely, the phase transition ...
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### Quantum ising/heisenberg model, states representation

I am working with a hamiltonian which looks like this (Heisenberg model) I have made a program which computes this hamiltonian using Pauli matrices (spin 1/2). My working space is then the tensor ...
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569 views

### How to calculate the string order parameter (for Haldane phase) in density matrix renormalization group?

The ground state of the spin-1 chain is the Haldane phase, which is known to be a symmetry protected topological phase and cannot be detected by conventional order parameter (beyond the Landau-...
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### What is the difference between Bosonic and Fermionic symmetry protected topological phases (SPT)

I am reading the paper Braiding statistics approach to Symmetry Protected Topological Phases'' by Levin and Gu. In this paper two spin models considered describe spin-1/2 particles in (1+2) ...