# Questions tagged [topological-phase]

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### Algebra of Time Reversal and Particle Hole Symmetry in 10-fold Classification of Topological Insulator/superconductor

In the ten fold classification of TI/TSC, when time reversal symmetry $\mathcal{T}$ and particle hole symmetry $\mathcal{P}$ are both present, i.e., in the symmetry classes BDI, DIII, CII, CI, for all ...
1answer
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### Time-reversal (explicitly) broken surface of $(3+1)$-dimensional topological insulator

Let us consider the surface of $(3+1)$-dimensional topological insulator, which is protected by the charge conservation $U(1)_Q$ and a time-reversal symmetry $\mathbb{Z}_2^T$. Such a surface, if not ...
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### Does a topological charge always need to be an integer

Does a topological charge always need to be an integer, I see many papers where people talk about non-integer topological charges due to boundary conditions. According to the formula for the ...
0answers
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### Why are degenerate ground states interesting?

Studying the Su-Schrieffer-Heeger chain I have learned that the model has two different phases, one which is called topological and the other one trivial. In the notes it says that these phases are ...
0answers
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### Topological phases and quantum information

I am concerned about the theorem saying that there is no topological order in 1d. According to the seminal paper https://arxiv.org/pdf/1008.3745.pdf, there are no non-trivial topological phases in 1d (...
0answers
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1answer
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### 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 ...
1answer
81 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 ...
0answers
53 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, ...
3answers
303 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 ...
1answer
199 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 ...
1answer
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### 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 ...
2answers
77 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 ...
1answer
174 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?