Questions tagged [symmetry-protected]

Symmetry Protected refers to the symmetry protection by Symmetry Protected Topological order (SPT order). It is beyond the Landau-Ginzburg theory. See https://en.wikipedia.org/wiki/Symmetry_protected_topological_order

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What is topological about topological (Dirac or Weyl) semimetals?

The following is my rough understanding of topological phases of matter (please let me know if it is incorrect.) Topologically ordered phases of matter are topological in the sense that they are ...
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What are the differences between Haldane phase, non-interacting topological insulator/superconductor, and SPT order?

Haldane phase, and non-interacting topological insulator/superconductor are often regarded as examples of symmetry protected topological (SPT) orders.
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Low energy description of Symmetry Enriched Topological phases

Prelude: low energy description of Symmetry Protected Topological (SPT) phases It is known [1] that the low energy effective description of SPT phases, protected by a group $G$ is an invertible ...
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Classification of higher Symmetry Protected Topological (SPT) phases

Suppose that we have a $d$ dimensional bosonic SPT phase, protected by some $p$-form symmetry, $G^{[p]}$. Suppose also that it is classified within group cohomology, so that we don't have to run into ...
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Chern-Simons theory with a discrete gauge symmetry

Let us consider a Chern-Simons theory on a $3$-manifold $M$ (can be a spin manifold with a given spin structure if needed) with a discrete-symmetry gauge field e.g. $\mathbb{Z}_n$ symmetry. It can be ...
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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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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
123 views

The ground state degeneracy of a single spin 1/2 under $SU(2)$ spin-rotation symmetry

Let us consider a single spin 1/2 in (0+1) dimension. It is expected that when we add more interaction onto such single spin, the energy gap cannot be opened as long as the Hamiltonian possesses $SU(2)...
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Relationship between different $Z_{16}$ classifications

I find that there exist two classifications which have a $Z_{16}$ group structure: The sixteen fold way of classifying Majorana fermions, vortex systems appearing in Kitaev's paper on his honeycomb ...
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't Hooft twisted torus construction and its relation to characteristic (e.g. Stiefel-Whitney) class

It is known that the $PSU(2) = SO(3)$ and there is an associated global anomaly labeled by the second Stiefel-Whitney class $w_2$. This second Stiefel-Whitney class $w_2$ can detect the 1+1 ...