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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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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50 views

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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80 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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128 views

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 ...