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Classification of symmetry protected topological phases in quantum spin chains

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arxiv 2110.04671 v1 pith:SKOX3YKS submitted 2021-10-10 math-ph cond-mat.str-elmath.MP

Yoshiko Ogata This is my paper · ORCID
classification math-phcond-mat.str-elmath.MP
keywords phasesquantumspinsymmetryclassificationprotectedsystemstopological
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abstract

We consider the classification problem of symmetry protected topological (SPT) phases on quantum spin systems. SPT phases are gapped short-range-entangled quantum phases with a symmetry $G$. We explain that in one and two-dimensional quantum spin systems, there are $H^{2}(G, U(1))$/ $H^{3}(G, U(1))$-valued invariant, confirming a physicists conjecture.

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Cited by 1 Pith paper

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  1. Gauging Quantum Phases: A Matrix Product State Approach

    quant-ph 2025-04 accept novelty 7.0 of 10

    Gauging maps 1D SPT phases with abelian symmetry to phases with maximally non-commutative SPT order plus symmetry breaking, generalizing the Kennedy-Tasaki transformation to non-MNC phases.

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