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Weak topological phases in the presence of interactions

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arxiv 2410.10031 v2 pith:AXTFPGX4 submitted 2024-10-13 math-ph cond-mat.str-elhep-thmath.MP

Omar Antolín Camarena , Arun Debray , Cameron Krulewski , Natalia Pacheco-Tallaj , Daniel Sheinbaum , Luuk Stehouwer This is my paper
classification math-phcond-mat.str-elhep-thmath.MP
keywords phasestheoryweakinteractionstorusfreeinteractingpotential
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abstract

We study weak symmetry-protected topological phases (SPTs) in the presence of short-range interactions. By comparing homotopical free and interacting classifications of these SPTs, we predict their stability under interactions as well as identify potential intrinsically-interacting phases. We mathematically compute the groups of weak phases in dimensions zero through three for all tenfold-way symmetry types using homotopy theory; specifically, we use Atiyah's Real $\mathit{KR}$-theory and the low-energy invertible field theory ansatz of Freed--Hopkins for the free and interacting cases, resp. Our computational techniques involve T-duality, which relates $K$-theory of the spatial torus with $K$-theory of the Brillouin torus, and a binomial formula for computing generalized cohomology of a torus. Our results carry potential implications for theoretical and experimental studies of weak phases.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence

    math-ph 2026-07 conditional novelty 6.0 of 10

    Crystalline SPT phases with symmorphic symmetry should be classified by a fully equivariant Freed–Hopkins invertible-field-theory ansatz, equipped with a natural free-to-interacting map from equivariant K-theory.

  2. Weak in the boundary: How weak SPT phases spoil anomaly matching

    cond-mat.str-el 2025-07 conditional novelty 6.0 of 10

    Weak SPT phases with a boundary are not classified by the same cohomology groups as on the infinite periodic system; the difference is a lower-dimensional group of phases that the boundary trivializes.

  3. Free phases of Majorana fermions: Tenfold ways compared

    math-ph 2025-07 conditional novelty 6.0 of 10

    Neutral free fermion SPT phases protected by a real Z2-graded C*-algebra A are classified by the real K-theory group K_2(A^op), unifying charged and neutral tenfold-way classifications via Morita equivalence.

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