Connection between Free-Fermion and Interacting Crystalline Symmetry-Protected Topological Phases

2024/11/28 by Lee, Chen-Shen, Shiozaki, Ken, Hsieh, Chang-Tse
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2411.19287

Abstract

We present a framework for investigating the effects of interactions on crystalline symmetry-protected topological (SPT) phases. Within this framework, one can establish a direct connection between the equivalence classes of free-fermion systems and their corresponding interacting classes. A central component of this framework is the Atiyah-Hirzebruch spectral sequence, which provides a systematic way to represent crystalline SPT phases as SPT phases with internal symmetries on subspaces. We demonstrate the application of this approach through examples in various dimensions: 1d systems with U(1) and reflection symmetry, 2d systems with U(1) and C_n rotation symmetry, and 3d systems with U(1) and inversion symmetry.

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