Twisted Boundary Condition and Lieb-Schultz-Mattis Ingappability for Discrete Symmetries

2020/10/31 by Yuan Yao, Masaki Oshikawa · 58 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Boundary value problem #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Degeneracy (biology) #Discrete symmetry #Geometry #Ground state #Homogeneous space #Lattice (music) #Mathematical physics #Mathematics #Physics #Projective representation #Projective test #Pure mathematics #Quantum #Quantum many-body systems #Quantum mechanics #Symmetry (geometry) #Theoretical physics #Translational symmetry #cond-mat.stat-mech #cond-mat.str-el #hep-th #math-ph #math.MP

paper · pdf · doi:10.1103/physrevlett.126.217201

published in Physical Review Letters 126(21), 217201 (American Physical Society) · 1+5 figures

arxiv created 2021/02/22 · openalex publication_date 2021/05/24 · arxiv updated 2021/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We discuss quantum many-body systems with lattice translation and discrete on-site symmetries. We point out that, under a boundary condition twisted by a symmetry operation, there is an exact degeneracy of ground states if the unit cell forms a projective representation of the on-site discrete symmetry. Based on the quantum transfer matrix formalism, we show that, if the system is gapped, the ground-state degeneracy under the twisted boundary condition also implies a ground-state (quasi)degeneracy under the periodic boundary conditions. This gives a compelling evidence for the recently proposed Lieb-Schultz-Mattis-type ingappability due to the on-site discrete symmetry in two and higher dimensions.

Citations

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