Lieb-Schultz-Mattis theorems for symmetry protected topological phases

Abstract

The Lieb-Schultz-Mattis (LSM) theorem and its descendants represent a class of powerful no-go theorems that rule out any short-range-entangled (SRE) symmetric ground state irrespective of the specific Hamiltonian, based only on certain microscopic inputs such as symmetries and particle filling numbers. In this work, we introduce and prove a new class of LSM-type theorems, where any symmetry-allowed SRE ground state must be a symmetry-protected topological (SPT) phase with robust gapless edge states. The key ingredient is to replace the lattice translation symmetry in usual LSM theorems by magnetic translation symmetry. These theorems provide new insights into numerical models and experimental realizations of SPT phases in interacting bosons and fermions.

7+8 pages, 2 figures, 2 tables

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Cited by in corpus (16)

• Building crystalline topological phases from lower-dimensional states
• Intrinsic and emergent anomalies at deconfined critical points
• Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems
• Fermionic Lieb-Schultz-Mattis Theorems and Weak Symmetry-Protected Phases
• Rotation Symmetry-Protected Topological Phases of Fermions
• AKLT models on decorated square lattices are gapped
• Universal Relation among Many-Body Chern Number, Rotation Symmetry, and Filling
• (SPT-)LSM theorems from projective non-invertible symmetries
• Reviving the Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• Projectification of point group symmetries with a background flux and Lieb-Schultz-Mattis theorem
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Quasi-one-dimensional Hall physics in the Harper-Hofstadter-Mott model
• Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints
• Bosonic SET to SPT Transition under Dyonic LSM Theorem
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
• Emergent Symmetry-Protected Topological Phases via Polyakov Confinement in Quantum Spin Systems