Universal Relation among Many-Body Chern Number, Rotation Symmetry, and Filling

Abstract

Understanding the interplay between the topological nature and the symmetry property of interacting systems has been a central matter of condensed matter physics in recent years. In this Letter, we establish nonperturbative constraints on the quantized Hall conductance of many-body systems with arbitrary interactions. Our results allow one to readily determine the many-body Chern number modulo a certain integer without performing any integrations, solely based on the rotation eigenvalues and the average particle density of the many-body ground state.

arXiv comment5+13 pages, 3+6 figures; v3: minor edits, to appear in Physical Review Letters

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Cited by in corpus (18)

• Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene
• Generalized homology and Atiyah-Hirzebruch spectral sequence in crystalline symmetry protected topological phenomena
• A many-body index for quantum charge transport
• Many-body Chern number without integration
• Insensitivity of bulk properties to the twisted boundary condition
• Filling-enforced constraint on the quantized Hall conductivity on a periodic lattice
• Non-local topological electromagnetic phases of matter
• A generalized boundary condition applied to Lieb-Schultz-Mattis type ingappabilities and many-body Chern numbers
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Rational indices for quantum ground state sectors
• Symmetry indicators in commensurate magnetic flux
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• A many-body Fredholm index for ground state spaces and Abelian anyons
• Random spin-orbit gates in the system of a Topological insulator and a Quantum dot
• Topological Phase Transitions of Interacting Fermions in the Presence of a Commensurate Magnetic Flux
• Topological constraints on the electronic band structure of hexagonal lattice in a magnetic field
• Localization phase diagram of the Hexagonal Lattice with irrational magnetic flux