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

TL;DR

This paper derives nonperturbative constraints linking the many-body Chern number, rotation symmetry, and filling in interacting systems, enabling determination of topological invariants from symmetry eigenvalues and density without complex calculations.

Contribution

It establishes a universal relation that allows calculation of the many-body Chern number modulo an integer using symmetry eigenvalues and particle density, bypassing integration.

Findings

Provides a formula connecting Chern number, rotation eigenvalues, and filling.

Enables determination of topological invariants from symmetry data.

Applicable to systems with arbitrary interactions.

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.