Many-body Euler topology

TL;DR

This paper introduces many-body Euler numbers as a new topological invariant for interacting systems, enabling the identification of nontrivial topology in time-reversal symmetric many-body spectra, supported by calculations in a topological Hubbard model.

Contribution

It proposes many-body Euler numbers as a novel topological invariant and develops a classification scheme for interacting topological phases using symmetry indicators.

Findings

Introduced many-body Euler numbers for topological characterization.

Performed calculations in a topological Hubbard model demonstrating phases.

Established a classification scheme for interacting topological phases.

Abstract

Integer and fractional Chern insulators exhibit a nonzero quantized anomalous Hall conductivity due to a spontaneous breaking of time reversal symmetry. To identify nontrivial topology in their time-reversal symmetric many-body spectra, we introduce many-body Euler numbers as a counterpart to many-body Chern numbers. Exemplarily, we perform calculations in a topological Hubbard model that can realize Chern and fractional Chern insulating phases. Furthermore, we lay out a classification scheme to realize different topological phases in interacting systems using symmetry indicators in analogy to topological band theory.