Many-Body Invariants for Chern and Chiral Hinge Insulators

Abstract

We construct new many-body invariants for 2d Chern and 3d chiral hinge insulators, which are characterized by quantized pumping of dipole and quadrupole moments. The invariants that we devise are written entirely in terms of many-body ground state wavefunctions on a torus geometry with a set of unitary operators. We provide a number of supporting evidences for our invariants via topological field theory interpretation, adiabatic pumping argument, and direct mapping to free-fermion band indices. We finally confirm our invariants by numerical computations including infinite density matrix renormalization group on a quasi-one-dimensional system. The many-body invariants therefore explicitly encircle several different pillars of theoretical descriptions of topological phases.

arXiv comment5+6 pages, 2+1 figures

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• A real-space many-body marker for correlated ${\mathbb{Z}}_2$ topological insulators
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• Many-body multipole index and bulk-boundary correspondence
• Many-body Chern insulator in the Kondo lattice model on a triangular lattice
• Many-Body Quadrupolar Sum Rule for Higher-Order Topological Insulator