Generalized Real-space Chern Number Formula and Entanglement Hamiltonian

TL;DR

This paper extends a real-space Chern number formula to higher orders and demonstrates its use in connecting entanglement Hamiltonians with Hall conductance in non-interacting fermionic systems.

Contribution

It introduces a generalized formula for the real-space Chern number applicable to higher orders and validates proposals linking entanglement Hamiltonians to Hall conductance.

Findings

Generalized the Chern number formula to higher orders.

Proved the connection between entanglement Hamiltonian and Hall conductance.

Validated proposals for extracting conductance from ground states.

Abstract

We generalize a real-space Chern number formula for gapped free fermions to higher orders. Using the generalized formula, we prove recent proposals for extracting thermal and electric Hall conductance from the ground state via the entanglement Hamiltonian in the special case of non-interacting fermions, providing a concrete example of the connection between entanglement and topology in quantum phases of matter.