Topological Hamiltonian as an Exact Tool for Topological Invariants

TL;DR

This paper introduces the topological Hamiltonian as an exact method to determine topological invariants in interacting topological insulators and superconductors, capturing surface state information beyond physical spectra.

Contribution

It proposes the topological Hamiltonian concept, providing a new exact approach to compute topological invariants in interacting systems.

Findings

Topological Hamiltonian encodes gapless surface states.

Eigenvalues differ from physical energy spectra.

Provides an exact tool for topological invariants.

Abstract

We propose the concept of `topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of topological Hamiltonian are significantly different from the physical energy spectra, but we show that topological Hamiltonian contains the information of gapless surface states, therefore it is an exact tool for topological invariants.