Disentangled topological numbers by a purification of entangled mixed states for non-interacting fermion systems

TL;DR

This paper introduces a method to decompose topological invariants like the Chern number and Z2 Berry phase into contributions from disentangled subsystems, aiding the analysis of complex and disordered fermionic systems.

Contribution

The authors extend the concept of entanglement-based topological invariants to include a disentangled Chern number and apply it to systems with particle-hole symmetry, revealing new insights into topological phases.

Findings

Entanglement Chern number remains invariant under adiabatic deformations to disentangled states.

The disentangled Z2 Berry phase characterizes topological properties in systems with vanishing Chern number.

Application to weak topological phases shows edge states can exist without a nonzero Chern number.

Abstract

We argue that the entanglement Chern number proposed recently is invariant under the adiabatic deformation of a gapped many-body groundstate into a {\it disentangled/purified} one, which implies a partition of the Chern number into subsystems (disentangled Chern number). We generalize the idea to another topological number, the Z$_2$ Berry phase for a system with particle-hole symmetry, and apply it to a groundstate in a weak topological phase where the Chern number vanishes but the groundstate nevertheless has edge states. This entanglement Berry phase is especially useful for characterizing random systems with nontrivial edge states.