Entropic topological invariant for a gapped one-dimensional system

TL;DR

This paper introduces an entropic topological invariant as a robust order parameter for one-dimensional gapped systems, capable of distinguishing topological phases and stable against local perturbations.

Contribution

It proposes a novel entropic order parameter based on ground state entanglement entropy, applicable to disordered and interacting systems, and demonstrates its stability and topological discrimination.

Findings

Order parameter distinguishes Majorana from trivial chains.

Invariant under finite-depth local quantum circuits.

Potential for experimental measurement in optical lattices.

Abstract

We propose an order parameter for a general one-dimensional gapped system with an open boundary condition. The order parameter can be computed from the ground state entanglement entropy of some regions near one of the boundaries. Hence, it is well-defined even in the presence of arbitrary interaction and disorder. We also show that it is invariant under a finite-depth local quantum circuit, suggesting its stability against an arbitrary local perturbation that does not close the energy gap. Further, it can unambiguously distinguish Majorana chain from a trivial chain under a global fermion parity conservation. We argue that the order parameter can be in principle measured in an optical lattice system.