Entanglement topological invariants for one-dimensional topological superconductors

TL;DR

This paper introduces entanglement-based topological invariants for one-dimensional topological superconductors, providing a quantifiable, robust, and experimentally accessible way to identify topological phases through entanglement properties.

Contribution

It defines new entanglement-based topological invariants for 1D superconductors, supported by theoretical, exact, and numerical evidence, and discusses their quantization and experimental measurability.

Findings

Invariants are quantized to 0 or log 2.

Transitions show scaling behavior with entanglement critical exponents.

Invariants are experimentally measurable with current techniques.

Abstract

Entanglement is known to serve as an order parameter for true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors. These order parameters quantitatively capture the entanglement that is possible to distill from the ground state manifold, and are thus quantized to 0 or log 2. Their robust quantization property is inferred from the underlying lattice gauge theory description of topological superconductors, and is corroborated via exact solutions and numerical simulations. Transitions between topologically trivial and non-trivial phases are accompanied by scaling behavior, a hallmark of genuine order parameters, captured by entanglement critical exponents. These order parameters are experimentally measurable utilizing state-of-the-art techniques.