Entanglement, subsystem particle numbers and topology in free fermion systems

TL;DR

This paper explores the connection between entanglement, particle numbers, and topology in free fermion systems, proposing new topological indices and analyzing their behavior under disorder, with implications for experimental estimation of entanglement entropy.

Contribution

It introduces a new topological invariant based on subsystem particle numbers to distinguish quantum spin Hall states and studies its behavior in disordered systems.

Findings

Spin-projected particle numbers distinguish quantum spin Hall states.

A new topological index signals phase transitions under disorder.

Subsystem particle number fluctuations estimate entanglement entropy.

Abstract

We study the relationship between bipartite entanglement, subsystem particle number and topology in a half-filled free fermion system. It is proposed that the spin-projected particle numbers can distinguish the quantum spin Hall state from other states, and can be used to establish a new topological index for the system. Furthermore, we apply the new topological invariant to a disordered system and show that a topological phase transition occurs when the disorder strength is increased beyond a critical value. It is also shown that the subsystem particle number fluctuation displays behavior very similar to that of the entanglement entropy. This provides a lower-bound estimation for the entanglement entropy, which can be utilized to obtain an estimate of the entanglement entropy experimentally.