Information measures for a local quantum phase transition: Lattice fermions in a one-dimensional harmonic trap

TL;DR

This paper investigates a local quantum phase transition in one-dimensional lattice fermions under harmonic confinement using quantum information measures, revealing entanglement entropy as an effective order parameter and contrasting eigenstate entanglement behaviors across the transition.

Contribution

It introduces the use of bipartite entanglement entropy as an order parameter for local quantum phase transitions in trapped fermions and analyzes eigenstate entanglement properties across the transition.

Findings

Entanglement entropy characterizes the local quantum phase transition.

Eigenstate entanglement entropy shows different temperature dependence below and above the transition.

Eigenstate entanglement entropy reflects fingerprints of the phase transition at finite energy densities.

Abstract

We use quantum information measures to study the local quantum phase transition that occurs for trapped spinless fermions in one-dimensional lattices. We focus on the case of a harmonic confinement. The transition occurs upon increasing the characteristic density and results in the formation of a band-insulating domain in the center of the trap. We show that the ground-state bipartite entanglement entropy can be used as an order parameter to characterize this local quantum phase transition. We also study excited eigenstates by calculating the average von Neumann and second Renyi eigenstate entanglement entropies, and compare the results with the thermodynamic entropy and the mutual information of thermal states at the same energy density. While at low temperatures we observe a linear increase of the thermodynamic entropy with temperature at all characteristic densities, the average eigenstate entanglement entropies exhibit a strikingly different behavior as functions of temperature below and above the transition. They are linear in temperature below the transition but exhibit activated behavior above it. Hence, at nonvanishing energy densities above the ground state, the average eigenstate entanglement entropies carry fingerprints of the local quantum phase transition.