Two-Point Entanglement Near a Quantum Phase Transition

TL;DR

This paper investigates how two-point entanglement behaves near quantum phase transitions, revealing its universal properties and connection to correlation length in exactly solvable models.

Contribution

It demonstrates the universality and finite size scaling of two-point entanglement in a class of exactly solvable one-dimensional spin models.

Findings

Two-point entanglement saturates with a characteristic length scale.

The entanglement length matches the correlation length.

Two-point entanglement's prediction power is universal for distant points.

Abstract

In this work, we study the two-point entanglement S(i,j), which measures the entanglement between two separated degrees of freedom (ij) and the rest of system, near a quantum phase transition. Away from the critical point, S(i,j) saturates with a characteristic length scale $\xi_E$, as the distance |i-j| increases. The entanglement length $\xi_E$ agrees with the correlation length. The universality and finite size scaling of entanglement are demonstrated in a class of exactly solvable one dimensional spin model. By connecting the two-point entanglement to correlation functions in the long range limit, we argue that the prediction power of a two-point entanglement is universal as long as the two involved points are separated far enough.