Finite-Size Geometric Entanglement from Tensor Network Algorithms

TL;DR

This paper investigates finite-size effects on geometric entanglement in quantum spin chains using tensor network algorithms, revealing a universal correction behavior at criticality.

Contribution

It introduces a tensor network approach to compute finite-size geometric entanglement and analyzes its correction behavior at critical points in quantum spin models.

Findings

Finite-size correction to geometric entanglement per site scales as 1/n at criticality.

The correction coefficient may be universal across models.

Tensor network algorithms effectively compute entanglement in finite systems.

Abstract

The global geometric entanglement is studied in the context of newly-developed tensor network algorithms for finite systems. For one-dimensional quantum spin systems it is found that, at criticality, the leading finite-size correction to the global geometric entanglement per site behaves as $b/n$, where $n$ is the size of the system and $b$ a given coefficient. Our conclusion is based on the computation of the geometric entanglement per spin for the quantum Ising model in a transverse magnetic field and for the spin-1/2 XXZ model. We also discuss the possibility of coefficient $b$ being universal.