An efficient computation of geometric entanglement for two-dimensional quantum lattice systems

TL;DR

This paper introduces a tensor network method to efficiently compute geometric entanglement in 2D quantum lattice systems, enabling detection of quantum phase transitions and agreement with Monte Carlo results.

Contribution

It presents a novel tensor network algorithm for calculating geometric entanglement in 2D systems, overcoming previous computational challenges.

Findings

Successfully applied to quantum Ising and XYX models

Detected factorizing fields in the models

Results agree with Quantum Monte Carlo simulations

Abstract

The geometric entanglement per lattice site, as a holistic measure of the multipartite entanglement, serves as a universal marker to detect quantum phase transitions in quantum many-body systems. However, it is very difficult to compute the geometric entanglement due to the fact that it involves a complicated optimization over all the possible separable states. In this paper, we propose a systematic method to efficiently compute the geometric entanglement per lattice site for quantum many-body lattice systems in two spatial dimensions in the context of a newly-developed tensor network algorithm based on an infinite projected entangled pair state representation. It is tested for quantum Ising model in a transverse magnetic field and anisotropic spin 1/2 anti-ferromagnetic XYX model in an external magnetic field on an infinite-size square lattice. In addition, the geometric entanglement per lattice site is able to detect the so-called factorizing field. Our results are in a quantitative agreement with Quantum Monte Carlo simulations.