An efficient computation of geometric entanglement for two-dimensional quantum lattice systems
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.
Cite
@article{arxiv.1106.2129,
title = {An efficient computation of geometric entanglement for two-dimensional quantum lattice systems},
author = {Hong-Lei Wang and Qian-Qian Shi and Sheng-Hao Li and Huan-Qiang Zhou},
journal= {arXiv preprint arXiv:1106.2129},
year = {2011}
}
Comments
4+ pages, 4 figures