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arXiv · 1106.2129

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

Hong-Lei Wang·Qian-Qian Shi·Sheng-Hao Li·Huan-Qiang Zhou
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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.

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Hong-Lei Wang, Qian-Qian Shi, Sheng-Hao Li, Huan-Qiang Zhou. 2011-06-10. An efficient computation of geometric entanglement for two-dimensional quantum lattice systems. https://arxiv.org/abs/1106.2129

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