find that the second and the third types are related to a point of dual symmetry and a fully polarized phase, respectively.'
author:
- 'Qian-Qian Shi'
- 'Hong-Lei Wang'
- 'Sheng-Hao Li'
- Sam Young Cho
- 'Murray T. Batchelor'
- 'Huan-Qiang Zhou'
title: |
    Geometric entanglement and quantum phase transitions\
    in two-dimensional quantum lattice models
---

Introduction
============

Of the various measures of entanglement in quantum many-body systems [@review], geometric entanglement is a measure of the multipartite entanglement contained in a pure state. More precisely stated, the geometric entanglement (GE) quantifies the distance between a given quantum state wavefunction and the closest separable (unentangled) state [@review; @hba; @tcw]. GE has been shown to serve as an alternative marker to locate critical points for quantum many-body lattice systems undergoing quantum phase transitions. This was demonstrated explicitly for a number of one-dimensional (1D) quantum systems [@wei; @ow] for which the GE diverges near the critical point with an amplitude proportional to the central charge of the underlying conformal field theory at criticality [@central; @scopy]. Moreover, for 1D quantum systems at criticality, the leading finite-size correction to the GE per lattice site is universal [@qqs; @jean; @hu], and related to the Affleck-Ludwig 