Eur. Phys. J. B (2016) 89: 225
https://doi.org/10.1140/epjb/e2016-70230-4

Regular Article

Global geometric entanglement and quantum phase transition in three-leg spin-3/2 Heisenberg tubes

¹ Department of Applied Physics, Xi’an Jiaotong University, Xi’an 710049, P.R. China
² School of Science, Xi’an Polytechnic University, Xi’an 710048, P.R. China
³ Centre for Modern Physics and Department of Physics, Chongqing University, Chongqing 400044, P.R. China

^a e-mail: chenaiminxa@163.com

Received: 15 April 2016
Received in final form: 15 June 2016
Published online: 17 October 2016

Abstract

Based on the tensor network representations, we have developed an efficient scheme to calculate the global geometric entanglement as a multipartite entanglement measure for the three-leg spin tubes. From the geometric entanglement, the phase diagram of a spin-3 / 2 isosceles triangle spin tube has been investigated varying the base interaction α. Two Berezinsky-Kosterlitz-Thouless phase transitions are estimated to be α_c1 ≃ 0.68 and α_c2 ≃ 3.85, respectively. Then, even though the spin tube is in gapless spin liquid phases for α < α_c1 and α >α_c2, the geometrical structure difference between the groundstate wavefunctions for the two regions is found to reflect the global geometric entanglement that contains bipartite and multipartite contributions. Further, the phase transition points from the von Neumann entropies and fidelity are consistent with that from the geometric entanglement. As a result, the global geometric entanglement can be used to explore a geometrical nature of quantum phases as well as an indicator for quantum phase transitions in many-body lattice systems.