Eur. Phys. J. B (2017) 90: 196
https://doi.org/10.1140/epjb/e2017-80077-8

Regular Article

Quantum phase transition in the one-dimensional quantum Heisenberg XYZ model with Dzyaloshinskii–Moriya interaction

¹ School of Science, Xi’an Polytechnic University, Xi’an 710048, P.R. China
² Department of Applied Physics, Xi’an Jiaotong University, Xi’an 710049, P.R. China
³ College of Medical Informatics, Chongqing Medical University, Chongqing 400016, P.R. China
⁴ School of Public Health and Management, Chongqing Medical University, Chongqing 400016, P.R. China

Received: 3 February 2017
Received in final form: 16 August 2017
Published online: 16 October 2017

Abstract

We investigated the quantum phase transition occurred in one-dimensional quantum Heisenberg XYZ model with Dzyaloshinskii–Moriya interaction via the infinite matrix product state representation with the infinite time evolving block decimation method. Entanglement entropy and local order parameter in and near the transition point are given. Scaling relation plays crucial roles on identifying a quantum system with a physically different phase. The scaling relation of the entanglement entropy, local order parameter and finite correlation length with the truncation dimension are also obtained. All the interesting results give a theoretical justification for the high accuracy of infinite time evolved block decimation algorithm which works in the thermodynamical limit.