Study on Quantum Phase Transition of 2-D Quantum System by Tensor Network Algorithm

Abstract

With the deepening of people's understanding of quantum phase transitions, various efficient numerical algorithms have developed rapidly. It is necessary to develop tensor network algorithms to efficiently generate the ground state wave function of quantum many-body system and then calculate the ground state fidelity per site. This mini review article aims to discusses the tensor network algorithm for studying 2-dimensional quantum lattice systems, namely projected entangled pair state, and introduce how to characterize phase transitions in quantum many-body systems from a novel perspective-fidelity. It includes the wave function updating of projected entangled pair state and the tensor network contraction scheme, which can be used to calculate the ground-state fidelity per site of the quantum system, and the phase diagram of the ground-state can be determined without any knowledge of the order of the 2-dimensional quantum system, thus indicating that tensor network algorithms can provide a means to describe quantum phase transitions.