Criticality in Two-Dimensional Quantum Systems: Tensor Network Approach

TL;DR

This paper introduces a tensor network-based method using iPEPS to identify and characterize criticality in 2D quantum systems by analyzing the boundary state of an effective 1D Hamiltonian.

Contribution

It presents a novel scheme leveraging boundary states of iPEPS to faithfully detect criticality in 2D quantum many-body systems, verified on various models.

Findings

Boundary state correlation length distinguishes critical from gapped states.

Boundary state entanglement spectrum indicates criticality.

Method successfully applied to RVB states and XXZ model.

Abstract

Determination and characterization of criticality in two-dimensional (2D) quantum many-body systems belong to the most important challenges and problems of quantum physics. In this paper we propose an efficient scheme to solve this problem by utilizing the infinite projected entangled pair state (iPEPS), and tensor network (TN) representations. We show that the criticality of a 2D state is faithfully reproduced by the ground state (dubbed as boundary state) of a one-dimensional effective Hamiltonian constructed from its iPEPS representation. We demonstrate that for a critical state the correlation length and the entanglement spectrum of the boundary state are essentially different from those of a gapped iPEPS. This provides a solid indicator that allows to identify the criticality of the 2D state. Our scheme is verified on the resonating valence bond (RVB) states on kagom\'e and square lattices, where the boundary state of the honeycomb RVB is found to be described by a $c=1$ conformal field theory. We apply our scheme also to the ground state of the spin-1/2 XXZ model on honeycomb lattice, illustrating the difficulties of standard variational TN approaches to study the critical ground states. Our scheme is of high versatility and flexibility, and can be further applied to investigate the quantum criticality in many other phenomena, such as finite-temperature and topological phase transitions.