Tensor network approach to the two-dimensional fully frustrated XY model and a chiral ordered phase

TL;DR

This paper introduces a tensor network framework to analyze the two-dimensional fully frustrated XY model, accurately identifying two close phase transitions, including a BKT transition and a chiral order transition, without relying on predefined order parameters.

Contribution

The authors develop a tensor network method that encodes frustration-induced local rules, enabling precise detection of phase transitions in the frustrated XY model without prior order parameter assumptions.

Findings

Identified two close phase transitions at T_c1≈0.4459 and T_c2≈0.4532.

Detected a BKT transition related to XY spin phase coherence.

Observed a chiral order transition with broken Z_2 symmetry.

Abstract

A general framework is proposed to solve the two-dimensional fully frustrated XY model for the Josephson junction arrays in a perpendicular magnetic field. The essential idea is to encode the ground-state local rules induced by frustrations in the local tensors of the partition function. The partition function is then expressed in terms of a product of one-dimensional transfer matrix operator, whose eigen-equation can be solved by an algorithm of matrix product states rigorously. The singularity of the entanglement entropy for the one-dimensional quantum analogue provides a stringent criterion to distinguish various phase transitions without identifying any order parameter a prior. Two very close phase transitions are determined at $T_{c1}\approx 0.4459$ and $T_{c2}\approx 0.4532$, respectively. The former corresponding to a Berezinskii-Kosterlitz-Thouless phase transition describing the phase coherence of XY spins, and the latter is an Ising-like continuous phase transition below which a chirality order with spontaneously broken $Z_2$ symmetry is established.