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arXiv · 2112.03550

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

Feng-Feng Song·Guang-Ming Zhang
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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.

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Feng-Feng Song, Guang-Ming Zhang. 2021-12-07. Tensor network approach to the two-dimensional fully frustrated XY model and a chiral ordered phase. https://doi.org/10.1103/physrevb.105.134516

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