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

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 Tc1 ≈ 0.4459 and Tc2 ≈ 0.4532, respectively. The former corresponding to a Berezinskii-Kosterlitz-Thouless phase transition describing the phase coherence of Cooper pairs, and the latter is an Ising-like continuous phase transition below which a chirality order with spontaneously broken time-reversal symmetry is established. This intermediate temperature phase represents a bosonic metallic phase and a local order parameter is given by the phase differences of the Cooper pairs on four lattice sites of each plaquette.

The planted XY model: thermodynamics and inference

“…This model was further studied in its discretized version in [19] for a mixture distribution that interpolates between ferromagnetic and uniformly distributed couplings and with interactions on a sparse random graph. Finally, the short range gauge glass model has also been extended to the quantum setting in [20] and has further physical relevance [21]. The model considered in this work, Hamiltonian (4), is closely related to H GG .…”