Tensor network approach to the two-dimensional fully frustrated XY model and a chiral ordered phase
Feng-Feng Song, Guang-Ming Zhang
Abstract
A general framework is proposed to solve the two-dimensional (2D) 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 a 1D transfer matrix operator, whose eigenequation can be solved by an algorithm of matrix product states rigorously. The singularity of the entanglement entropy for the 1D quantum analog provides a stringent criterion to distinguish various phase transitions without identifying a priori order parameter. Two very close phase transitions are determined at ${T}_{c1}\ensuremath{\approx}0.4459$ and ${T}_{c2}\ensuremath{\approx}0.4532$, respectively. The former corresponds 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.