Hybrid Berezinskii-Kosterlitz-Thouless and Ising topological phase transition in the generalized two-dimensional XY model using tensor networks

TL;DR

This paper uses tensor network methods to map and analyze a generalized 2D XY model, revealing a novel hybrid BKT and Ising topological phase transition and a complex phase diagram with multiple critical points.

Contribution

It introduces a tensor network approach to identify a new hybrid BKT and Ising universality class of topological phase transition in the generalized XY model.

Findings

Identification of a hybrid BKT and Ising topological transition.

Complete phase diagram with multiple critical points.

Existence of a multi-critical point where three transition lines meet.

Abstract

In tensor network representation, the partition function of a generalized two-dimensional XY spin model with topological integer and half-integer vortex excitations is mapped to a tensor product of one-dimensional quantum transfer operator, whose eigen-equation can be solved by an algorithm of variational uniform matrix product states. Using the singularities of the entanglement entropy, we accurately determine the complete phase diagram of this model. Both the integer vortex-antivortex binding and half-integer vortex-antivortex binding phases are separated from the disordered phase by the usual Berezinskii-Kosterlitz-Thouless (BKT) transitions, while a continuous topological phase transition exists between two different vortex binding phases, exhibiting a logarithmic divergence of the specific heat and exponential divergence of the spin correlation length. A new hybrid BKT and Ising universality class of topological phase transition is thus established. We further prove that three phase transition lines meets at a multi-critical point, from which a deconfinement crossover line extends into the disordered phase.