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In tensor network representation, the partition function of a generalizedtwo-dimensional XY spin model with topological integer and half-integer vortexexcitations is mapped to a tensor product of one-dimensional quantum transferoperator, whose eigen-equation can be solved by an algorithm of variationaluniform matrix product states. Using the singularities of the entanglemententropy, we accurately determine the complete phase diagram of this model. Boththe integer vortex-antivortex binding and half-integer vortex-antivortexbinding phases are separated from the disordered phase by the usualBerezinskii-Kosterlitz-Thouless (BKT) transitions, while a continuoustopological phase transition exists between two different vortex bindingphases, exhibiting a logarithmic divergence of the specific heat andexponential divergence of the spin correlation length. A new hybrid BKT andIsing universality class of topological phase transition is thus established.We further prove that three phase transition lines meets at a multi-criticalpoint, from which a deconfinement crossover line extends into the disorderedphase.

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