Thermodynamic phase transition driven by topological excitations and their tensor network approach

The fundamental concepts of phases and phase transitions constitute the cornerstone of our understanding of the physical universe. The historical development of the phase transition theory from Landau's spontaneous symmetry breaking paradigm to modern topological phase transition theories represents a major milestone in the evolution of numerous scientific disciplines. From the perspective of emergent philosophy, the interplay of topological excitations leads to enriched physical phenomena. One prominent prototype is the Berezinskii-Kosterlitz-Thouless (BKT) phase transition, where unbinding of integer vortices occurs in the absence of spontaneous breaking of continuous U(1) symmetry. Using the state-of-the-art tensor network methods, we express the partition function of the two-dimensional XY-related system in terms of a product of one-dimensional transfer operators. From the singularities of the entanglement entropy of the one-dimensional transfer operator, we accurately determine the complete phase diagram. This method provides new insights into the emergent phenomenon driven by topological excitations, and sheds new light on future studies of 2D systems with continuous symmetries.