Tensor network approach to the fully frustrated XY model on a kagome lattice with a fractional vortex-antivortex pairing transition

Abstract

We have developed a tensor network approach to the two-dimensional fully frustrated classical XY spin model on the kagome lattice, and clarified the nature of the possible phase transitions of various topological excitations.We find that the standard tensor network representation for the partition function does not work due to the strong frustrations in the low temperature limit. To avoid the direct truncation of the Boltzmann weight, based on the duality transformation, we introduce a new representation to build the tensor network with local tensors lying on the centers of the elementary triangles of the kagome lattice. Then the partition function is expressed as a product of one-dimensional transfer matrix operators, whose eigen-equation can be solved by the variational uniform matrix product state algorithm accurately. The singularity of the entanglement entropy for the one-dimensional quantum operator provides a stringent criterion for the possible phase transitions. Through a systematic numerical analysis of thermodynamic properties and correlation functions in the thermodynamic limit, we prove that the model exhibits a single Berezinskii-Kosterlitz-Thouless phase transition only, which is driven by the unbinding of $1/3$ fractional vortex-antivortex pairs determined at $T_c\simeq 0.075J_1$ accurately. The absence of long-range order of chirality or quasi-long range order of integer vortices has been verified in the whole finite temperature range. Thus the long-standing controversy about the phase transitions in this fully frustrated XY model on the kagome lattice is solved rigorously, which provides a plausible way to understand the charge-6e superconducting phase observed experimentally in the two-dimensional kagome superconductors.

arXiv comment14 pages, 13 figures, submitted version for publication

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• Chiral kagome superconductivity modulations with residual Fermi arcs in KV3Sb5 and CsV3Sb5
• Unified tensor network theory for frustrated classical spin models in two dimensions
• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• Theory of charge-6e condensed phase in Kagome lattice superconductors
• Phase coherence of charge-$6e$ superconductors via a frustrated Kagome XY antiferromagnet
• Long-range Ising spins models emerging from frustrated Josephson junctions arrays with topological constraints
• Interplay of frustration and quantum fluctuations in a spin-1/2 anisotropic square lattice
• Monte Carlo study on low-temperature phase diagrams of the $J_1$-$J_2$ classical $XY$ kagome antiferromagnet
• Emergent Intermediate Phase in the $J_1$-$J_2$ XY model from Tensor Network Approaches
• Superfluid dome in the spatially modulated two-dimensional XY model