Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks

Abstract

We apply variational tensor-network methods for simulating the Kosterlitz-Thouless phase transition in the classical two-dimensional XY model. In particular, using uniform matrix product states (MPS) with non-abelian O(2) symmetry, we compute the universal drop in the spin stiffness at the critical point. In the critical low-temperature regime, we focus on the MPS entanglement spectrum to characterize the Luttinger-liquid phase. In the high-temperature phase, we confirm the exponential divergence of the correlation length and estimate the critical temperature with high precision. Our MPS approach can be used to study generic two-dimensional phase transitions with continuous symmetries.

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• Berezinskii-Kosterlitz-Thouless transition from Neural Network Flows
• Vestigial $d$-wave charge-$4e$ Superconductivity from Bidirectional Pair Density Waves
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