Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks
Statistical Mechanics
2020-01-01 v1 Quantum Physics
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.
Cite
@article{arxiv.1907.04576,
title = {Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks},
author = {Laurens Vanderstraeten and Bram Vanhecke and Andreas M. Laeuchli and Frank Verstraete},
journal= {arXiv preprint arXiv:1907.04576},
year = {2020}
}