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

(2019) PHYSICAL REVIEW E. 100(6).
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  • QUTE (Quantum tensor networks and entanglement)
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.
Keywords
MATRIX PRODUCT STATES, MONTE-CARLO, PHASE-TRANSITIONS, RENORMALIZATION, VORTICES, DENSITY

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Citation

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MLA
Vanderstraeten, Laurens, et al. “Approaching the Kosterlitz-Thouless Transition for the Classical XY Model with Tensor Networks.” PHYSICAL REVIEW E, vol. 100, no. 6, 2019, doi:10.1103/physreve.100.062136.
APA
Vanderstraeten, L., Vanhecke, B., Läuchli, A. M., & Verstraete, F. (2019). Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks. PHYSICAL REVIEW E, 100(6). https://doi.org/10.1103/physreve.100.062136
Chicago author-date
Vanderstraeten, Laurens, Bram Vanhecke, Andreas M. Läuchli, and Frank Verstraete. 2019. “Approaching the Kosterlitz-Thouless Transition for the Classical XY Model with Tensor Networks.” PHYSICAL REVIEW E 100 (6). https://doi.org/10.1103/physreve.100.062136.
Chicago author-date (all authors)
Vanderstraeten, Laurens, Bram Vanhecke, Andreas M. Läuchli, and Frank Verstraete. 2019. “Approaching the Kosterlitz-Thouless Transition for the Classical XY Model with Tensor Networks.” PHYSICAL REVIEW E 100 (6). doi:10.1103/physreve.100.062136.
Vancouver
1.
Vanderstraeten L, Vanhecke B, Läuchli AM, Verstraete F. Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks. PHYSICAL REVIEW E. 2019;100(6).
IEEE
[1]
L. Vanderstraeten, B. Vanhecke, A. M. Läuchli, and F. Verstraete, “Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks,” PHYSICAL REVIEW E, vol. 100, no. 6, 2019.
@article{8647429,
  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.},
  articleno    = {062136},
  author       = {Vanderstraeten, Laurens and Vanhecke, Bram and Läuchli, Andreas M. and Verstraete, Frank},
  issn         = {2470-0045},
  journal      = {PHYSICAL REVIEW E},
  keywords     = {MATRIX PRODUCT STATES,MONTE-CARLO,PHASE-TRANSITIONS,RENORMALIZATION,VORTICES,DENSITY},
  language     = {eng},
  number       = {6},
  pages        = {14},
  title        = {Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks},
  url          = {http://dx.doi.org/10.1103/physreve.100.062136},
  volume       = {100},
  year         = {2019},
}

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