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Residual entropies for three-dimensional frustrated spin systems with tensor networks

Laurens Vanderstraeten (UGent) , Bram Vanhecke (UGent) and Frank Verstraete (UGent)
Author
Organization
Project
  • QUTE (Quantum tensor networks and entanglement)
  • ERQUAF (Entanglement and Renormalisation for Quantum Fields)
Abstract
We develop a technique for calculating three-dimensional classical partition functions using projected entangled-pair states (PEPS). Our method is based on variational PEPS optimization algorithms for two-dimensional quantum spin systems, and allows us to compute free energies directly in the thermodynamic limit. The main focus of this work is classical frustration in three-dimensional many-body systems leading to an extensive ground-state degeneracy. We provide high-accuracy results for the residual entropy of the dimer model on the cubic lattice, water ice I-h, and water ice I-c. In addition, we show that these systems are in a Coulomb phase by computing the dipolar form of the correlation functions. As a further benchmark of our methods, we calculate the critical temperature and exponents of the Ising model on the cubic lattice.
Keywords
ICE, FORMULATION, STATISTICS, CRYSTALS, PHASE

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Citation

Please use this url to cite or link to this publication:

MLA
Vanderstraeten, Laurens, Bram Vanhecke, and Frank Verstraete. “Residual Entropies for Three-dimensional Frustrated Spin Systems with Tensor Networks.” PHYSICAL REVIEW E 98.4 (2018): n. pag. Print.
APA
Vanderstraeten, Laurens, Vanhecke, B., & Verstraete, F. (2018). Residual entropies for three-dimensional frustrated spin systems with tensor networks. PHYSICAL REVIEW E, 98(4).
Chicago author-date
Vanderstraeten, Laurens, Bram Vanhecke, and Frank Verstraete. 2018. “Residual Entropies for Three-dimensional Frustrated Spin Systems with Tensor Networks.” Physical Review E 98 (4).
Chicago author-date (all authors)
Vanderstraeten, Laurens, Bram Vanhecke, and Frank Verstraete. 2018. “Residual Entropies for Three-dimensional Frustrated Spin Systems with Tensor Networks.” Physical Review E 98 (4).
Vancouver
1.
Vanderstraeten L, Vanhecke B, Verstraete F. Residual entropies for three-dimensional frustrated spin systems with tensor networks. PHYSICAL REVIEW E. 2018;98(4).
IEEE
[1]
L. Vanderstraeten, B. Vanhecke, and F. Verstraete, “Residual entropies for three-dimensional frustrated spin systems with tensor networks,” PHYSICAL REVIEW E, vol. 98, no. 4, 2018.
@article{8582922,
  abstract     = {We develop a technique for calculating three-dimensional classical partition functions using projected entangled-pair states (PEPS). Our method is based on variational PEPS optimization algorithms for two-dimensional quantum spin systems, and allows us to compute free energies directly in the thermodynamic limit. The main focus of this work is classical frustration in three-dimensional many-body systems leading to an extensive ground-state degeneracy. We provide high-accuracy results for the residual entropy of the dimer model on the cubic lattice, water ice I-h, and water ice I-c. In addition, we show that these systems are in a Coulomb phase by computing the dipolar form of the correlation functions. As a further benchmark of our methods, we calculate the critical temperature and exponents of the Ising model on the cubic lattice.},
  articleno    = {042145},
  author       = {Vanderstraeten, Laurens and Vanhecke, Bram and Verstraete, Frank},
  issn         = {2470-0045},
  journal      = {PHYSICAL REVIEW E},
  keywords     = {ICE,FORMULATION,STATISTICS,CRYSTALS,PHASE},
  language     = {eng},
  number       = {4},
  pages        = {8},
  title        = {Residual entropies for three-dimensional frustrated spin systems with tensor networks},
  url          = {http://dx.doi.org/10.1103/PhysRevE.98.042145},
  volume       = {98},
  year         = {2018},
}

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