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

Laurens Vanderstraeten (Corresponding author), Bram Vanhecke, Frank Verstraete

Publications: Contribution to journalArticlePeer Reviewed


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.
Original languageEnglish
Article number042145
Number of pages8
JournalPhysical Review E
Issue number4
Publication statusPublished - 29 Oct 2018

Austrian Fields of Science 2012

  • 103025 Quantum mechanics
  • 103015 Condensed matter
  • 103029 Statistical physics


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