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arXiv · 1805.10598

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

Laurens Vanderstraeten·Bram Vanhecke·Frank Verstraete
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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.

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Laurens Vanderstraeten, Bram Vanhecke, Frank Verstraete. 2018-05-27. Residual entropies for three-dimensional frustrated spin systems with tensor networks. https://doi.org/10.1103/physreve.98.042145

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