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

TL;DR

This paper introduces a tensor network-based method to compute partition functions and residual entropies in three-dimensional frustrated spin systems, providing high-accuracy results and insights into their phases and critical behavior.

Contribution

It develops a novel tensor network approach for 3D classical systems, enabling direct thermodynamic limit calculations of free energies and residual entropies.

Findings

Accurate residual entropy for dimer model and water-ice phases

Identification of Coulomb phase via correlation functions

Determination of critical temperature and exponents for 3D Ising model

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.