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

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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Cited by in corpus (38)

• Differentiable Programming Tensor Networks
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• Tropical Tensor Network for Ground States of Spin Glasses
• Simulation of three-dimensional quantum systems with projected entangled-pair states
• Hyper-optimized approximate contraction of tensor networks with arbitrary geometry
• A scaling hypothesis for projected entangled-pair states
• Tensor network approach to the two-dimensional fully frustrated XY model and a chiral ordered phase
• Solving frustrated Ising models using tensor networks
• Topological fracton quantum phase transitions by tuning exact tensor network states
• Tensor-network approach to phase transitions in string-net models
• Symmetric cluster expansions with tensor networks
• Continuous matrix product operator approach to finite temperature quantum states
• Partial lifting of degeneracy in the $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice
• Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
• Artificial out-of-plane Ising antiferromagnet on the kagome lattice with very small further neighbour couplings
• Tensor network approach to the fully frustrated XY model on a kagome lattice with a fractional vortex-antivortex pairing transition
• Hidden geometry and dynamics of complex networks: Spin reversal in nanoassemblies with pairwise and triangle-based interactions
• Unified tensor network theory for frustrated classical spin models in two dimensions
• Variational corner transfer matrix renormalization group method for classical statistical models
• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
• Collective Monte Carlo updates through tensor network renormalization
• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• An Efficient Simulation Protocol for Determining the Density of States: Combination of Replica-Exchange Wang-Landau Method and Multicanonical Replica-Exchange Method
• Efficient tensor network algorithm for layered systems
• Efficient calculation of three-dimensional tensor networks
• Calculation of the Residual Entropy of Ice Ih by Monte Carlo simulation with the Combination of the Replica-Exchange Wang-Landau algorithm and Multicanonical Replica-Exchange Method
• Polarization Plateaus in Hexagonal Water Ice $I_h$
• Contrasting pseudo-criticality in the classical two-dimensional Heisenberg and ${\mathrm{RP}}^2$ models: zero-temperature phase transition versus finite-temperature crossover
• Magnetization process and ordering of the $S=1/2$ pyrochlore magnet in a field
• Residual entropy from temperature incremental Monte Carlo method
• Single-layer tensor network approach for three-dimensional quantum systems
• Residual Entropy of a Two-dimensional Ising Model with Crossing and Four-spin Interactions
• Exact Results for the Residual Entropy of Ice Hexagonal Monolayer
• Bridging Rokhsar-Kivelson Type and Generic Quantum Phase Transitions via Thermofield Double States
• Residual Entropy of Ice: A Study Based on Transfer Matrices
• Finite Correlation Length Scaling of Disorder Parameter at Quantum Criticality
• Efficient optimization of variational tensor-network approach to three-dimensional statistical systems
• Equivalence of residual entropy of hexagonal and cubic ices from tensor network methods