Thermal bosons in 3d optical lattices via tensor networks

Abstract

Ultracold atoms in optical lattices are one of the most promising experimental setups to simulate strongly correlated systems. However, efficient numerical algorithms able to benchmark experiments at low-temperatures in interesting 3d lattices are lacking. To this aim, here we introduce an efficient tensor network algorithm to accurately simulate thermal states of local Hamiltonians in any infinite lattice, and in any dimension. We apply the method to simulate thermal bosons in optical lattices. In particular, we study the physics of the (soft-core and hard-core) Bose-Hubbard model on the infinite pyrochlore and cubic lattices with unprecedented accuracy. Our technique is therefore an ideal tool to benchmark realistic and interesting optical-lattice experiments.

arXiv comment6 pages, 4 figures + Appendix

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• Simulation of three-dimensional quantum systems with projected entangled-pair states
• Gauging tensor networks with belief propagation
• Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model
• Thermodynamics of 3D Kitaev quantum spin liquids via tensor networks
• Fermionic tensor network contraction for arbitrary geometries
• Single-layer tensor network approach for three-dimensional quantum systems
• Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
• Valence-Bond Solid phases in the spin-$1/2$ Kekule-Heisenberg model
• Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems