A quantum Monte Carlo algorithm for Bose-Hubbard models on arbitrary graphs

Abstract

We propose a quantum Monte Carlo algorithm capable of simulating the Bose-Hubbard model on arbitrary graphs, obviating the need for devising lattice-specific updates for different input graphs. We show that with our method, which is based on the recently introduced Permutation Matrix Representation Quantum Monte Carlo [Gupta, Albash and Hen, J. Stat. Mech. (2020) 073105], the problem of adapting the simulation to a given geometry amounts to generating a cycle basis for the graph on which the model is defined, a procedure that can be carried out efficiently and and in an automated manner. To showcase the versatility of our approach, we provide simulation results for Bose-Hubbard models defined on two-dimensional lattices as well as on a number of random graphs.

13 pages, 7 figures

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• Bose-Einstein Condensation in Magnetic Insulators
• Supersolid hardcore bosons on the triangular lattice
• Monte Carlo study of two-dimensional Bose-Hubbard model
• Supersolids versus phase separation in two-dimensional lattice bosons
• Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices
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Cited by in corpus (6)

• Specialising Neural-network Quantum States for the Bose Hubbard Model
• A universal black-box quantum Monte Carlo approach to quantum phase transitions
• Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs
• Bose-Einstein condensation in exotic lattice geometries
• Advanced measurement techniques in quantum Monte Carlo: The permutation matrix representation approach
• A quantum Monte Carlo algorithm for arbitrary high-spin Hamiltonians