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.

arXiv comment13 pages, 7 figures

References in corpus (35)

• The cold atom Hubbard toolbox
• Stochastic series expansion method with operator-loop update
• Bose-Einstein Condensation in Magnetic Insulators
• Supersolid hardcore bosons on the triangular lattice
• Monte Carlo study of two-dimensional Bose-Hubbard model
• Supersolid Order from Disorder: Hard-Core Bosons on the Triangular Lattice
• Persistent supersolid phase of hard-core bosons on the triangular lattice
• Phase separation in supersolids
• Supersolids versus phase separation in two-dimensional lattice bosons
• Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices
• Supersolid phase of hardcore bosons on triangular lattice
• Nature of the quantum phase transitions in the two-dimensional hardcore boson model
• Supersolids in the Bose-Hubbard Hamiltonian
• Valence Bond Solids and Their Quantum Melting in Hard-Core Bosons on the Kagome Lattice
• Revealing Superfluid--Mott-Insulator Transition in an Optical Lattice
• Loop updates for variational and projector quantum Monte Carlo simulations in the valence-bond basis
• Recent developments in Quantum Monte-Carlo simulations with applications for cold gases
• Ground state projection of quantum spin systems in the valence bond basis
• Bose glass and Mott insulator phase in the disordered boson Hubbard model
• Dynamical mean field solution of the Bose-Hubbard model
• On the Coexistence of Diagonal and off-Diagonal Long-Range Order, a Monte Carlo Study
• Phase Diagram of Commensurate Two-Dimensional Disordered Bose Hubbard Model
• Excitation spectra of strongly correlated lattice bosons and polaritons
• Ground-State Phase Diagram of the Two-Dimensional Extended Bose-Hubbard Model
• Temperature changes when adiabatically ramping up an optical lattice
• Cold bosons in optical lattices: a tutorial for Exact Diagonalization
• Quantum glass phases in the disordered Bose-Hubbard model
• The Extended Bose Hubbard Model on the Two Dimensional Honeycomb Lattice
• Effect of Doublon-Holon Binding on Mott transition---Variational Monte Carlo Study of Two-Dimensional Bose Hubbard Models
• Phase diagrams of the extended Bose-Hubbard model in one dimension by Monte-Carlo simulation with the help of a stochastic-series expansion
• Supersolidity and phase diagram of softcore bosons in a triangular lattice
• Bosons in optical lattices - from the Mott transition to the Tonks-Girardeau gas
• Permutation Matrix Representation Quantum Monte Carlo
• Phase diagram of the Bose-Hubbard model on a ring-shaped lattice with tunable weak links
• Bose-Hubbard model on a star lattice

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• 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