Stochastic Series Expansion Quantum Monte Carlo

Ejaaz Merali, Isaac J. S. De Vlugt, Roger G. Melko

Arrays of Rydberg atoms are a powerful platform to realize strongly-interacting quantum many-body systems. A common Rydberg Hamiltonian is free of the sign problem, meaning that its equilibrium properties are amenable to efficient simulation by quantum Monte Carlo (QMC). In this paper, we develop a Stochastic Series Expansion QMC algorithm for Rydberg atoms interacting on arbitrary lattices. We describe a cluster update that allows for the efficient sampling and calculation of physical observables for typical experimental parameters, and show that the algorithm can reproduce experimental results on large Rydberg arrays in one and two dimensions.

Stephen Fahy

Patrik Henelius, Peter Fröbrich, P. J. Kuntz +2 more

The stochastic series expansion quantum Monte Carlo method is used to study thin ferromagnetic films, described by a Heisenberg model including local anisotropies. The magnetization curve is calculated, and the results compared to Schwinger boson and many-body Green's function calculations. A transverse field is introduced in order to study the reorientation effect, in which the magnetization changes from out of plane to in plane. Since the approximate theoretical approaches above differ significantly from each other, and the Monte Carlo method is free of systematic errors, the calculation provides an unbiased check of the approximate treatments. By studying quantum spin models with local anisotropies, varying spin size, and a transverse field, we also demonstrate the general applicability of the recent cluster-loop formulation of the stochastic series expansion quantum Monte Carlo method.

Itay Hen, Tameem Albash, Lalit Gupta

Matthew Clifford Wilson

Itay Hen, Tameem Albash

We study the performance of the Off-Diagonal Expansion quantum Monte Carlo algorithm on quantum spin glasses, specifically, 3-regular random antiferromagnets augmented with a transverse magnetic field. We demonstrate the advantages, sometimes by orders of magnitude, of the technique by comparing its runtimes against existing state-of-the-art schemes such as Path Integral quantum Monte Carlo and Stochastic Series Expansion.