Analytical and numerical study of trapped strongly correlated bosons in two- and three-dimensional lattices

TL;DR

This paper combines numerical quantum Monte Carlo simulations with analytical methods to study the ground-state properties of trapped strongly correlated bosons in two- and three-dimensional lattices, revealing coexistence of superfluid and insulating regions.

Contribution

It introduces a comprehensive approach using both numerical and analytical techniques to analyze inhomogeneous bosonic systems in higher dimensions, including validation of analytical approximations.

Findings

Spin-wave method accurately reproduces Monte Carlo results

Superfluid and insulating domains coexist in trapped systems

Analytical expressions match numerical data for homogeneous case

Abstract

We study the ground-state properties of trapped inhomogeneous systems of hardcore bosons in two- and three-dimensional lattices. We obtain our results both numerically, using quantum Monte Carlo techniques, and via several analytical approximation schemes, such as the Gutzwiller-mean-field approach, a cluster-mean-field method and a spin-wave analysis which takes quantum fluctuations into account. We first study the homogeneous case, for which simple analytical expressions are obtained for all observables of interest, and compare the results with the numerical ones. We obtain the equation of state of the system along with other thermodynamic properties such as the free energy, kinetic energy, superfluid density, condensate fraction and compressibility. In the presence of a trap, superfluid and insulating domains coexist in the system. We show that the spin-wave-based method reproduces the quantum Monte-Carlo results for global as well as for local quantities with a high degree of accuracy. We also discuss the validity of the local density approximation in those systems. Our analysis can be used to describe bosons in optical lattices where the onsite interaction U is much larger than the hopping amplitude t.