Phase diagram of the hardcore Bose-Hubbard model on a checkerboard superlattice

TL;DR

This paper maps out the complete phase diagram of the hardcore Bose-Hubbard model with a checkerboard superlattice in 2D and 3D, combining analytical and numerical methods to identify phase boundaries and compare approximation schemes.

Contribution

It provides the first comprehensive phase diagram for this model, including analytical boundaries and numerical results validated against various approximation methods.

Findings

Analytical phase boundaries between superfluid and trivial insulators.

Numerical determination of the superfluid to half-filled Mott insulator boundary.

Assessment of approximation schemes' accuracy in describing phase and momentum distribution.

Abstract

We obtain the complete phase diagram of the hardcore Bose-Hubbard model in the presence of a period-two superlattice in two and three dimensions. First we acquire the phase boundaries between the superfluid phase and the `trivial' insulating phases of the model (the completely-empty and completely-filled lattices) analytically. Next, the boundary between the superfluid phase and the half-filled Mott-insulating phase is obtained numerically, using the stochastic series expansion (SSE) algorithm followed by finite-size scaling. We also compare our numerical results against the predictions of several approximation schemes, including two mean-field approaches and a fourth-order strong-coupling expansion (SCE), where we show that the latter method in particular is successful in producing an accurate picture of the phase diagram. Finally, we examine the extent to which several approximation schemes, such as the random phase approximation and the strong-coupling expansion, give an accurate description of the momentum distribution of the bosons inside the insulating phases.