Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects

We investigate the phase diagrams of theoretical models describing bosonic atoms in a lattice in the presence of randomly localized impurities. By including multiband and nonlinear hopping effects we enrich the standard model containing only the chemical-potential disorder with the site-dependent hopping term. We compare the extension of the MI and the BG phase in both models using a combination of the local mean-field method and a Hartree-Fock-like procedure, as well as the Gutzwiller-ansatz approach. We show analytical argument for the presence of triple points in the phase diagram of the model with chemical-potential disorder. These triple points, however, cease to exist after the addition of the hopping disorder.

Figure 1

Comparison of the numerical and theoretical boundaries of the Mott lobes for the Hamiltonians (a), (d) $H_1$, (b), (e) $H_2$, and (c), (f) $H_3$ in one dimension (first column) and two dimensions (second column). The numerical results for one dimension were obtained for $L=100,1000,10000$ and in two dimensions for $L=40,50,80$. Theoretical boundaries (with shaded area) are based on the analysis of the random variables characterizing spectrum of the matrix $\mathcal{R}$ [conditions in Eqs. (16) and (17)] in the thermodynamic limit.

Figure 2

Variance of the eigenvalues of $\mathcal{R}$ for 1D (dashed lines) and 2D systems (continuous lines) described by the Hamiltonians $H_1$ (orange), $H_2$ (green), and $H_3$ (purple).

Figure 3

Typical distribution of the SF clusters, i.e., the regions of the lattice with nonzero local occupation by the “superfluid” particles, in the systems described by Hamiltonians $H_1$, $H_2$, $H_3$. In the first column the clusters do not percolate, hence the phase is identified as the Bose glass. In the second column, the clusters begin to percolate and the SF phase emerges.

Figure 4

Bose-glass regions for Hamiltonians $H_1$, $H_2$, $H_3$ (from top to bottom). Black line (with circles) gives the MI-BG border, red line (triangles) corresponds to Gutzwiller ansatz BG-SF border obtained using superfluid fraction threshold, green line (squares) estimates the same border using HF percolation approach. Note that the latter is consistently higher than the SF prediction.