Superfluid to Mott-Insulator Transition in Bose-Hubbard Models

We study the superfluid-insulator transition in Bose-Hubbard models in one-, two-, and three-dimensional cubic lattices by means of a recently proposed variational wave function. In one dimension, the variational results agree with the expected Berezinskii-Kosterlitz-Thouless scenario of the interaction-driven Mott transition. In two and three dimensions, we find evidence that, across the transition, most of the spectral weight is concentrated at high energies, suggestive of preformed Mott-Hubbard sidebands. This result is compatible with the experimental data by Stoferle et al. [Phys. Rev. Lett. 92, 130403 (2004)].

Figure 1

Variational results for the Jastrow potential $v_q$ multiplied by $q^2$ in one and two dimensions and by $|q{|}^3$ in three dimensions for increasing values of $U/t$ (from bottom to top). Upper panel: 1D case for 60 (circles) and 100 (triangles) sites. Middle panel: 2D case for $20\times 20$ (circles), $26\times 26$ (squares), and $30\times 30$ (triangles) clusters (along the (1, 0) direction). Lower panel: 3D case for $8\times 8\times 8$ (circles), $10\times 10\times 10$ (squares), and $12\times 12\times 12$ (triangles) clusters [along the (1,0,0) direction].

Figure 2

Density structure factor $N_q$ divided by $|q|$ calculated with variational Monte Carlo (left panels) and GFMC (right panels) simulations in one dimension (upper panels) and two dimensions (lower panels). In one dimension, $L=60$ (full symbols) and $L=150$ (empty symbols) and $U/t=1.6$, 1.8, 2, 2.2, 2.4, 2.5. and 3. In two dimensions, $L=12\times 12$ (closed symbols) and $16\times 16$ (open symbols) for the variational calculation ($U/t=10$, 10.2, 10.4, 10.6, and 10.8) and for the GFMC calculation ($U/t=8$, 8.2, 8.4, 8.6, and 8.8). All cases are shown from top to bottom for increasing values of $U/t$.

Figure 3

Upper panel: Density structure factor $N_q$ calculated by the variational Monte Carlo calculations for three dimensions and $U/t=20$. Lower panels: $N_q$ for nonoptimized wave functions with $v_q\sim {\beta }_{3\mathrm{D}}/|q{|}^3$ for two values of ${\beta }_{3\mathrm{D}}$.

Figure 4

Variational results for the average energy of density excitations $E(q)$ of Eq. (4) in one, two, and three dimensions.