Superfluid to Mott-Insulator Transition in Bose-Hubbard Models

Abstract

We study the superfluid-insulator transition in Bose-Hubbard models in one-, two-, and threedimensional 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 evidences that, across the transition, most of the spectral weight is concentrated at high energies, suggestive of pre-formed Mott-Hubbard side-bands. This result is compatible with the experimental data by Stoferle et al. [Phys. Rev. Lett. 92, 130403 (2004)].

Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids

“…The initial state is chosen to be the variational Jastrow ground state of H (U i ) with |Φ 0 the noninteracting-boson ground state of H (0). This choice provides an excellent approximation of the exact ground state of H (U i ) [14,15]. For instance, the superfluid-insulator transition is obtained for U var c 5 and U var c 21 in 1D and 2D respectively, in fair agreement with exact results [16,17].…”

“…2v m and 2v s . The latter ones are computed as v m = max{∂ E(q)/∂ q} and v s = lim q→0 ∂ E(q)/∂ q, where E(q) is the energy of the density modes |ψ(q) = ρ(q) |ψ 0 , with ρ(q) the Fourier transform of the density operator [14,18]. We generically find that the light-cone velocity significantly differs from twice both these velocities.…”

Bose-Hubbard ground state: Extended Bogoliubov and variational methods compared with time-evolving block decimation

“…As recently proposed in Ref. [24], we choose the subspace of wave functions having the Bijl-DingleJastrow form [22,23]:…”

“…[24]. Namely, minimization is performed by means of the power method, and at each step a Monte-Carlo algorithm computes all the average quantities relevant to the minimization procedure.…”

“…The accuracy and complexity of the method depend on the choice of the subspace. Recently, the Bijl-Dingle-Jastrow form [22,23] was proposed as an interesting variational ansatz for bosons in a lattice [24].…”