Superfluid, Mott-insulator, and mass-density-wave phases in the one-dimensional extended Bose-Hubbard model

Abstract

We use the finite-size density-matrix-renormalization-group (FSDMRG) method to obtain the phase diagram of the one-dimensional (d = 1) extended Bose-Hubbard model for density ρ = 1 in the U − V plane, where U and V are, respectively, onsite and nearest-neighbor interactions. The phase diagram comprises three phases: Superfluid (SF), Mott Insulator (MI) and Mass Density Wave (MDW). For small values of U and V , we get a reentrant SF-MI-SF phase transition. For intermediate values of interactions the SF phase is sandwiched between MI and MDW phases with continuous SF-MI and SF-MDW transitions. We show, by a detailed finite-size scaling analysis, that the MI-SF transition is of Kosterlitz-Thouless (KT) type whereas the MDW-SF transition has both KT and two-dimensional-Ising characters. For large values of U and V we get a direct, first-order, MI-MDW transition. The MI-SF, MDW-SF and MI-MDW phase boundaries join at a bicritical point at (U, V ) = (8.5 ± 0.05, 4.75 ± 0.05).

Ferromagnetism in a two-component Bose-Hubbard model with synthetic spin-orbit coupling

“…We expect that the Mott-superfluid transitions in both PM phases and FM phases are of BerezinskiiKosterlitz-Thouless(BKT) 40 type. This can be verified by a finite-size scaling analysis 41,42 of the charge gap ∆ c . Close to the critical point, the gap ∆ c scales as…”

Dipolar-induced resonance for ultracold bosons in a quasi-one-dimensional optical lattice

“…The narrow MDW domain which appears in the phase diagram for small V /U is well within the validity range of our atom-dimer Hamiltonian. By contrast, the MDW phase domain previously predicted using the standard EBHM [23,25] occurs in an extended domain corresponding to large values of V /U .…”

“…The different insulating phases can subsequently be told apart by examining the ground-state wavefunction. Figure 3 compares the physically accessible phase diagram obtained using the single-band EBHM [23] (taking Ω = 0 in Eq. (4)) with the atom-dimer phase diagram (Ω = 0).…”

“…Up to now, their standard theoretical description has relied on the Extended Bose-Hubbard Model (EBHM) accounting for the interaction between nearest and more distant neighbors [1]. The 1D EBHM has revealed the occurrence, beyond the standard Mott-Insulator (MI) and superfluid (SF) phases, of a Mass Density Wave (MDW) phase [18,23] and a Haldane Insulator phase [24,25] .…”

Phase diagram of a bosonic ladder with two coupled chains

“…Here n max is the number of states kept at each site, which is in general infinity, but we truncate it for a feasible numerical calculation. We keep n max = 4 in this calculation which is found to be sufficient for the values of U considered here [9]. The value of M is chosen such that the truncation error in our calculation is always less than 10 −5 .…”