Excitation and dynamics in the extended Bose-Hubbard model

Abstract

The one-dimensional extended bosonic Hubbard model has been shown to exhibit a variety of phases ranging from Mott insulator and superfluid to exotic supersolids and Haldane insulators depending on the filling and the relative value of the contact (U ) and near neighbor (V ) interaction strengths. In this paper we use the density matrix renormalization group and the time evolving block decimation numerical methods to study in detail the dynamics and excitation spectra of this model in its various phases. In particular, we study in detail the behavior of the charge and neutral gaps which characterize the Mott, charge density and Haldane insulating phases. We also show that in addition to the gapless modes at k = 0, the supersolid phase exhibits gapless modes at a finite k which depends on the filling.

Extended Bose-Hubbard model with dipolar and contact interactions

“…In this section we will calculate how the locations of the transitions between these phases change for the Hamiltonian (1), depending on dipolar interaction strength d. We will not, however, recover a full phase diagram, but instead we focus on two lines, given by the constraints V /U = 0.75 and U/t = 3. The first of these values is chosen because it covers three of the phases achievable in EBH model (DW, HI and SF) and has been already extensively analyzed 25,26 , while the second one allows us to examine the MI phase (in addition to DW and HI, which are also present in that case).…”

Haldane phase on the sawtooth lattice: Edge states, entanglement spectrum, and the flat band

“…Therefore, for 0.13 ≤ V ≤ 0.256 the system is in the Haldane insulating phase. To confirm that this is indeed a HI phase, one could calculate the string order parameter 18,19,[23][24][25][26] by using the Wannier operators as the "site" operators. However, the nonlocality of the Wannier states leads to extremely complicated expressions in terms of the local operators a i , which makes it impractical to compute this Wannier-string order parameter.…”

“…As explained above, the gap behavior and the density profiles are very reminiscent of the MI-HI-CDW transitions in the usual EBH model 18,19,[23][24][25][26] . To emphasize this point, we have used Eq.…”

“…This phase, called the Haldane insulator (HI), is closely related to the Haldane phase 20 appearing in integer spin chains and realized in the AKLT state 21,22 . The phase diagram of this model was elaborated and the excitation spectra studied using quantum Monte Carlo (QMC) simulations and density matrix renormalization group (DMRG) calculations [23][24][25][26] . Another situation where unconventional phases may be encountered is that of strong geometrical frustration, for example in the particle kinetic energy.…”

Interaction-driven dynamical quantum phase transitions in a strongly correlated bosonic system

“…This model has attracted considerable attention over the past decades, resulting in a good understanding of its equilibrium phases [43,44,[46][47][48][49]. These include a superfluid phase for weak interactions, a Mott insulator (MI) for dominating U , a density wave (DW) phase for dominating V , and the topologically nontrivial Haldane insulator (HI), which occurs for intermediate parameters.…”