Extended Boson Hubbard Model Research Articles

The MFA ground states for the extended Bose-Hubbard model with a three-body constraint

We address the intensively studied extended bosonic Hubbard model (EBHM) with truncation of the on-site Hilbert space to the three lowest occupation states n=0,1,2 in frames of the S=1 pseudospin formalism. Similar model was recently proposed to describe the charge degree of freedom in a model high-T c cuprate with the on-site Hilbert space reduced to the three effective valence centers, nominally Cu1+;2+;3+. With small corrections the model becomes equivalent to a strongly anisotropic S=1 quantum magnet in an external magnetic field. We have applied a generalized mean-field approach and quantum Monte-Carlo technique for the model 2D S=1 system with a two-particle transport to find the ground state phase with its evolution under deviation from half-filling.

Unusual Finite-Temperature Phase Diagram for Semi-hard-core Bosons in Two Dimensions

The extended bosonic Hubbard model (EBHM) is a paradigmatic model for the highly topical field of ultracold gases in optical lattices. Using quantum Monte Carlo simulations, we have determined the finite-temperature phase diagram of the EBHM with truncation of the on-site Hilbert space to the three lowest occupation states: n = 0, 1, 2 (semi-hard-core boson Hubbard model) given nearest-neighbor repulsion, however, both positive and negative values of the on-site boson–boson coupling U. This model is equivalent to an anisotropic spin-1 XXZ model (\(n=S_z+1\)) in a magnetic field. In the limit of large negative U (the boson–boson attraction), the model turns into the well-known model of hard-core bosons whose rich phase diagram demonstrates several puzzling features, in particular, signatures of an unusual reentrant behavior with a charge ordering upon increasing the temperature. We have shown that the rise of the correlation parameter U to positive values (the boson–boson repulsion) expectedly leads to a lowering of the temperature of the superfluid transition and unexpectedly to the more and more pronounced “reentrance” effect.

Excitation and dynamics in the extended Bose-Hubbard model

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.

Pseudospin S = 1 formalism and skyrmion-like excitations in the three-body constrained extended Bose–Hubbard model

We discuss the most prominent and intensively studied S = 1 pseudospin formalism for the extended bosonic Hubbard model (EBHM) with the on-site Hilbert space truncated to the three lowest occupation states n = 0, 1, 2. The EBHM Hamiltonian is a paradigmatic model for the highly topical field of ultracold gases in optical lattices. The generalized non-Heisenberg effective pseudospin Hamiltonian does provide a deep link with a boson system and a physically clear description of “the myriad of phases,” from uniform Mott insulating phases and density waves to two types of superfluids and supersolids. We argue that the 2D pseudospin system is prone to a topological phase separation and focus on several types of unconventional skyrmion-like topological structures in 2D boson systems, which have not been analyzed until now. The structures are characterized by a complicated interplay of insulating and two superfluid phases with a single- boson and two-boson condensation, respectively.

Competition between the Haldane insulator, superfluid and supersolid phases in the one-dimensional Bosonic Hubbard Model

We use quantum Monte Carlo (QMC), density matrix renormalization group (DMRG) and time evolution block decimation (TEBD) to study the competition between several exotic quantum phases in the one-dimensional extended bosonic Hubbard model and map its phase diagram. Of particular interest is the Haldane insulating phase which we show to be present only for density p = 1. We also show that the supersolid phase is present for a wide range of parameters including commensurate densities.

Quantum phases, supersolids and quantum phase transitions of interacting bosons in frustrated lattices

By using the dual vortex method (DVM), we develop systematically a simple and effective scheme to use the vortex degree of freedoms on dual lattices to characterize the symmetry breaking patterns of the boson insulating states in the direct lattices. Then we apply our scheme to study quantum phases and phase transitions in an extended boson Hubbard model slightly away from 1/3 (2/3) filling on frustrated lattices such as triangular and Kagome lattice. In a triangular lattice at 1/3, we find a X-CDW, a stripe CDW phase which was found previously by a density operator formalism (DOF). Most importantly, we also find a new CDW-VB phase which has both local CDW and local VB orders, in sharp contrast to a bubble CDW phase found previously by the DOF. In the Kagome lattice at 1/3, we find a VBS phase and a 6-fold CDW phase. Most importantly, we also identify a CDW-VB phase which has both local CDW and local VB orders which was found in previous QMC simulations. We also study several other phases which are not found by the DVM. By analyzing carefully the saddle point structures of the dual gauge fields in the translational symmetry breaking sides and pushing the effective actions slightly away from the commensurate filling f=1/3(2/3), we classified all the possible types of supersolids and analyze their stability conditions. In a triangular lattice, there are X-CDW supersolid, stripe CDW supersolid, but absence of any valence bond supersolid (VB-SS). There are also a new kind of supersolid: CDW-VB supersolid. In a Kagome lattice, there are 6-fold CDW supersolid, stripe CDW supersolid, but absence of any valence bond supersolid (VB-SS). There are also a new kind of supersolid: CDW-VB supersolid. We show that independent of the types of the SS, the quantum phase transitions from solids to supersolids driven by a chemical potential are in the same universality class as that from a Mott insulator to a superfluid, therefore have exact exponents z=2, ν=1/2, η=0 (with logarithmic corrections). Excitation spectra of all these insulating phases and supersolid phases are also studied. Implications on QMC simulations with both nearest neighbor and next nearest neighbor interactions in both lattices are given. Some possible intrinsic problems of the DOF in identifying the insulating phases are also pointed out.

Characterizing symmetry breaking patterns in a lattice by dual degrees of freedom

A duality transformation in quantum field theory is usually established first through partition functions. It is always important to explore the dual relations between various correlation functions in the transformation. Here, we explore such a dual relation to study quantum phases and phase transitions in an extended boson Hubbard model at 1/3 (2/3) filling on a triangular lattice. We develop systematically a simple and effective way to use the vortex degrees of freedom on dual lattices to characterize both the density wave and valence bond symmetry breaking patterns of the boson insulating states in the direct lattices. In addition to a checkerboard charge density wave (X-CDW) and a stripe CDW, we find a novel CDW-VBS phase which has both local CDW and local valence bond solid (VBS) orders. Implications for Quantum Monte Carlo simulations are addressed. The possible experimental realizations of cold atoms loaded on optical lattices are discussed.

Global phase diagram of three-dimensional extended Boson Hubbard model: A continuous-time quantum Monte Carlo study

We present the global phase diagram of the extended boson Hubbard model on a simple cubic lattice by quantum Monte Carlo simulation with the worm update algorithm. Four kinds of phases are supported by this model, including superfluid, supersolid, Mott, and charge density wave (CDW) states, which are identified in the phase diagram of chemical potential $\ensuremath{\mu}$ versus nearest-neighbor interaction $V$. By changing the chemical potential, a continuous transition is found from the Mott phase to a superfluid phase without breaking the translational symmetry. For an insulating CDW state, adding particles to it gives rise to a continuous transition to a supersolid phase, while removing particles usually leads to a first-order transition to either a supersolid or superfluid phase. By tuning the nearest-neighbor interaction, one can realize the transition between two insulating phases, Mott and CDW, with the same particle density, which turns out to be first order. We also confirm the result in Phys. Rev. B 79, 094503 (2009) that a supersolid phase with average particle density less than 1/2 can exist in a small region of the $\ensuremath{\mu}$-$V$ phase diagram.

Momentum distribution of the hard-core extended boson Hubbard model in one dimension

We investigate the momentum distribution associated with quantum phase transitions between a superfluid and a charge-density-wave state in the one-dimensional hard-core extended boson Hubbard model at half filling by using the Lanczos exact diagonalization method. The momentum distribution shows distinct features in different regions. At the Heisenberg point, it shows a universal behavior. In the superfluid phase, the Luttinger-liquid parameters are easily obtained from the finite-size scaling behaviors of the zero-momentum occupancy. Also the signature of a charge-density wave can be identified in the insulating phase.

Quantum phase transitions and the hidden order in a two-chain extended boson Hubbard model at half-odd-integer fillings

We study the phase diagram of two weakly coupled one-dimensional dipolar boson chains at half-odd-integer fillings. We find that the system contains a rich phase diagram. Four different phases are found. They are the Mott insulators, the single-particle resonant superfluid, the paired superfluid, and the bond-density or interchain density waves. Moreover, the Mott insulating phase can be further classified according to a hidden string order parameter, which is analogous to the one investigated recently in the one-dimensional boson Mott insulator at integer fillings.

Supersolidity from defect condensation in the extended boson Hubbard model

We study the ground-state phase diagram of the hard-core extended boson Hubbard model on the square lattice with both nearest- and next-nearest-neighbor hoppings and repulsions, using Gutzwiller mean-field theory and quantum Monte Carlo simulations. We observe the formation of supersolid states with checkerboard, striped, and quarter-filled crystal structures when the system is doped away from commensurate fillings. In the striped supersolid phase, a strong anisotropy in the superfluid density is obtained from the simulations; however, the transverse component remains finite, indicating a true two-dimensional superflow. We find that upon doping, the striped supersolid transitions directly into the supersolid with quarter-filled crystal structure, via a first-order stripe melting transition.

Supersolids versus Phase Separation in Two-Dimensional Lattice Bosons

We study the nature of the ground state of the two-dimensional extended boson Hubbard model on a square lattice by quantum Monte Carlo methods. We demonstrate that strong but finite on-site interaction U along with a comparable nearest-neighbor repulsion V result in a thermodynamically stable supersolid ground state for densities larger than 1/2, in contrast to fillings less than 1/2 or for very large U, where the checkerboard supersolid is unstable towards phase separation. We discuss the relevance of our results to realizations of supersolids using cold bosonic atoms in optical lattices.

Phase transitions in an interacting boson model with near-neighbor repulsion.

We study the order of the zero temperature quantum phase transitions at density \ensuremath{\rho}=1 in the one-dimensional extended boson Hubbard model by examining the order parameter distribution and hysteresis effects. The phase diagram of the model at \ensuremath{\rho}=1/2, a generalization of the spin-1/2 XXZ Hamiltonian, is also obtained, and the possibility of a supersolid region is discussed.