One-dimensional Bosonic Hubbard Model Research Articles

Quantum phase transitions in the matrix product states of the one-dimensional boson Hubbard model

We study quantum phase transitions in the matrix product states of the one-dimensional boson Hubbard model, whose amount of entanglement is limited by the size of the matrices used in the representation of the states. By measuring entanglement entropy and other physical properties, we observe that the Mott-insulator-to-superfluid transitions occur sharp and continuous, accompanied by shifting transition points that are not blurred by finite entanglement effects. This strongly suggests that the transition always occurs between the Mott insulator and a mean-field-like compressible state, followed by the more entangled superfluid state. Both $O(2)$ and the commensurate-incommensurate transitions are studied, whose properties can be characterized by entanglement spectra and critical exponents.

Superfluid weight and polarization amplitude in the one-dimensional bosonic Hubbard model

We calculate the superfluid weight and the polarization amplitude for the one-dimensional bosonic Hubbard model focusing on the strong-coupling regime. Other than analytic calculations we apply two methods: variational Monte Carlo based on the Baeriswyl wave function and exact diagonalization. The former gives zero superfluid response at integer filling, while the latter gives a superfluid response at finite hopping. From the polarization amplitude we derive the variance and the associated size scaling exponent. Again, the variational study does not produce a finite superfluid weight at integer filling (size scaling exponent is near one), but the Fourier transform of the polarization amplitude behaves in a similar way to the result of exact diagonalization, with a peak at small hopping, and suddenly decreasing at the insulator-superfluid transition. On the other hand, exact diagonalization studies result in a finite spread of the total position which increases with the size of the system. In the superfluid phase the size scaling exponent is two as expected. Importantly, our work addresses the ambiguities that arise in the calculation of the superfluid weight in variational calculations, and we comment on the prediction of Anderson about the superfluid response of the model at integer filling.

Variational Monte Carlo method for the Baeriswyl wave function: Application to the one-dimensional bosonic Hubbard model

A variational Monte Carlo method for bosonic lattice models is introduced. The method is based on the Baeriswyl projected wavefunction. The Baeriswyl wavefunction consists of a kinetic energy based projection applied to the wavefunction at infinite interaction, and is related to the shadow wavefunction already used in the study of continuous models of bosons. The wavefunction at infinite interaction, and the projector, are represented in coordinate space, leading to an expression for expectation values which can be evaluated via Monte Carlo sampling. We calculate the phase diagram and other properties of the bosonic Hubbard model. The calculated phase diagram is in excellent agreement with known quantum Monte Carlo results. We also analyze correlation functions.

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.

Competing phases, phase separation, and coexistence in the extended one-dimensional bosonic Hubbard model

We study the phase diagram of the one-dimensional bosonic Hubbard model with contact $(U)$ and near neighbor $(V)$ interactions focusing on the gapped Haldane insulating (HI) phase which is characterized by an exotic nonlocal order parameter. The parameter regime $(U,V$, and $\ensuremath{\mu})$ where this phase exists and how it competes with other phases, such as the supersolid (SS) phase, is incompletely understood. We use the stochastic Green function quantum Monte Carlo algorithm as well as the density matrix renormalization group to map out the phase diagram. Our main conclusions are that the HI exists only at $\ensuremath{\rho}=1$, the SS phase exists for a very wide range of parameters (including commensurate fillings), and displays power law decay in the one-body Green function. In addition, we show that at fixed integer density, the system exhibits phase separation in the $(U,V)$ plane.

Hydrodynamic long-time tails after a quantum quench

After a quantum quench, a sudden change of parameters, generic many-particle quantum systems are expected to equilibrate. A few collisions of quasiparticles are usually sufficient to establish approximately local equilibrium. Reaching global equilibrium is, however, much more difficult as conserved quantities have to be transported for long distances to build up a pattern of fluctuations characteristic for equilibrium. Here we investigate the quantum quench of the one-dimensional bosonic Hubbard model from infinite to finite interaction strength $U$ using semiclassical methods for weak and exact diagonalization for strong quenches. Equilibrium is approached only slowly, as ${t}^{\ensuremath{-}1/2}$ with subleading corrections proportional to ${t}^{\ensuremath{-}3/4}$, consistent with predictions from hydrodynamics. We show that these long-time tails determine the relaxation of a wide range of physical observables.

Competing Supersolid and Haldane Insulator Phases in the Extended One-Dimensional Bosonic Hubbard Model

The Haldane insulator is a gapped phase characterized by an exotic nonlocal order parameter. The parameter regimes at which it might exist, and how it competes with alternate types of order, such as supersolid order, are still incompletely understood. Using the stochastic Green function quantum MonteCarlo algorithm and density matrix renormalization group, we study numerically the ground state phase diagram of the one-dimensional bosonic Hubbard model with contact and near neighbor repulsive interactions. We show that, depending on the ratio of the near neighbor to contact interactions, this model exhibits charge density waves, superfluid, supersolid, and the recently identified Haldane insulating phases. We show that the Haldane insulating phase exists only at the tip of the unit-filling charge density wave lobe and that there is a stable supersolid phase over a very wide range of parameters.

Exact study of the one-dimensional boson Hubbard model with a superlattice potential

We use Quantum Monte Carlo simulations and exact diagonalization to explore the phase diagram of the Bose-Hubbard model with an additional superlattice potential. We first analyze the properties of superfluid and insulating phases present in the hard-core limit where an exact analytic treatment is possible via the Jordan-Wigner transformation. The extension to finite on-site interaction is achieved by means of quantum Monte Carlo simulations. We determine insulator/superfluid phase diagrams as functions of the on-site repulsive interaction, superlattice potential strength, and filling, finding that insulators with fractional occupation numbers, which are present in the hard-core case, extend deep into the soft-core region. Furthermore, at integer fillings, we find that the competition between the on-site repulsion and the superlattice potential can produce a phase transition between a Mott insulator and a charge density wave insulator, with an intermediate superfluid phase. Our results are relevant to the behavior of ultracold atoms in optical superlattices which are beginning to be studied experimentally.

Magnetic phase diagram of a frustrated ferrimagnetic ladder: Relation to the one-dimensional boson Hubbard model

We study the magnetic phase diagram of two coupled mixed-spin $(1,{1/2})$ Heisenberg chains as a function of the frustration parameter related to diagonal exchange couplings. The analysis is performed by using spin-wave series and exact numerical diagonalization techniques. The obtained phase diagram--containing the Luttinger liquid phase, the plateau phase with a magnetization per rung $M=1/2$, and the fully polarized phase--is closely related to the generic $(J/U,\mu/U)$ phase diagram of the one-dimensional boson Hubbard model.

Mott domains of bosons confined on optical lattices.

In the absence of a confining potential, the boson-Hubbard model exhibits a superfluid to Mott insulator quantum phase transition at commensurate fillings and strong coupling. We use quantum Monte Carlo simulations to study the ground state of the one-dimensional bosonic Hubbard model in a trap. Some, but not all, aspects of the Mott insulating phase persist. Mott behavior occurs for a continuous range of incommensurate fillings, very different from the unconfined case, and the establishment of the Mott phase does not proceed via a traditional quantum phase transition. These results have important implications for interpreting experiments on ultracold atoms on optical lattices.

One-dimensional disordered bosonic Hubbard model: A density-matrix renormalization group study.

We use the density-matrix renormalization group to study the one-dimensional bosonic Hubbard model, with and without disorder. We obtain the gaps in all phases, certain correlation functions, and the superfluid density. A finite-size-scaling analysis enables us to obtain an accurate phase diagram and the {beta} function at the superfluid{endash}Mott insulator transition and the Kosterlitz-Thouless essential singularity in the pure case. We also obtain coupling constants used in effective field theories for this system. {copyright} {ital 1996 The American Physical Society.}

Bethe ansatz for the one-dimensional boson Hubbard model.

The Bethe ansatz (BA) for the one-dimensional boson Hubbard model is studied. Even though the model cannot be solved exactly by this method, it is argued that it gives an excellent approximation for densities \ensuremath{\rho}\ensuremath{\le}1. This claim is substantiated by a detailed study of the internal consistency of the BA solution, and by comparison with quantum Monte Carlo simulations.