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arXiv:1701.00613 · Physical review. B./Physical review. B

Phase diagrams of the extended Bose-Hubbard model in one dimension by Monte-Carlo simulation with the help of a stochastic-series expansion

Keima Kawaki, Yoshihito Kuno, Ikuo Ichinose

Published May 1, 2017• 25 citations
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Abstract

In this paper, we study phase diagrams of the extended Bose-Hubbard model (EBHM) in one dimension by means of the quantum Monte-Carlo (QMC) simulation using the stochastic-series expansion (SSE). In the EBHM, there exists a nearest-neighbor repulsion as well as the on-site repulsion. In the SSE-QMC simulation, the highest particle number at each site, ${n}_{c}$, is also a controllable parameter, and we found that the phase diagrams depend on the value of ${n}_{c}$. It is shown that in addition to the Mott insulator, superfluid, density wave, the phase so-called Haldane insulator, and supersolid appear in the phase diagrams, and their locations in the phase diagrams are clarified.

DOI
10.1103/physrevb.95.195101

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In this paper, we study phase diagrams of the extended Bose-Hubbard model (EBHM) in one dimension by means of the quantum Monte-Carlo (QMC) simulation using the stochastic-series expansion (SSE). In the EBHM, there exists a nearest-neighbor repulsion as well as the on-site repulsion. In the SSE-QMC simulation, the highest particle number at each site, nc{n}_{c}nc​, is also a controllable parameter, and we found that the phase diagrams depend on the value of nc{n}_{c}nc​. It is shown that in addition to the Mott insulator, superfluid, density wave, the phase so-called Haldane insulator, and supersolid appear in the phase diagrams, and their locations in the phase diagrams are clarified.
In this paper, we study detailed phase diagrams of the extended Bose-Hubbard model (EBHM) in one dimension by means of the quantum Monte-Carlo (QMC) simulation using the stochastic-series expansion (SSE). In the EBHM, there exists a nearest-neighbor repulsion as well as the on-site repulsion. In the SSE-QMC simulation, the highest particle number at each site, ncn_cnc​, is also controllable parameter, and we found that the phase diagram depends on the value of ncn_cnc​. It is shown that in addition to the Mott insulator, superfluid, density wave, the phase so-called Haldane insulator and supersolid appear in the phase diagrams, and their locations in the phase diagrams are clarified.
We consider a one-dimensional Bose-Hubbard model (BHM) with on-site double-well potentials and study the effect of nearest-neighbor repulsion and cavity-mediated long-range interactions by calculating the ground-state phase diagrams with quantum Monte-Carlo simulations. We show that when the intra-well repulsion is as strong as the on-site repulsion a dimerized Mott insulator phase appears at the tip of the dimerized Density Wave phase for a density of one particle per double well. Furthermore, we find a dimerized Haldane insulator phase in the double-well BHM with nearest-neighbor interaction, which is identical to a dimerized BHM with repulsive interactions up to the third neighbor.
We consider a one-dimensional Bose-Hubbard model (BHM) with on-site double-well potentials and study the effect of nearest-neighbor repulsion and cavity-mediated long-range interactions by calculating the ground-state phase diagrams with quantum Monte Carlo simulations. We show that when the intrawell repulsion is as strong as the on-site repulsion, a dimerized Mott-insulator phase appears at the tip of the dimerized density-wave phase for a density of one particle per double well. Furthermore, we find a dimerized Haldane-insulator phase in the double-well BHM with nearest-neighbor interaction, which is identical to a dimerized BHM with repulsive interactions up to the third neighbor.
In this paper, we study atomic quantum simulations of (1+1)(1+1)(1+1)-dimensional((1+1)(1+1)(1+1)D) U(1) gauge-Higgs models (GHMs) defined on a lattice. We explain how U(1) lattice GHMs appear from an extended Bose-Hubbard model (EBHM) describing ultra-cold atoms with a nearest neighbor repulsion in a 1D optical lattice. We first study a phase diagram of the 1D EBHM at low fillings by means of a quantum Monte-Carlo(MC) simulation. Next, we study the EBHM at large fillings and also GHMs by the MC simulations in the path-integral formalism and show that there are four phases, i.e., the Higgs phase(superfluid), the confinement phase (Mott insulator), and phases corresponding to the density wave and the supersolid. With the obtained phase diagrams, we investigate the relationship between the two models. Finally, we study real-time dynamic of an electric flux in the GHMs by the Gross-Pitaevskii equations and the truncated Wigner approximation.
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 Monte Carlo 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.
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 VVV. 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 $\ensuremath{\mu}$-VVV phase diagram.