Quantum Monte Carlo (QMC) simulations and the Local Density Approximation (LDA) are used to map the constant particle number (canonical) trajectories of the Bose Hubbard Hamiltonian confined in a harmonic trap onto the $(μ/U,t/U)$ phase diagram of the uniform system. Generically, these curves do not intercept the tips of the Mott insulator (MI) lobes of the uniform system. This observation necessitates a clarification of the appropriate comparison between critical couplings obtained in experiments on trapped systems with those obtained in QMC simulations. The density profiles and visibility are also obtained along these trajectories. Density profiles from QMC in the confined case are compared with LDA results.
We establish the full groundstate phase diagram of disordered Bose-Hubbard model in two-dimensions at unity filling factor via quantum Monte Carlo simulations. Similarly to the three-dimensional case we observe extended superfluid regions persisting up to extremely large values of disorder and interaction strength which, however, have small superfluid fractions and thus low transition temperatures. In the vicinity of the superfluid--insulator transition of the pure system, we observe an unexpectedly weak---almost not resolvable---sensitivity of the critical interaction to the strength of (weak…
We analyze the classical and quantum dynamics of the driven dissipative Bose-Hubbard dimer. Under variation of the driving frequency, the classical system is shown to exhibit a bifurcation to the limit cycle, where its steady-state solution corresponds to periodic oscillation with the frequency unrelated to the driving frequency. This bifurcation is shown to lead to a peculiarity in the stationary single-particle density matrix of the quantum system. The case of the Bose-Hubbard trimer, where the discussed limit cycle bifurcates into a chaotic attractor, is briefly discussed.
The phase transitions at finite temperatures in the systems described by the Bose-Fermi-Hubbard model are investigated in this work in the framework of the selfconsistent random phase approximation. The case of the hard-core bosons is considered and pseudospin formalism is used. The density-density correlator is calculated in the random phase approximation and the possibilities of transitions from superfluid to supersolid phases are investigated. It is shown that the transitions between uniform and charge ordered phases can be of the second or the first order, depending on the system parameter…
The phase transitions in the Bose-Hubbard model are investigated. A single-particle Green's function is calculated in the random phase approximation and the formalism of the Hubbard operators is used. The regions of existence of the superfluid and Mott insulator phases are established and the $(μ,t)$ (the chemical potential -- transfer parameter) phase diagrams are built. The influence of temperature change on this transition is analyzed and the phase diagram in the $(T,μ)$ plane is constructed. The role of thermal activation of the ion hopping is investigated by taking into account the temper…
It is well known that using the conventional non-Hermitian but ${\cal PT}-$symmetric Bose-Hubbard Hamiltonian with real spectrum one can realize the Bose-Einstein condensation (BEC) process in an exceptional-point limit of order $N$. Such an exactly solvable simulation of the BEC-type phase transition is, unfortunately, incomplete because the standard version of the model only offers an extreme form of the limit characterized by a minimal geometric multiplicity $K=1$. In our paper we describe a rescaled and partitioned direct-sum modification of the linear version of the Bose-Hubbard model whi…
The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, Josephson junction arrays, and certain narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to study the supersolid part of the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice. We add disorder to the extended Bose-Hubbard model and find that the maximum critical temperature for the supersol…
Checkerboard Bose Hubbard Ladders using Transmon Arrays
Cornell University（康奈尔大学）；Google Quantum AI（谷歌量子人工智能）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）
We show that a finite Hubbard-phonon interacting system exhibits phonon BEC at sufficiently low temperature. We also have the gauge symmetry breaking for phonons. The key tools are a unitary transformation introduced by Arai and Hirokawa \protect{\cite{AH1}} and the Araki-Woods representation. This system is essentially the same as a free system or the van Hove model.
We study the zero temperature phase diagram of the disordered spin-1 Bose-Hubbard model in a 2-dimensional square lattice. To this aim, we use a mean field Gutzwiller ansatz and a probabilistic mean field perturbation theory. The spin interaction induces two different regimes corresponding to a ferromagnetic and antiferromagnetic order. In the ferromagnetic case, the introduction of disorder reproduces analogous features of the disordered scalar Bose-Hubbard model, consisting in the formation of a Bose glass phase between Mott insulator lobes. In the antiferromagnetic regime the phase diagram …
A strong coupling expansion, based on the Kato-Bloch perturbation theory, which has recently been proposed by Eckardt et al. [Phys. Rev. B 79, 195131] and Teichmann et al. [Phys. Rev. B 79, 224515] is implemented in order to study various aspects of the Bose-Hubbard and the Jaynes-Cummings lattice model. The approach, which allows to generate numerically all diagrams up to a desired order in the interaction strength is generalized for disordered systems and for the Jaynes-Cummings lattice model. Results for the Bose-Hubbard and the Jaynes-Cummings lattice model will be presented and compared w…
