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arXiv:1004.5531 · Physical Review A

Superfluid-insulator transitions in attractive Bose-Hubbard model with three-body constraint

Yu-Wen Lee, Min-Fong Yang

Published Jun 24, 2010• 29 citations
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Abstract

By means of the method of the effective potential, the phase transitions from the Mott insulating state to either the atomic or the dimer superfluid state in the three-body constrained attractive Bose lattice gas are analyzed. Because of the appearance of the Feshbach resonance coupling between the two kinds of order parameters in the derived Ginzburg-Landau function, it is found that the continuous Mott-insulator--superfluid transitions can be preempted by first-order ones. Since the employed approach can provide accurate predictions of phase boundaries in the strong coupling limit, where the dimer superfluid phase can emerge, our work sheds light on the search of this phase in real ultracold Bose gases in optical lattices.

DOI
10.1103/physreva.81.061604

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By means of the method of the effective potential, the phase transitions from the Mott insulating state to either the atomic or the dimer superfluid state in the three-body constrained attractive Bose lattice gas are analyzed. Because of the appearance of the Feshbach resonance coupling between the two kinds of order parameters in the derived Ginzburg-Landau function, it is found that the continuous Mott-insulator--superfluid transitions can be preempted by first-order ones. Since the employed approach can provide accurate predictions of phase boundaries in the strong coupling limit, where the dimer superfluid phase can emerge, our work sheds light on the search of this phase in real ultracold Bose gases in optical lattices.
The effect of nearest-neighbor repulsion on the ground-state phase diagrams of three-body constrained attractive Bose lattice gases is explored numerically. When the repulsion is turned on, in addition to the uniform Mott insulating state and two superfluid phases (the atomic and the dimer superfluids), a dimer checkerboard solid state appears at unit filling, where boson pairs form a solid with checkerboard structure. We find also that the first-order transitions between the uniform Mott insulating state and the atomic superfluid state can be turned into the continuous ones as the repulsion is increased. Moreover, the stability regions of the dimer superfluid phase can be extended to modest values of the hopping parameter by tuning the strength of the repulsion. Our conclusions hence shed light on the search of the dimer superfluid phase in real ultracold Bose gases in optical lattices.
By means of quantum Monte Carlo simulations implemented with a two-loop update scheme, the finite-temperature phase diagram of a three-body constrained attractive Bose lattice gas is investigated. The nature of the thermal phase transitions around the dimer superfluid and the atomic superfluid is unveiled. We find that the Z2{Z}_{2}Z2​ symmetry breaking transitions between these two superfluid phases are of first order even at nonzero temperatures. More interestingly, the thermal transition from the dimer superfluid to the normal fluid is found to be consistent with the Kosterlitz-Thouless type but giving an anomalous universal stiffness jump. It demonstrates that this transition is driven by unbinding of pairs of fractional vortices.
We analyze theoretically a spinor Bose gas loaded into a three-dimensional cubic optical lattice. In order to account for different superfluid phases of spin-1 bosons in the presence of an external magnetic field, we work out a Ginzburg-Landau theory for the underlying spin-1 Bose-Hubbard model. In particular at zero temperature, we determine both the Mott and the superfluid phases for the competition between the anti-ferromagnetic interaction and the linear Zeeman effect within the validity range of the Ginzburg-Landau theory. Moreover, we find that the phase transition between the superfluid and Mott insulator phases is of second order and that the transitions between the respective superfluid phases for anti-ferromagnetic interaction can be both of first and second order.
We examine the equilibrium properties of lattice bosons with attractive on-site interactions in the presence of a three-body hard-core constraint that stabilizes the system against collapse and gives rise to a dimer superfluid phase. Employing quantum Monte Carlo simulations, the ground state phase diagram of this system on the square lattice is analyzed. In particular, we study the quantum phase transition between the atomic and dimer superfluid regime and analyze the nature of the superfluid-insulator transitions. Evidence is provided for the existence of a tricritical point along the saturation transition line, where the transition changes from being first order to a continuous transition of the dilute Bose gas of holes. The Berzinskii-Kosterlitz-Thouless transition from the dimer superfluid to the normal fluid is found to be consistent with an anomalous stiffness jump, as expected from the unbinding of half-vortices.
We analyze theoretically the emergence of different superfluid phases of spin-1 bosons in a three-dimensional cubic optical lattice by generalizing the recently developed Ginzburg–Landau theory for the Bose–Hubbard model to a spinor Bose gas. In particular at zero temperature, our theory distinguishes within its validity range between various superfluid phases for an anti-ferromagnetic interaction with an external magnetic field. In addition, we determine that the superfluid–Mott insulator phase transition is of second order and that the transitions between the respective superfluid phases with anti-ferromagnetic interaction can be both of first and second order.
We analyze the ground-state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising-type transition from a conventional atomic superfluid to a dimer superfluid with vanishing atomic condensate. The study builds on an exact mapping of the constrained model to a theory of coupled bosons with polynomial interactions, proposed in a related paper [S. Diehl, M. Baranov, A. Daley, and P. Zoller, Phys. Rev. B 82, 064509 (2010).]. In this framework, we focus by analytical means on aspects of the phase diagram which are intimately connected to interactions, and are thus not accessible in a mean-field plus spin-wave approach. First, we determine shifts in the mean-field phase border, which are most pronounced in the low-density regime. Second, the investigation of the strong coupling limit reveals the existence of a ``continuous supersolid,'' which emerges as a consequence of enhanced symmetries in this regime. We discuss its experimental signatures. Third, we show that the Ising-type phase transition, driven first order via the competition of long-wavelength modes at generic fillings, terminates into a true Ising quantum critical point in the vicinity of half filling.