Strong-coupling perturbation theory for the extended Bose-Hubbard model

We studied all possible ground states, including supersolid (SS) phases and phase separations of hard-core-and soft-core-extended Bose-Hubbard models with fixed boson densities by using the Gutzwiller variational wave function and the linear programming method. We found that the phase diagram of the soft-core model depends strongly on its transfer integral. Furthermore, for a large transfer integral, we showed that an SS phase can be the ground state even below or at half filling against the phase separation. We also found that the density difference between nearest-neighbor sites, which indicates the density order of the SS phase, depends strongly on the boson density and transfer integral.

Section: Effect Of Improved Calculation On the Energy Of The Solidmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gutzwiller study of extended Hubbard models with fixed boson densities

Kimura

2011

“…The following fitting method is called chemical-potential fitting [31,38]. Here A(t) ≈ a + bt + ct 2 + dt 3 and B(t) ≈ α + βt + γt 2 + δt 3 are the regular functions of t. The parameter zν is the critical exponent in the model.…”

Section: Extrapolation Of Phase-boundary Curvesmentioning

confidence: 99%

Strong-coupling expansion for the spin-1 Bose-Hubbard model

Kimura

2013

In this study, we perform a strong-coupling expansion up to third order of the hopping parameter t for the spin-1 Bose-Hubbard model with antiferromagnetic interaction. As expected from previous studies, the Mott insulator phase is considerably more stable against the superfluid phase when filling with an even number of bosons than when filling with an odd number of bosons. The phaseboundary curves are consistent with the perturbative mean-field theory in the limit of infinite dimensions. The critical value of the hopping parameter t C at the peak of the Mott lobe depends on the antiferromagnetic interaction. This result indicates the reliability of the strong-coupling expansion when U 2 possesses large (intermediate) values for Mott lobe with an even (odd) number of bosons. Moreover, in order to improve our results, we apply a few extrapolation methods up to infinite order in t. The fitting results of the phase-boundary curves agree better with those of the perturbative mean-field approximation. In addition, the linear fit error of t C is very small for the strong antiferromagnetic interaction. * tkimura@kanagawa-u.ac.jp

“…(14)- (15) of Ref. [13] for the particle and hole gaps apply provided that we use t,U,μ,V nn →t,Ũ,μ,V a . Including the corrections from Eqs.…”

Section: Mott-superfluid Transitionmentioning

confidence: 99%

“…Iskin and Freericks [13] have calculated the phase diagram of a Bose-Hubbard model with nearest-neighbor interaction using a third-order strong coupling expansion. They calculated the energy of particle and hole defects in the Mott-insulating phase.…”

Section: Mott-superfluid Transitionmentioning

confidence: 99%

Variational polaron method for Bose-Bose mixtures

Benjamin

Demler

2014

We study degenerate mixtures of heavy bosons and light superfluid bosons using a variational polaron transformation. We consider the Mott-insulator-superfluid transition of the heavy species and find that at T = 0 interaction favors the superfluid phase of the heavy species. Our analytic results agree well with numerically exact quantum Monte Carlo simulations in two dimensions. We then show that in three dimensions the variational polaron transformation can be combined with a Gutzwiller approximation to give good results.