Process-chain approach to the Bose-Hubbard model: Ground-state properties and phase diagram

Teichmann, Niklas; Hinrichs, Dennis; Holthaus, Martin; Eckardt, André

doi:10.1103/physrevb.79.224515

Cited by 52 publications

(63 citation statements)

References 37 publications

(89 reference statements)

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“…The method of the effective potential, developed in Refs. [79,80] as a combination of the mean-field theory and high-order SCE, as well as the nonperturbative renormalization group approach [330] lead to almost the same results which are considerably larger than (J/U ) c ≈ 0.0429 predicted by the standard mean-field theory [see Eq. (332)].…”

Section: Transition At Commensurate Fillingsmentioning

confidence: 84%

“…Higher-order calculations [251,252] and extrapolation to the infinite order [52,54,251,252] allow to reach perfect agreement with exact numerical results. QMC data for the filling factor n l = 1 in two [328] and three [204] dimensions were also reproduced with the high accuracy using the MEP [79,80,336], the B-DMFT [85,86], and the NPRG approach [330]. The POA gives also a high accuracy in three dimensions [331,332].…”

Section: Generic Transitionmentioning

confidence: 90%

“…(269)- (276) and Refs. [53,80]) and remains valid in higher dimensions. The second-order correlation functions decay also faster along the lattice diagonals than along the axes.…”

Section: Higher-order Correlation Functionsmentioning

confidence: 91%

“…In Refs. [79,80,270], the method was developed such that it became possible to do calculations in principle for arbitrary d and n. With the aid of the scaling theory it is possible to extrapolate to the infinite order of J/U [52,54,251]. Here we present analytical results for one-dimensional and isotropic hypercubic lattices of arbitrary dimensions.…”

Section: Extended Fermionizationmentioning

confidence: 99%

“…Attempts to correct the mean-field theory incorporating distance-dependent quantum correlations were undertaken by several authors. These include random phase approximation [76,77], cluster mean field [78], method of effective potential [79,80], dynamical mean-field theory (DMFT). The latter is probably the most successful approach but computationally quite demanding.…”

Section: Introductionmentioning

confidence: 99%

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Ultracold bosons with short-range interaction in regular optical lattices

2016

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During the last decade, many exciting phenomena have been experimentally observed and theoretically predicted for ultracold atoms in optical lattices. This paper reviews these rapid developments concentrating mainly on the theory. Different types of the bosonic systems in homogeneous lattices of different dimensions as well as in the presence of harmonic traps are considered. An overview of the theoretical methods used for these investigations as well as of the obtained results is given. Available experimental techniques are presented and discussed in connection with theoretical considerations. Eigenstates of the interacting bosons in homogeneous lattices and in the presence of harmonic confinement are analyzed. Their knowledge is essential for understanding of quantum phase transitions at zero and finite temperature.

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Section: Transition At Commensurate Fillingsmentioning

confidence: 84%

Section: Generic Transitionmentioning

confidence: 90%

“…(269)- (276) and Refs. [53,80]) and remains valid in higher dimensions. The second-order correlation functions decay also faster along the lattice diagonals than along the axes.…”

Section: Higher-order Correlation Functionsmentioning

confidence: 91%

Section: Extended Fermionizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ultracold bosons with short-range interaction in regular optical lattices

2016

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Perturbative calculation of critical exponents for the Bose–Hubbard model

2013

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We develop a strategy for calculating critical exponents for the Mott insulator-to-superfluid transition shown by the Bose-Hubbard model. Our approach is based on the field-theoretic concept of the effective potential, which provides a natural extension of the Landau theory of phase transitions to quantum critical phenomena. The coefficients of the Landau expansion of that effective potential are obtained by high-order perturbation theory. We counteract the divergency of the weak-coupling perturbation series by including the seldom considered Landau coefficient a6 into our analysis. Our preliminary results indicate that the critical exponents for both the condensate density and the superfluid density, as derived from the two-dimensional Bose-Hubbard model, deviate by less than 1% from the best known estimates computed so far for the three-dimensional XY universality class.

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Exact Solutions of an Extended Bose-Hubbard Model with E 2 Symmetry

et al. 2014

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An extended Bose-Hubbard (BH) model with number-dependent multi-site and infinite-range hopping is proposed, which, similar to the original BH model, describes a phase transition between the delocalized superfluid (SF) phase and localized Mott insulator (MI) phase. It is shown that this extended model with local Euclidean E2 symmetry is exactly solvable when on-site local potential or disorder is included, while the model without local potential or disorder is quasi-exactly solvable, which means only a part of the excited states including the ground state being exactly solvable. As applications of the exact solution for the ground state, phase diagram of the model in 1D without local potential and on-site disorder for filling factor ρ = 1 with M = 6 sites and that with M = 10 are obtained. The probabilities to detect n particles on a single site, Pn, for n = 0, 1, 2 as functions of the control parameter U/t in these two cases are also calculated. It is shown that the critical point in Pn and in the entanglement measure is away from that of the SF-MI transition determined in the phase analysis. It is also shown that the the model-independent entanglement measure is related with Pn, which, therefore, may be practically useful because Pn is measurable experimentally. [8,9], the density matrix renormalization group (DMRG) method [10][11][12] were used, from which ground state properties of the model have been studied extensively. Extensions of the model to include on-site disorder [1,13,14], longer ranged interactions [5,15], long-range hopping [16,17], infinite-range hopping [1,18], and pair-correlated hopping [19], etc. have also been made, in which, generally, more complicated phase structures emerge. Though many properties of the BH model have been known quite well from the above mentioned approximate calculations, it will be helpful if there is a similar model that can be solved exactly or quasi-exactly, because exactly and quasi-exactly solvable models may offer valuable insight and their solutions may be used as the basis in approximation methods.

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Process-chain approach to the Bose-Hubbard model: Ground-state properties and phase diagram

Cited by 52 publications

References 37 publications

Ultracold bosons with short-range interaction in regular optical lattices

Ultracold bosons with short-range interaction in regular optical lattices

Perturbative calculation of critical exponents for the Bose–Hubbard model

Exact Solutions of an Extended Bose-Hubbard Model with E 2 Symmetry

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