One-dimensional Bose-Hubbard model with pure three-body interactions

Sowiński, Tomasz

doi:10.2478/s11534-014-0481-8

Cited by 7 publications

(6 citation statements)

References 31 publications

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“…Finally, it is worth noting that the seemingly exotic version of the model ( 79) with a vanishing two-body term U = 0 has also been discussed in detail in Silva-Valencia and Souza (2012), Sowiński (2014), where the one-dimensional case has been addressed using DMRG calculations. For that model, the first insulating lobe for ρ = 1 vanishes and the stability of higher Mott lobes increases with increasing filling ρ.…”

Section: Bose-hubbard Models With Local Three-body Interactionmentioning

confidence: 94%

Non-standard Hubbard models in optical lattices: a review

et al. 2015

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Originally, the Hubbard model was derived for describing the behavior of strongly correlated electrons in solids. However, for over a decade now, variations of it have also routinely been implemented with ultracold atoms in optical lattices, allowing their study in a clean, essentially defect-free environment. Here, we review some of the vast literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After giving an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so-called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighbor sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation for the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, the effects related to higher Bloch bands also become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis, Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher p orbitals, as well as models that dynamically couple spin and orbital degrees of freedom. Finally, we review mean-field nonlinear Schrödinger models of the Salerno type that share with the non-standard Hubbard models nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of consideration. We conclude by listing some open problems, to be addressed in the future.

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Section: Bose-hubbard Models With Local Three-body Interactionmentioning

confidence: 94%

Non-standard Hubbard models in optical lattices: a review

et al. 2015

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“…These transformations lead to an effective phase model with 11) and exact expressions for the two coefficients…”

Section: Methodsmentioning

confidence: 99%

“…(20) and (ii) single and pair condensate order parameters in the full version (11). The single hopping is t/U = 0.085 and the chemical potential is µ/U = 1.5.…”

Section: Methodsmentioning

confidence: 99%

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Pairing Mechanism at Finite Temperatures in Bosonic Systems

Krzywicka

Polak

2023

Acta Phys. Pol. A

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The pure Bose-Hubbard model, a staple of optical lattice-related research that describes bosonic condensation, is examined at finite temperatures. Advanced analytical methods are used, most importantly path integrals and quantum rotors. A first-order trace approximation is commonly applied while integrating over bosonic fields to obtain a phase-only model. Here, a second-order trace approximation is considered instead. This extension leads to an effective phase model with two types of superfluid, i.e., standard Bose-Einstein condensation and additional temperature-driven bosonic pair condensation. This effective model is further treated with a self-consistent harmonic approximation in order to compare the two superfluids. This analysis shows that the pairing mechanism strengthens the condensate phase at finite temperatures.

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“…The non-trivial effect of the three-body Interaction, W , on the Second MI Lobe a typical phase diagram of the model variation with W/U = 1 shows that the BKT point for this lobe for W/U = 0 is at t/U = 0.3 while the BKT point for W/U = 1 is located at t/U = 0.38. [18,17,16,19].…”

Section: Bose-hubbard Model With Three-body On-site Interactionmentioning

confidence: 99%

Emergent Phases in an Extended Bose-Hubbard Model with Three-body On-site Interaction

Otobrise,

Adegoke

2020

Preprint

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We study the Extended Bose-Hubbard Model with a three-body onsite interaction. Using an exact diagonalization method and a variational Matrix Product States algorithm, Alps mps-optim, we compute and analyse the energy charge gap and finite system correlation functions to obtain the phase boundaries and determine the phases and phase transitions of the model. For V U = 0.6 and W U = 0, we show the emergence of the Haldane insulator (HI) phase at the tip of the ρ = 1 charge density wave (CDW) lobe and for V U = 0.6 and W U = 1, we show the emergence of the supersolid (SS) phase at the tip of the ρ = 1/2 charge density wave (CDW) lobe. We also show that the effect of the inclusion of both the three-body onsite and nearest neighbor interactions on the phase diagram of the model for filling factor ρ = 2 is to stabilize the Mott insulator (MI) phase such that the system remains in the MI phase for all values of V U .

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One-dimensional Bose-Hubbard model with pure three-body interactions

Cited by 7 publications

References 31 publications

Non-standard Hubbard models in optical lattices: a review

Non-standard Hubbard models in optical lattices: a review

Pairing Mechanism at Finite Temperatures in Bosonic Systems

Emergent Phases in an Extended Bose-Hubbard Model with Three-body On-site Interaction

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