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arXiv:1304.4835 · Physical Review A

Criticality in the Bose-Hubbard model with three-body repulsion

Tomasz Sowiński, Ravindra W. Chhajlany, Omjyoti Dutta, Luca Tagliacozzo, Maciej Lewenstein

Published Oct 20, 2015• 16 citations
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Abstract

We study the attractive Bose-Hubbard model with a tunable, on-site three-body constraint. It is shown that the critical behavior of the system undergoing a phase transition from pair superfluid to superfluid at unit filling depends on the value of the three-body repulsion. In particular, we calculate critical exponents and the central charge governing the quantum phase transition.

DOI
10.1103/physreva.92.043615

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We study the attractive Bose-Hubbard model with a tunable, on-site three-body constraint. It is shown that the critical behavior of the system undergoing a phase transition from pair superfluid to superfluid at unit filling depends on the value of the three-body repulsion. In particular, we calculate critical exponents and the central charge governing the quantum phase transition.
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.
Abstract The extended Bose-Hubbard model with pure three-body local interactions is studied using the Density Matrix Renormalization Group approach. The shapes of the first two insulating lobes are discussed, and the values of the critical tunneling for which the system undergoes the quantum phase transition from insulating to superfluid phase are predicted. It is shown that stability of insulating phases, in contrast to the standard Bose-Hubbard model, is enhanced for larger fillings. It is also shown that, on the tip of the boundary of the insulating phase, the model under consideration belongs to the Berenzinskii-Kosterlitz-Thouless universality class.
1. Introduce quantum phase transition in the Bose-Hubbard model. 2. Emphasize vanishing energy scales and universality at the quantum critical point. 3. Introduce microscopic theories to describe the quantum phase transition, and explicitly show the vanishing of energy scales and the critical exponents. 4. Illustrate the emergent Lorentz symmetry and the Higgs mode at the quantum critical point of the Bose-Hubbard model with the particle-hole symmetry. 5. Discuss an experimental probe of the superfluid to the Mott insulator phase transition. 6. Show that the repulsive and the attractive Fermi-Hubbard models are related by the particle-hole symmetry. 7. Discuss the origin of antiferromagnetic order in the repulsive Fermi-Hubbard model at half-filling. 8. Introduce the enlarged SO(4)SO(4)SO(4) symmetry of the Fermi-Hubbard model at half-filling and zero spin imbalance and its physical concequence. 9. Introduce important unsolved challenge issues in the Fermi-Hubbard model. 10. Introduce the concept of eigenstate thermalization hypothesis and many-body localization as opposite to thermalization. 11. Introduce a few metrics to characterize the many-body localization. 12. Emphasize the role of entanglement entropy in characterizing quantum thermalization, and discuss how to measure entanglement entropy in ultracold atom systems.
We present a Monte Carlo study of the Bose glass to superfluid transition in the three-dimensional Bose-Hubbard model. Simulations are performed on the classical (3+1)(3+1)(3+1) dimensional link-current representation using the geometrical worm algorithm. Finite-size scaling analysis (on lattices as large as $16\ifmmode\times\else\texttimes\fi{}16\ifmmode\times\else\texttimes\fi{}16\ifmmode\times\else\texttimes\fi{}512$ sites) of the superfluid stiffness and the compressibility is consistent with a value of the dynamical critical exponent z=3z=3z=3, in agreement with existing scaling and renormalization group arguments that z=dz=dz=d. We find also a value of $\ensuremath{\nu}=0.70(12)$ for the correlation length exponent, satisfying the relation $\ensuremath{\nu}\ensuremath{\ge}2∕d$. However, a detailed study of the correlation functions, $C(r,\ensuremath{\tau})$, at the quantum critical point are not consistent with this value of zzz. We speculate that this discrepancy could be due to the fact that the correlation functions have not reached their true asymptotic behavior because of the relatively small spatial extent of the lattices used in the present study.
We obtain the complete quantum phase diagram of bosons on a two-leg ladder in the presence of attractive onsite and repulsive interchain nearest-neighbor interactions by imposing the onsite three-body constraint. We find three distinct phases; namely, the atomic superfluid (ASF), dimer superfluid (DSF), and the dimer rung insulator (DRI). In the absence of the interchain nearest-neighbor repulsion, the system exhibits a transition from the ASF to the DSF phase with increasing onsite attraction. However, the presence of the interchain nearest-neighbor repulsion stabilizes a gapped DRI phase, which is flanked by the DSF phase. We also obtain the phase diagram of the system for different values of the interchain nearest-neighbor interaction. By evaluating different order parameters, we obtain the complete phase diagram and the properties of the phase transitions using the self-consistent cluster mean-field theory.