The Bose–Hubbard model with an effective off-site three-body tunneling, characterized by jumps towards one another, between one atom on a site and a pair atoms on the neighborhood site, is studied systematically on a one-dimensional (1D) lattice, by using the density matrix renormalization group method. The off-site trimer superfluid, condensing at momentum k = 0 , emerges in the softcore Bose–Hubbard model but it disappears in the hardcore Bose–Hubbard model. Our results numerically verify that the off-site trimer superfluid phase derived in the momentum space from [ Phys. Rev. A 81 , 011601(R) (2010)] is stable in the thermodynamic limit. The off-site trimer superfluid phase, the partially off-site trimer superfluid phase and the Mott insulator phase are found, as well as interesting phase transitions, such as the continuous or first-order phase transition from the trimer superfluid phase to the Mott insulator phase. Our results are helpful in realizing this novel off-site trimer superfluid phase by cold atom experiments.
Abstract We investigate the chaotic phase of the Bose–Hubbard model (Pausch et al 2021 Phys. Rev. Lett. 126 150601) in relation to the bosonic embedded random matrix ensemble, which mirrors the dominant few-body nature of many-particle interactions, and hence the Fock space sparsity of quantum many-body systems. The energy dependence of the chaotic regime is well described by the bosonic embedded ensemble, which also reproduces the Bose–Hubbard chaotic eigenvector features, quantified by the expectation value and eigenstate-to-eigenstate fluctuations of fractal dimensions. Despite this agreement, in terms of the fractal dimension distribution, these two models depart from each other and from the Gaussian orthogonal ensemble as Hilbert space grows. These results provide further evidence of a way to discriminate among different many-body Hamiltonians in the chaotic regime.
By generalizing the traditional single-site strong coupling expansion approach to a cluster one, we study the zero-temperature phase diagram of bosonic atoms in a trimerized Kagomé optical lattice. Some new features are present in this system. Due to the strong intra-trimer hopping interaction, there will be a new Mott insulator (MI), which is by definition incompressible but with a fractional filling per trimer. This is different from the traditional MI, which has an integral filling and originates only from the repulsive interaction between particles. We investigate the MI-to-superfluid transition and the nature of the fractional MI by calculating the critical exponents of phase transitions and the low-lying energy excitation spectra of quasiparticles (quasihole). We will show how the low-energy properties of this system can be understood qualitatively as a Bose-Hubbard model in triangular lattice from the point of view of the cluster strong coupling expansion. We also discuss how our results are related to experiment by studying the Bragg spectroscopy.
The chaotic phase of the tilted Bose-Hubbard model is identified as a function of energy, tilt strength, and particle interaction, from the eigenstate structure and the statistical features of the energy spectrum. Our analysis reveals that the chaotic phase of the bare Bose-Hubbard Hamiltonian can be enhanced by the presence of a moderate tilt. We further unveil the development and scaling of the chaotic regime from the perspective of a homogeneous density configuration typically used in cold atom experiments, providing a valuable phase diagram for future theoretical and experimental studies of this system.
We study the energy redistribution of interacting bosons in a ring-shaped quantum trimer as the coupling strength between neighboring sites of the corresponding Bose-Hubbard Hamiltonian undergoes a sudden change $\ensuremath{\delta}k$. Our analysis is based on a threefold approach combining linear response theory calculations as well as semiclassical and random matrix theory considerations. The $\ensuremath{\delta}k$ borders of applicability of each of these methods are identified by direct comparison with the exact quantum-mechanical results. We find that while the variance of the evolving quantum distribution shows a remarkable quantum-classical correspondence (QCC) for all $\ensuremath{\delta}k$ values, other moments exhibit this QCC only in the nonperturbative $\ensuremath{\delta}k$ regime.
By the photoassociation method, the trimer superfluid phase disappears in the one-dimensional state-dependent optical lattice if the ratio of the three-body interaction
W to the trimer tunneling
J is kept at
W/J=12 [W. Z. Zhang et al., Phys. Rev. A 90, 033622 (2014)]. To search for a trimer superfluid and trimer supersolid, we load the cold atom into two-dimensional lattices, whose coordinate number
z and kinetic energy $\ensuremath{-}zJ$ are respectively larger and lower than those of a one-dimensional lattice. Herein, we study the Bose-Hubbard model, which has an additional trimer tunneling term, a three-body interaction, and a next-nearest repulsion. The on-site trimer and trimer superfluid exist if the on-site two-body repulsion and three-body repulsion are smaller than some thresholds. With atom-tunneling terms, the phase transitions from trimer superfluid phase to both atom superfluid and atom supersolid phases are first order. With
W/J=12, in a one-dimensional lattice, the trimer superfluid phase does not exist at all. In contrast, the trimer superfluid phase exists in the lower density regions $0<\ensuremath{\rho}<2$ on the square lattice if
J is not very large. The trimer superfluid phase emerges in a wider range $0<\ensuremath{\rho}<3$ in the triangular lattice, or in the cubic lattice
(z=6). When the three-body interaction is turned on, a trimer supersolid phase emerges due to the classical degeneracy between the quasitrimer solid and the trimer solid being broken by the quantum fluctuation. The phase transitions from the trimer supersolid phase to the quasitrimer solid are first order and the phase transition from the trimer supersolid phase to trimer solid is continuous. Our results, obtained by mean-field and quantum Monte Carlo methods, will be helpful in realizing the trimer superfluid and supersolid by cold-atom experiments.