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.
We use the mean-field method, the quantum Monte Carlo method and the density-matrix-renormalization-group method to study the trimer superfluid phase and the quantum phase diagram of the Bose-Hubbard model in a one-dimensional optical lattice, with an explicit trimer-tunneling term. Theoretically, we derive the explicit trimer hopping terms, such as ${a}_{i}^{3\ifmmode\dagger\else\textdagger\fi{}}{a}_{j}^{3}$, by the Schrieffer-Wolf transformation. In practice, the trimer superfluid described by these terms is driven by photoassociation. The phase transition between the trimer superfluid phase and other phases are also studied. Without the on-site interaction, the phase transition between the trimer superfluid phase and the Mott insulator phase is continuous. Turning on the on-site interaction, the phase transitions are first order with Mott insulators of atoms filling 1 and 2. With nonzero atom tunneling, the phase transition is first order from the atom superfluid to the trimer superfluid. In the trimer superfluid phase, the winding numbers can be divided by three without any remainder. The power-law decay exponent is
1/2 for the nondiagonal correlation ${a}_{i}^{\ifmmode\dagger\else\textdagger\fi{}3}{a}_{j}^{3}$, i.e., the same as the exponent of the correlation ${a}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{a}_{j}$ in hardcore bosons. The density-dependent atom-tunneling term ${n}_{i}^{2}{a}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{a}_{j}$ and pair-tunneling term ${n}_{i}{a}_{i}^{\ifmmode\dagger\else\textdagger\fi{}2}{a}_{j}^{2}$ are also studied. With these terms, the phase transition from the empty phase to atom superfluid is first order and different from the cases without the density-dependent terms. The effects of finite three-body interactions and finite temperatures are also studied. Our results will be helpful in realizing the trimer superfluid by a cold-atom experiment.
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.
We use the density-matrix renormalization group method to investigate ground-state and dynamic properties of the one-dimensional Bose-Hubbard model, the effective model of ultracold bosonic atoms in an optical lattice. For fixed maximum site occupancy n b = 5, we calculate the phase boundaries between the Mott insulator and the "superfluid" phase for the lowest two Mott lobes. We extract the Tomonaga-Luttinger parameter from the density-density correlation function and determine accurately the critical interaction strength for the Mott transition. For both phases, we study the momentum distribution function in the homogeneous system, and the particle distribution and quasi-momentum distribution functions in a parabolic trap. With our zero-temperature method we determine the photoemission spectra in the Mott insulator and in the "superfluid" phase of the one-dimensional Bose-Hubbard model. In the insulator, the Mott gap separates the quasi-particle and quasi-hole dispersions. In the "superfluid" phase the spectral weight is concentrated around zero momentum.
The Mott-insulator--superfluid transition for ultracold bosonic atoms in an optical lattice has been extensively studied in the framework of the Bose-Hubbard model with two-body on-site interactions. In this paper, we analyze the additional effect of the three-body on-site interactions on this phase transition in an optical lattice and the transitions between the various phases that arise in an optical superlattice. Using the mean-field theory and the density matrix renormalization group method, we find the phase diagrams depicting the relationships between various physical quantities in an optical lattice and superlattice. We also propose a possible experimental signature to observe the on-site three-body interactions.
We study the one-dimensional Bose-Hubbard model describing the superfluid-Mott insulator quantum phase transition of cold atoms in optical lattices. We show that derivatives of the variance of the on-site atom number occupation, computed with respect to the parameter driving the transition, have extrema that are located off the critical point even in the thermodynamic limit. We discuss whether such extrema provide solid evidence of the quantum Berezinskii-Kosterlitz-Thouless transition taking place in this system. The calculations are done for systems with the mean number of atoms per lattice site equal to either one or two. They also characterize the nearest-neighbor correlation function, which is typically discussed in the context of time-of-flight images of cold atoms.
The search and characterization of supersolid phases remain a central topic in condensed matter physics. Inspired by the experimental discovery of local superfluid and insulating phases in two-dimensional moiré optical lattices [Meng et al., Nature 615, 231 (2023)], we systematically explore the emergence of a local supersolid (
lSS) phase in a one-dimensional Bose-Hubbard model subjected to a moiré potential, using the density-matrix renormalization group method. We impose a maximum site occupation
nmax=2 to realize the soft-core boson constraint. In the absence of nearest-neighbor repulsion, we identify the conventional superfluid, local superfluid, Mott insulator, and moiré-induced insulator phases. When the nearest-neighbor repulsion is turned on, the
lSS phase emerges in the strong-moiré regime. This phase is uniquely characterized by three key signatures: (i) coexisting local staggered density order and local off-diagonal coherence within isolated moiré supercells; (ii) exponentially decaying global off-diagonal correlations; and (iii) a vanishing global structure factor in the thermodynamic limit, while the local structure factor remains finite. These features clearly distinguish the
lSS from the conventional global supersolid (SS) phase, which exhibits algebraic correlations and a finite global structure factor. Our results provide a complete microscopic picture of local quantum phases in moiré lattices and offer clear experimental observables for detecting
lSS states with ultracold atoms.