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Register a new userTensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model
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We analyze real-time dynamics of the two-dimensional Bose-Hubbard model after a sudden quench starting from the Mott insulator by means of the two-dimensional tensor-network method. Calculated single-particle correlation functions are found to be in good agreement with a recent experiment [Y. Takasu {it et al.}, Sci. Adv. {bf 6}, eaba9255 (2020)], which cross validates the experiment and the numerical simulation. By estimating the phase and group velocities from the single-particle and density-density correlation functions, we predict how these velocities vary in the moderate interaction region, which will be useful for future experiments.
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We study the dynamical properties of a few bosons confined in an one-dimensional split hard wall trap with the interaction strength varying from the weakly to strongly repulsive regime. The system is initially prepared in one side of the double well by setting the barrier strength of the split trap to be infinity and then the barrier strength is suddenly changed to a finite value. Both exact diagonalization method and Bose-Hubbard model (BHM) approximation are used to study the dynamical evolution of the initial system. The exact results based on exact diagonaliztion verify the enhancement of correlated tunneling in the strongly interacting regime. Comparing results obtained by two different methods, we conclude that one-band BHM approximation can well describe the dynamics in the weakly interacting regime, but is not efficient to give quantitatively consistent results in the strongly interacting regime. Despite of the quantitative discrepancy, we validate that the form of correlated tunneling gives an important contribution to tunneling in the large interaction regime. To get a quantitative description for the dynamics of bosons in the strongly interacting regime, we find that a multi-band BHM approximation is necessary.
Bosonic lattice systems with non-trivial interactions represent an intriguing platform to study exotic phases of matter. Here, we study the effects of extended correlated hopping processes in a system of bosons trapped in a lattice geometry. The interplay between single particle tunneling terms, correlated hopping processes and on-site repulsion is studied by means of a combination of exact diagonalization, strong coupling expansion and cluster mean field theory. We identify a rich ground state phase diagram where, apart the usual Mott and superfluid states, superfluid phases with interesting clustering properties occur.
Ultracold atoms in optical lattices provide a unique opportunity to study Bose- Hubbard physics. In this work we show that by considering a spatially varying onsite interaction it is possible to manipulate the motion of excitations above the Mott phase in a Bose-Hubbard system. Specifically, we show that it is possible to engineer regimes where excitations will negatively refract, facilitating the construction of a flat lens.
An exciting development in the field of correlated systems is the possibility of realizing two-dimensional (2D) phases of quantum matter. For a systems of bosons, an example of strong correlations manifesting themselves in a 2D environment is provided by helium adsorbed on graphene. We construct the effective Bose-Hubbard model for this system which involves hard-core bosons $(Uapproxinfty)$, repulsive nearest-neighbor $(V>0)$ and small attractive $(V<0)$ next-nearest neighbor interactions. The mapping onto the Bose-Hubbard model is accomplished by a variety of many-body techniques which take into account the strong He-He correlations on the scale of the graphene lattice spacing. Unlike the case of dilute ultracold atoms where interactions are effectively point-like, the detailed microscopic form of the short range electrostatic and long range dispersion interactions in the helium-graphene system are crucial for the emergent Bose-Hubbard description. The result places the ground state of the first layer of $^4$He adsorbed on graphene deep in the commensurate solid phase with $1/3$ of the sites on the dual triangular lattice occupied. Because the parameters of the effective Bose-Hubbard model are very sensitive to the exact lattice structure, this opens up an avenue to tune quantum phase transitions in this solid-state system.
We address the effects of quenched disorder averaging in the time-evolution of systems of ultracold atoms in optical lattices in the presence of noise, imposed by of an environment. For bosonic systems governed by the Bose-Hubbard Hamiltonian, we quantify the response of disorder in Hamiltonian parameters in terms of physical observables, including bipartite entanglement in the ground state and report the existence of disorder-induced enhancement in weakly interacting cases. For systems of two-species fermions described by the Fermi-Hubbard Hamiltonian, we find similar results. In both cases, our dynamical calculations show no appreciable change in the effects of disorder from that of the initial state of the evolution. We explain our findings in terms the statistics of the disorder in the parameters and the behaviour of the observables with the parameters.
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