Cluster mean-field analysis on quantum dynamics in a planar array of hardcore Bose-Hubbard chains with interchain interactions

We theoretically investigate the real-time dynamics of a two-dimensional array of hardcore Bose-Hubbard chains with nearest-neighbor (NN) interchain interactions using the cluster mean-field (CMF) approach. Such a model is relevant to dipolar Bose gases in optical lattices. We apply the matrix-product state (MPS) method on one-dimensional (1D) chains, treating each chain as a cluster, where the intrachain NN interaction (V₁) and intrachain NN hopping (J) are handled exactly. The interchain NN interaction V₂ is treated at the mean-field level by replacing the interchain coupling with the self-consistently calculated mean field via an iterative procedure. Consequently, each 1D chain is simulated independently with a MPS subject to an effective mean-field potential that accounts for the interchain correlations, enabling a computationally efficient approximation of an array of interacting 1D chains.

We first map out the ground state phase diagram, where we have charge-density-wave (CDW), sliding Luttinger liquid (SLL), and collapse phases. The CDW-SLL phase boundary is identified from the vanishing difference between mean fields on odd and even sites, while the SLL-collapse boundary is located by the divergent behavior of the Luttinger parameter. The phase boundaries obtained using exact diagonalization (ED) and density matrix renormalization group (DMRG) methods are systematically compared for small chain lengths before extending the analysis to longer chains using DMRG. Using relevant interaction regimes identified from the phase diagram, we study the non-equilibrium dynamics of harmonically trapped chains in the SLL phase following a sudden trap shift in one chain and evaluate CMF accuracy in capturing the dynamics against exact calculations. For longer chains, the propagation of center-of-mass oscillations characterizes the SLL phase.