Cluster Gutzwiller study of the Bose-Hubbard ladder: Ground-state phase diagram and many-body Landau-Zener dynamics

Abstract

We present a cluster Gutzwiller mean-field study for ground states and time-evolution dynamics in the Bose-Hubbard ladder (BHL), which can be realized by loading Bose atoms in double-well optical lattices. In our cluster mean-field approach, we treat each double-well unit of two lattice sites as a coherent whole for composing the cluster Gutzwiller ansatz, which may remain some residual correlations in each two-site unit. For a unbiased BHL, in addition to conventional superfluid phase and integer Mott insulator phases, we find that there are exotic fractional insulator phases if the inter-chain tunneling is much stronger than the intra-chain one. The fractional insulator phases can not be found by using a conventional mean-field treatment based upon the single-site Gutzwiller ansatz. For a biased BHL, we find there appear single-atom tunneling and interaction blockade if the system is dominated by the interplay between the on-site interaction and the inter-chain bias. In the many-body Landau-Zener process, in which the inter-chain bias is linearly swept from negative to positive or vice versa, our numerical results are qualitatively consistent with the experimental observation [Nat. Phys. 7, 61 (2011)]. Our cluster bosonic Gutzwiller treatment is of promising perspectives in exploring exotic quantum phases and time-evolution dynamics of bosonic particles in superlattices.

Quench dynamics of Rydberg-dressed bosons on two-dimensional square lattices

“…This has paved new ways to explore non-equilibrium dynamics in addition to static properties. Inspired by this, recent theoretical and experimental works have investigated Landau-Zener transition [35][36][37], Kibble-Zurek mechanism [38][39][40][41][42][43][44], transport [45][46][47], Higgs/Goldstone modes [48,49].…”

Cluster mean-field signature of entanglement entropy in bosonic superfluid-insulator transitions

“…In comparison with the exact diagonalization [15], which can only give phase crossovers, the calculation of EE via the cluster MF treatment may explore true phase transitions. As the cluster MF approach is a powerful tool for exploring most QPTs in various many-body quantum models (from Fermi-Hubbard model, Bose-Hubbard model to Heisenberg spin model) with different superlattice configurations (from doublewell lattices [34,[41][42][43][44][45], Kagomé lattices [35,36,39,46,47] to honeycomb lattices [48][49][50][51]), beyond extracting the signature of EE for bosonic SI transitions, we believe that our analysis can be easily extended to extract the signature of EE for other QPTs in quantum superlattice systems.…”

“…Therefore, it is impossible to extract EE via the conventional single-site MF approach. Fortunately, the cluster MF approach, or more generally, the composite boson MF theory [29], can reserve partial entanglement and have explored several new phases not found by the conventional single-site MF approach [30][31][32][33][34]. Can the cluster MF approach efficiently capture the signature of EE in the emerged QPTs?…”

Supersolid and pair correlations of the extended Jaynes-Cummings-Hubbard model on triangular lattices

“…The single-site MF has successfully predicted the SF-MI phase transition without long-range interaction (V =0) [35]. The cluster mean-field (CMF) will be more reasonable to predict the physics in the interaction systems (V =0) [36][37][38][39]. The basic idea is to divide the system into N c unit cells, and each unit cell contains nc sites.…”