Fractional quantum Hall effect in optical lattices

In this research, we study the bosonic fractional quantum Hall (FQH) states in a system of ultracold bosons in a two-dimensional optical lattice in the presence of a synthetic magnetic field, described by the bosonic Harper–Hofstadter Hamiltonian. We use the cluster Gutzwiller mean-field and exact diagonalization techniques in our work. We obtain incompressible states as ground states at various filling factors similar to those of the FQH states. We focus in particular on the ν = 1/2 FQH state, and it is characterized by the two-point correlation function and the many-body Chern number. We further investigate the effect of dipolar interaction on the ν = 1/2 FQH state. We find that the dipolar interaction stabilizes the FQH state against the competing superfluid state

Exact-diagonalization method for soft-core bosons in optical lattices using hierarchical wavefunctions

In this work, we describe a new technique for numerical exact-diagonalization. The method is particularly suitable for cold bosonic atoms in optical lattices, in which multiple atoms can occupy a lattice site. We describe the use of the method for Bose-Hubbard model as an example, however, the method is general and can be applied to other lattice models. The proposed numerical technique focuses in detail on how to construct the basis states as a hierarchy of wavefunctions. Starting from single-site Fock states we construct the basis set in terms of row-states and cluster-states. This simplifies the application of constraints and calculation of the Hamiltonian matrix. Each step of the method can be parallelized to accelerate the computation. In addition, we have illustrated the computation of the spatial bipartite entanglement entropy in the correlated $\nu =1/2$ fractional quantum Hall state.Comment: 11 pages, 6 figures, Comments are most welcom

Staggered superfluid phases of dipolar bosons in two-dimensional square lattices

We study the quantum ground state of ultracold bosons in a two-dimensional square lattice. The bosons interact via the repulsive dipolar interactions and s-wave scattering. The dynamics is described by the extended Bose-Hubbard model including correlated hopping due to the dipolar interactions, the coefficients are found from the second quantized Hamiltonian using the Wannier expansion with realistic parameters. We determine the phase diagram using the Gutzwiller ansatz in the regime where the coefficients of the correlated hopping terms are negative and can interfere with the tunneling due to single-particle effects. We show that this interference gives rise to staggered superfluid and supersolid phases at vanishing kinetic energy, while we identify parameter regions at finite kinetic energy where the phases are incompressible. We compare the results with the phase diagram obtained with the cluster Gutzwiller approach and with the results found in one dimension using DMRG.Comment: version close to accepted in Phys. Rev.

Fine-grained domain counting and percolation analysis in 2D lattice systems with linked-lists

We present a fine-grained approach to identify clusters and perform percolation analysis in a 2D lattice system. In our approach, we develop an algorithm based on the linked-list data structure and the members of a cluster are nodes of a path. This path is mapped to a linked-list. This approach facilitates unique cluster labeling in a lattice with a single scan. We use the algorithm to determine the critical exponent in the quench dynamics from Mott Insulator to superfluid phase of bosons in 2D square optical lattices. The result obtained are consistent with the Kibble-Zurek mechanism. We also employ the algorithm to compute correlation lengths using definitions based on percolation theory. And, use it to identify the quantum critical point of the Bose Glass to superfluid transition in the disordered 2D square optical lattices. In addition, we also compute the critical exponent of the transition.Comment: Comments are most welcom