10 research outputs found
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 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