Bosonic quantum Hall states in single-layer two-dimensional optical lattices

Abstract

Quantum Hall (QH) states of two dimensional (2D) single layer optical lattices are examined using Bose-Hubbard model (BHM) in presence of artificial gauge field. We study the QH states of both the homogeneous and inhomogeneous systems. For the homogeneous case we use cluster Gutzwiller mean-field (CGMF) theory with cluster sizes ranging from 2 × 2 to 5 × 5. We, then, consider the inhomogeneous case, which is relevant to experimental realization. In this case, we use CGMF and exact diagonalization (ED). The ED studies are using lattice sizes ranging from 3 × 3 to 4 × 12. Our results show that the geometries of the QH states are sensitive to the magnetic flux α and cluster sizes. For homogeneous system, among various combinations of 1/5 α 1/2 and filling factor ν, only the QH state of α = 1/4 with ν = 1/2, 1, 3/2 and 2 occur as ground states. For other combinations, the competing superfluid (SF) state is the ground state and QH state is metastable. For BHM with envelope potential, all the QH states observed in homogeneous system exist for box potentials, but none for the harmonic potential. The QH states also persist for very shallow Gaussian envelope potential. As a possible experimental signature we study the two-point correlations of the QH and SF states.

Charge and statistics of lattice quasiholes from density measurements: A tree tensor network study

“…(1) -see for instance Refs. [72][73][74]. In this respect, superimposing an additional harmonic confinement to the lattice further enriches an already complicated scenario.…”

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

“…We perform self-consistent calculation of φ p,q till the desired convergence is obtained. The details of using this method in our computations are given in our previous works [30,[38][39][40][41][42][43].…”

Quantum Hall States for $$\alpha = 1/3$$ α = 1 / 3 in Optical Lattices

“…First is the actual hopping term in the internal link of the cluster(δC) and the second term takes care of the boundary via mean fields. Our recent study [36] describes the decomposition of hopping term and CGMF method more clearly. After decomposition, the Hamiltonian for a single cluster(C) is expressed in the following waŷ…”

“…In contrast to these two phases, the QH states are incompressible states with zero order parameter and have incommensurate filling. Several previous works [17,18,[28][29][30][31][32][33][34][35][36] have theoretically explored the existence of FQH states in OLs using BHM with synthetic magnetic fields, the bosonic counterpart of the Harper-Hofstadter model [8,9]. These theoretical works have also examined the possible signatures of the FQH states.…”