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Communications in Theoretical Physics

Bose—Hubbard Model in Checkerboard Superlattices with a Magnetic Field

Beibing Huang, Shaolong Wan

Published May 1, 2011• 1 citation
Publisher

Abstract

In this paper we investigate classical and quantum phase transitions of Bose—Hubbard model in checkerboard superlattices with a magnetic field at the mean-field level. By analyzing stability of normal state phase boundaries are obtained analytically for zero and finite temperature in a unified theoretical frame and easily extended to the situation without the magnetic field. All results illustrate that the introduction of the magnetic field enhances the stability of normal state and Mott insulator. In addition we also note that the critical hopping term presents an oscillating behavior inversely following the upper boundary of Hofstadter butterfly.

DOI
10.1088/0253-6102/55/5/14

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In this paper we investigate classical and quantum phase transitions of Bose—Hubbard model in checkerboard superlattices with a magnetic field at the mean-field level. By analyzing stability of normal state phase boundaries are obtained analytically for zero and finite temperature in a unified theoretical frame and easily extended to the situation without the magnetic field. All results illustrate that the introduction of the magnetic field enhances the stability of normal state and Mott insulator. In addition we also note that the critical hopping term presents an oscillating behavior inversely following the upper boundary of Hofstadter butterfly.
We study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid--alternating-Mott insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well.
We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean-field theory and find that the critical hopping strength (t∕U)c{(t∕U)}_{c}(t∕U)c​ increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean-field theory.
We investigate the ground-state and finite-temperature phase diagrams of the Bose-Hubbard model on a honeycomb superlattice. The interplay between the superlattice potential depth $\mathrm{\ensuremath{\Delta}}/t$ and the on-site interaction U/tU/tU/t gives rise to three distinct quantum phases at zero temperature: a superfluid phase, a Mott insulator I phase with unit filling on each site, and a Mott insulator II phase characterized by density imbalance---double occupancy on one sublattice and vacancy on the other at unit filling. The SF-MI transitions are found to be continuous, consistent with second-order quantum phase transitions. We further extend our analysis to finite temperatures within the superfluid regime. Our work highlights how a honeycomb superlattice geometry enables access to interaction- and lattice-modulation-driven quantum phases, including a density-imbalanced Mott insulator and a robust superfluid regime, offering concrete theoretical predictions for cold-atom experiments.
We investigate the effects of artificial magnetic fields on the ground-state of the two-dimensional Bose-Hubbard model. Using an asymmetric Bose-Hubbard model, we demonstrate that anisotropic hopping amplitude localizes bosons and enlarges the insulating and supersolid regions. We show these increases in the presence of artificial gauge fields up to the symmetric point of the field. Moreover, our calculations exhibit real-space modulations of the superfluid and supersolid phases. The bosonic current exhibits vortices in these phases, whose configurations depend on the commensuration between the magnetic field and the lattice. Although the magnetic field explicitly breaks the translational symmetry of the square lattice, this symmetry is restored in the Mott insulator phase. The local densities shows a checkerboard pattern in the density-wave and supersolid phases, regardless of the magnetic field strength. We investigate thermal fluctuations and demonstrate the robustness of insulating and supersolid phases up to temperatures comparable to the interaction energy, which supports the feasibility of observing such phases in experiments.
We consider effects of artificial magnetic fields on the ground state of the two-dimensional Bose-Hubbard model. Using an asymmetric Bose-Hubbard model, we demonstrate that the frustrating hopping energy localizes bosons and enlarges insulators and supersolid borders. We show these increments in the presence of artificial gauge fields up to a symmetric point of the field. Moreover, our calculations exhibit the real space modulations of the superfluid and supersolid phases. The bosonic current exhibits vortices in these phases, which their configurations depend on the commensuration between the magnetic field and the lattice. Although the magnetic field breaks the translational symmetry of the square lattice explicitly, this symmetry is restored in the Mott insulator phase. The filling factor exhibits a checkerboard pattern in the density-wave and supersolid phases, regardless of the magnetic field strength. We explore thermal fluctuations and demonstrate the robustness of insulators and SS phases up to temperatures comparable to the interaction energy, which support the feasibility of observing such phases in experiments.