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Physical review. B, Condensed matter

Phase diagram for a modified Harper model

Klaus Stefan Drese, Martin Holthaus

Published Jun 1, 1997• 9 citations
Publisher

Abstract

We study a modification of Harper's model that emerges when a modulation of the hopping integrals is locked to the modulation of the on-site energies, as in the case of ultracold atoms in strongly detuned bichromatic standing light waves. The modified model is self-dual, so that its phase diagram can be obtained analytically. In this phase diagram there exists an extended region that corresponds to critical states.

DOI
10.1103/physrevb.55.r14693

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We study a modification of Harper's model that emerges when a modulation of the hopping integrals is locked to the modulation of the on-site energies, as in the case of ultracold atoms in strongly detuned bichromatic standing light waves. The modified model is self-dual, so that its phase diagram can be obtained analytically. In this phase diagram there exists an extended region that corresponds to critical states.
We suggest the possibility to realize an optical quasicrystal with ultracold atoms in far-detuned, bichromatic standing light waves. If the optical potentials created by the individual light waves have sufficiently different strength, one obtains an atom-optical realization of Harper's model. This model exhibits a metal-insulator transition at a certain value of the site-to-site hopping integral. Since this hopping integral is effectively renormalized by an additional oscillating force, one can switch from the regime of extended states to the regime of localized states by varying the amplitude of that force.
Recently, it has become apparent that when the interactions between polar molecules in optical lattices become strong, the conventional description using the extended Hubbard model has to be modified by additional terms, in particular a density-dependent tunneling term. We investigate here the influence of this term on the ground-state phase diagrams of the two-dimensional extended Bose–Hubbard model. Using quantum Monte Carlo simulations, we investigate the changes of the superfluid, supersolid and phase-separated parameter regions in the phase diagram of the system. By studying the interplay of the density-dependent hopping with the usual on-site interaction U and nearest-neighbor repulsion V , we show that the ground-state phase diagrams differ significantly from those expected from the standard extended Bose–Hubbard model.
We use the Gutzwiller ansatz and analyze the phase diagram of the extended Bose-Hubbard Hamiltonian with on-site (UUU) and nearest-neighbor (VVV) repulsions. For ddd-dimensional hypercubic lattices, when 2dV<U2\mathit{dV}<U2dV<U, it is well known that the ground state alternates between the charge-density-wave (CDW) and Mott insulators, and the supersolid (SS) phase occupies small regions around the CDW insulators. However, when 2dV>U2\mathit{dV}>U2dV>U, in this Rapid Communication, we show that the ground state has only CDW insulators, and more importantly, the SS phase occupies a much larger region in the phase diagram, existing up to very large hopping values which could be orders of magnitude higher than that of the well-known case. In particular, the SS-superfluid phase boundary increases linearly as a function of hopping when $2\mathit{dV}\ensuremath{\gtrsim}1.5U$, for which the prospects of observing the SS phase with dipolar Bose gases loaded into optical lattices is much higher.
We demonstrate that all of the salient features of the Harper-Hofstadter model can be implemented with ultracold atoms trapped in a bichromatic ring-shaped lattice. Using realistic sinusoidal lattice potentials rather than assume the idealized tight-binding picture, we determine the optimal conditions necessary to realize the critical point where the spectrum becomes fractal, and we identify the nature and cause of the departures from the discrete model predictions. We also show that even with a commensurate ring with a few lattice sites, the Aubry-Andr\'e localization transition can be realized. Localized states that behave like edge states with energies that reside in the band gaps can be generated by introducing a surprisingly small local perturbation within the ring. Spectrum oscillation arising from complex coupling can be implemented by uniform rotation of the ring, but with certain significant differences that are explained.