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Acta Physica Polonica A

Conductivity of Strongly Correlated Bosons in the Simple Cubic Lattice - Magnetic Field and Hopping Anisotropy Effects

Adam S. Sajna, T. P. Polak, R. Micnas

Published Feb 1, 2015• 2 citations
Publisher

Abstract

We investigate optical conductivity in three dimensional system of bosons under strong magnetic eld.In particular, we consider Bose Hubbard model in the strongly correlated limit, where Mott insulator phase emerges.For chosen rational number of magnetic ux per cell we show that response of the system gains complex peaks behavior on the order of frequency corresponding to on-site boson repulsive interaction.Moreover, when anisotropy in hopping energy for the direction parallel to magnetic eld is tuned up, the non-monotonous behavior of the optical conductivity could appear.The obtained results can be experimentally probed in the system of ultracold atoms loaded on an optical lattice.

DOI
10.12693/aphyspola.127.448

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We investigate optical conductivity in three dimensional system of bosons under strong magnetic eld.In particular, we consider Bose Hubbard model in the strongly correlated limit, where Mott insulator phase emerges.For chosen rational number of magnetic ux per cell we show that response of the system gains complex peaks behavior on the order of frequency corresponding to on-site boson repulsive interaction.Moreover, when anisotropy in hopping energy for the direction parallel to magnetic eld is tuned up, the non-monotonous behavior of the optical conductivity could appear.The obtained results can be experimentally probed in the system of ultracold atoms loaded on an optical lattice.
We study dynamical conductivity of strongly correlated bosons loaded in an optical lattice with restricted geometry in which gauge fields are present. We show that dynamics influenced by the uniform synthetic magnetic field combined with layered lattice structures changes into rich insulator-metallic behavior in the strongly correlated regime. Especially, the amplitude of optical conductivity for a given frequency is a nonmonotonous function of the number of layers LLL. In particular, conductivity for frequency corresponding to on-site interaction energy can abruptly vanish for a special number of applied layers. Moreover, such an insulating behavior is stable in the whole range of parameters in the Mott phase. This robustness arises from the complex gaplike behavior or from Dirac-like physics reflected in the quasiparticle energy spectra. Furthermore we show that a large interlayer tunneling anisotropy destabilizes the absence of conducting state. We also investigate the critical conductivity on the Mott-insulator--superfluid phase boundary and show the correspondence between the number of Hofstadter subbands and the number of layers. The obtained results also reveal that the value of critical conductivity gradually goes to zero when a three-dimensional system is approached. The experimental setup for generation of layered optical lattices is also proposed.
Topological phase engineering of neutral bosons loaded in an optical lattice opens a new window for manipulating of transport phenomena in such systems. Exploiting the Bose-Hubbard model and using the magnetic Kubo formula proposed in this paper we show that the optical conductivity abruptly changes for different flux densities in the Mott phase. Especially, when the frequency of the applied field corresponds to the on-site boson interaction energy, we observe insulator or metallic behavior for a given Hofstadter spectrum. We also prove that for different synthetic magnetic-field configurations the critical conductivity at the tip of the lobe is nonuniversal and depends on the energy minima of the spectrum. In the case of 1/21/21/2 and 1/31/31/3 flux per plaquette, our results are in good agreement with those of the previous Monte Carlo study. Moreover, we show that for half magnetic flux through the cell the critical conductivity suddenly changes in the presence of a superlattice potential with uniaxial periodicity.
Motivated by the recent advancements in experimental techniques in the cold atomic systems, we study the dependence of the conductivity on momentum in a system of strongly interacting bosons in an optical lattice. By employing the quantum rotor approach to the Bose-Hubbard model we calculate the current-current correlation function and subsequently obtain the analytic formula for the momentum-dependent longitudinal conductivity. We analyze the behavior of the conductivity for the square and cubic lattices in both, the superfluid and Mott insulator phases. As a consequence of the particle-hole symmetry, the conductivity for a uniformly filled lattice in the superfluid phase exhibits a linear dependence for a surprisingly wide range of momenta around k=0\mathbf{k}=0k=0. This allows us to predict the value of the group velocity of the particle excitations. We also consider the impact of finite temperature and discover that it leads to an additional conductivity channel, which is aligned along the direction of the probe field and located within the energy gap.
Motivated by recent experimental progress on measuring various correlation functions in systems of ultracold atoms in optical lattices, we study properties of the Bose-Hubbard model in external synthetic magnetic field to describe transport phenomena in a multiband strongly interacting bosonic systems. We calculate the conductivity both in the Mott insulator and superfluid phases and investigate its two main contributions: intra- and interband. It appears that the interband processes dominate the transport properties by at least an order of magnitude. Also, at finite temperatures, additional transport channels appear due to coupling of the thermally excited particles or holes to the external field.
The Hubbard model underlies our understanding of strongly correlated materials. Whereas its standard form only comprises interactions between particles at the same lattice site, extending it to encompass long-range interactions is predicted to profoundly alter the quantum behavior of the system. We realize the extended Bose-Hubbard model for an ultracold gas of strongly magnetic erbium atoms in a three-dimensional optical lattice. Controlling the orientation of the atomic dipoles, we reveal the anisotropic character of the onsite interaction and hopping dynamics and their influence on the superfluid-to-Mott insulator quantum phase transition. Moreover, we observe nearest-neighbor interactions, a genuine consequence of the long-range nature of dipolar interactions. Our results lay the groundwork for future studies of exotic many-body quantum phases.
The Hubbard model underlies our understanding of strongly correlated materials. Whereas its standard form only comprises interactions between particles at the same lattice site, extending it to encompass long-range interactions is predicted to profoundly alter the quantum behavior of the system. We realize the extended Bose-Hubbard model for an ultracold gas of strongly magnetic erbium atoms in a three-dimensional optical lattice. Controlling the orientation of the atomic dipoles, we reveal the anisotropic character of the onsite interaction and hopping dynamics and their influence on the superfluid-to-Mott insulator quantum phase transition. Moreover, we observe nearest-neighbor interactions, a genuine consequence of the long-range nature of dipolar interactions. Our results lay the groundwork for future studies of exotic many-body quantum phases.