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Acta Physica Polonica A

Hall Conductivity of Strongly Interacting Bosons in Optical Lattice

K. Patucha, B. Grygiel, T. A. Zaleski

Published Jan 1, 2019• 0 citations
Publisher

Abstract

We study the Hall conductivity of ultra-cold bosonic atoms in optical lattice described by the Bose-Hubbard model.We use the quantum rotor approximation, which allows to describe lattices with non-zero Chern numbers.As examples of such systems we consider square lattice in a synthetic magnetic field as well as the Haldane model.We derive formula for the Hall conductivity, which strongly resembles the famous TKNN formula.We investigate the behavior of conductivity depending on temperature and model parameters.It appears that bosonic systems substantially differ from the fermionic ones, e.g. the presence of non-zero Hall conductivity is not directly related to non-zero value of the Chern number.

DOI
10.12693/aphyspola.135.74

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We study the Hall conductivity of ultra-cold bosonic atoms in optical lattice described by the Bose-Hubbard model.We use the quantum rotor approximation, which allows to describe lattices with non-zero Chern numbers.As examples of such systems we consider square lattice in a synthetic magnetic field as well as the Haldane model.We derive formula for the Hall conductivity, which strongly resembles the famous TKNN formula.We investigate the behavior of conductivity depending on temperature and model parameters.It appears that bosonic systems substantially differ from the fermionic ones, e.g. the presence of non-zero Hall conductivity is not directly related to non-zero value of the Chern number.
Tempted by the progress in measurements of transport properties of ultracold atomic system and by the experimental methods of creating artificial gauge potentials, we study the Hall conductivity of strongly interacting bosonic particles in a lattice. We use the Haldane-Bose-Hubbard model in the quantum rotor approach to obtain a dependence of the Hall conductivity on the temperature, frequency, and model parameters. We identify two types of excitations contributing to the Hall conductivity, a generation of particle-hole pairs and a coupling of the thermally excited quasiparticles to the external field. We observe a strong influence of the Berry curvature on the transverse transport.
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.
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 ultra-cold bosonic systems in optical lattice using quantum rotor approach to calculate the currentcurrent correlations, which provides the information about conductivity of the system.The method allows us to go beyond mean-field approximation and track the behavior of the real part of the conductivity along the phase transition between the Mott insulator and superfluid state for various geometries of the lattice.In the phaseordered state at zero temperature, a discrete ingredient appears resulting from the long-range coherence in the system.
We study the transport of cold fermionic atoms trapped in optical lattices in the presence of artificial Abelian or non-Abelian gauge potentials. Such external potentials can be created in optical lattices in which atom tunneling is laser assisted and described by commutative or non-commutative tunneling operators. We show that the Hall-like transverse conductivity of such systems is quantized by relating the transverse conductivity to topological invariants known as Chern numbers. We show that this quantization is robust in non-Abelian potentials. The different integer values of this conductivity are explicitly computed for a specific non-Abelian system which leads to a fractal phase diagram.
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.