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arXiv:1501.05572 · Physical Review A

Conductivity of strongly correlated bosons in optical lattices in an Abelian synthetic magnetic field

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

Published Feb 24, 2014• 14 citations
arXivHTMLPDF

Abstract

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 $1/2$ and $1/3$ 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.

DOI
10.1103/physreva.89.023631

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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.
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.
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.
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.
Motivated by the recent progress in engineering artificial non-Abelian gauge fields for ultracold fermions in optical lattices, we investigate the time-reversal-invariant Hofstadter–Hubbard model. We include an additional staggered lattice potential and an artificial Rashba-type spin–orbit coupling term available in experiment. Without interactions, the system can be either a (semi)-metal, a normal or a topological insulator, and we present the non-Abelian generalization of the Hofstadter butterfly. Using a combination of real-space dynamical mean-field theory (RDMFT), analytical arguments, and Monte-Carlo simulations we study the effect of strong on-site interactions. We determine the interacting phase diagram, and discuss a scenario of an interaction-induced transition from a normal to a topological insulator. At half-filling and large interactions, the system is described by a quantum spin Hamiltonian, which exhibits exotic magnetic order due to the interplay of Rashba-type spin–orbit coupling and the artificial time-reversal-invariant magnetic field term. We determine the magnetic phase diagram: both for the itinerant model using RDMFT and for the corresponding spin model in the classical limit using Monte-Carlo simulations.
Motivated by the recent progress in engineering artificial non-Abelian gauge fields for ultracold fermions in optical lattices, we investigate the time-reversal-invariant Hofstadter–Hubbard model. We include an additional staggered lattice potential and an artificial Rashba-type spin–orbit coupling term available in experiment. Without interactions, the system can be either a (semi)-metal, a normal or a topological insulator, and we present the non-Abelian generalization of the Hofstadter butterfly. Using a combination of real-space dynamical mean-field theory (RDMFT), analytical arguments, and Monte-Carlo simulations we study the effect of strong on-site interactions. We determine the interacting phase diagram, and discuss a scenario of an interaction-induced transition from a normal to a topological insulator. At half-filling and large interactions, the system is described by a quantum spin Hamiltonian, which exhibits exotic magnetic order due to the interplay of Rashba-type spin–orbit coupling and the artificial time-reversal-invariant magnetic field term. We determine the magnetic phase diagram: both for the itinerant model using RDMFT and for the corresponding spin model in the classical limit using Monte-Carlo simulations.
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.