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Physical review. B./Physical review. B

Hall effect for interacting bosons in a lattice

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

Published Jun 25, 2018• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.97.214522

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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.
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.
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 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.
The anomalous Hall effect has had a profound influence on the understanding of many electronic topological materials but is much less studied in their bosonic counterparts. We predict that an intrinsic anomalous Hall effect exists in a recently realized bosonic chiral superfluid, a p-orbital Bose-Einstein condensate in a 2D hexagonal boron nitride optical lattice [Wang et al., Nature (London) 596, 227 (2021)NATUAS0028-083610.1038/s41586-021-03702-0]. We evaluate the frequency-dependent Hall conductivity within a multi-orbital Bose-Hubbard model that accurately captures the real experimental system. We find that in the high frequency limit, the Hall conductivity is determined by finite loop current correlations on the s-orbital residing sublattice, the latter a defining feature of the system's chirality. In the opposite limit, the dc Hall conductivity can trace its origin back to the noninteracting band Berry curvature at the condensation momentum, although the contribution from atomic interactions can be significant. We discuss available experimental probes to observe this intrinsic anomalous Hall effect at both zero and finite frequencies.
Quantum simulations are quickly becoming an indispensable tool for studying particle transport in correlated lattice models. One of the central topics in the study of transport is bad-metal behavior, characterized by the direct-current resistivity linear in temperature. In the fermionic Hubbard model, optical conductivity has been studied extensively, and a recent optical lattice experiment demonstrated bad-metal behavior in qualitative agreement with theory. Far less is known about transport in the bosonic Hubbard model. We investigate the conductivity in the Bose-Hubbard model and focus on the regime of strong interactions and high temperatures. We use numerically exact calculations for small lattice sizes. At weak tunneling, we find multiple peaks in the optical conductivity that stem from the Hubbard bands present in the many-body spectrum. This feature slowly washes out as the tunneling rate gets stronger. At high temperature, we identify a regime of TTT-linear resistivity, as expected. When the interactions are very strong, the leading inverse-temperature coefficient in conductivity is proportional to the tunneling amplitude. As the tunneling becomes stronger, this dependence takes quadratic form. At very strong coupling and half filling, we identify a separate linear resistivity regime at lower temperature, corresponding to the hard-core boson regime. Additionally, we unexpectedly observe that at half filling, in a big part of the phase diagram, conductivity is an increasing function of the coupling constant before it saturates at the hard-core-boson result. We explain this feature based on the analysis of the many-body energy spectrum and the contributions to conductivity of individual eigenstates of the system.