Conductivity of lattice bosons at high temperatures

TL;DR

This paper investigates high-temperature conductivity in the Bose-Hubbard model, revealing regimes of linear resistivity, spectral features, and the impact of interaction strength, using numerically exact small-lattice calculations.

Contribution

It provides the first detailed analysis of bosonic lattice conductivity at high temperatures, identifying new spectral and transport regimes and their dependence on interaction and tunneling.

Findings

Identification of T-linear resistivity at high temperature.

Observation of multiple peaks in optical conductivity at weak tunneling.

Discovery of a quadratic dependence of inverse-temperature coefficient on tunneling at strong interactions.

Abstract

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 the bad-metal behavior, characterized by the direct current (dc) resistivity linear in temperature. In the fermionic Hubbard model, optical conductivity has been studied extensively, and a recent optical lattice experiment has 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 $T$-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.