Magnon heat transport in a two-dimensional Mott insulator

TL;DR

This study investigates magnon contributions to thermal conductivity in a 2D Mott insulator using quantum Monte Carlo simulations, revealing peaks related to magnon excitations and scattering effects, shedding light on anomalies in insulating cuprates.

Contribution

It provides the first numerically exact analysis of thermal transport in a 2D Hubbard model, linking magnon behavior to thermal conductivity peaks in Mott insulators.

Findings

Thermal conductivity peaks align with magnon specific heat peaks at low temperatures.

Further cooling causes a sharp increase in thermal conductivity due to increased mean-free path.

Scattering effects such as phonons, disorder, and size limitations influence thermal transport.

Abstract

Whether or not anomalies in the thermal conductivity in insulating cuprates can be attributed to antiferromagnetic order and magnons in a 2D Mott insulator remains an intriguing open question. To shed light on this issue, we investigate the thermal conductivity $\kappa$ and its relationship with the specific heat $c_v$ in the half-filled 2D single-band Hubbard model, using the numerically exact determinant quantum Monte Carlo algorithm and maximum entropy analytic continuation. At low temperatures where the charge degrees of freedom are gapped-out and $c_v$ exhibits a clear magnon peak, we observe that thermal conductivity $\kappa$ also tends to form a peak at similar temperatures. Reducing temperature further produces a sharp upturn in $\kappa$, associated with an increasing mean-free path. We identify this as the high-temperature side of the anomalous peak in insulating cuprates, where the mean-free path eventually is cut-off by other scattering effects, including phonons, disorder, and physical size. Different scattering effects in our model are identified and analyzed in the thermal diffusivity.