Magnon heat transport in a 2D Mott insulator

Whether or not anomalies in the thermal conductivity from 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 specific heat $c_v$ of the half-filled 2D single-band Hubbard model using the numerically exact determinant quantum Monte Carlo algorithm and maximum entropy analytic continuation. Both $c_v$ and $kappa$ possess two peaks as a function of temperature, with scales related to the Hubbard interaction energy $U$ and spin superexchange energy $J$, respectively. At low temperatures where the charge degrees of freedom are gapped-out, our results for the contribution to both $c_v$ and the Drude weight associated with $kappa$ from the kinetic energy agree well with spin-wave theory for the spin-$frac{1}{2}$ antiferromagnetic Heisenberg model.

Numerical approaches for calculating the low-field dc Hall coefficient of the doped Hubbard model

Using determinant Quantum Monte Carlo, we compare three methods of evaluating the dc Hall coefficient $R_H$ of the Hubbard model: the direct measurement of the off-diagonal current-current correlator $chi_{xy}$ in a system coupled to a finite magnetic field (FF), $chi_{xy}^{text{FF}}$; the three-current linear response to an infinitesimal field as measured in the zero-field (ZF) Hubbard Hamiltonian, $chi_{xy}^{text{ZF}}$; and the leading order of the recurrent expansion $R_H^{(0)}$ in terms of thermodynamic susceptibilities. The two quantities $chi_{xy}^{text{FF}}$ and $chi_{xy}^{text{ZF}}$ can be compared directly in imaginary time. Proxies for $R_H$ constructed from the three-current correlator $chi_{xy}^{text{ZF}}$ can be determined under different simplifying assumptions and compared with $R_H^{(0)}$. We find these different quantities to be consistent with one another, validating previous conclusions about the close correspondence between Fermi surface topology and the sign of $R_H$, even for strongly correlated systems. These various quantities also provide a useful set of numerical tools for testing theoretical predictions about the full behavior of the Hall conductivity for strong correlations.