Quantum Monte Carlo calculations of the thermal conductivity of neutron star crusts

We use quantum Monte Carlo (QMC) techniques to calculate the static structure function $S(q)$ of a one-component ion lattice and use it to calculate the thermal conductivity κ of high-density solid matter expected in the neutron star crust. By making detailed comparisons with the results for the thermal conductivity obtained using standard techniques based on the one-phonon approximation (OPA) valid at low temperatures and the multiphonon harmonic approximation expected to be valid over a wide range of temperatures, we assess the temperature regime where $S(q)$ from the QMC can be used directly to calculate κ. We also compare the QMC results to those obtained using the classical Monte Carlo to quantitatively assess the magnitude of the quantum corrections. We found that quantum effects became relevant for the calculation of κ at a temperature of T0.30.16em0exΩP, where ΩP is the ion plasma frequency. At T0.10.16em0exΩP the quantum effects suppress κ by about 30%. The comparison with the results of the OPA indicates that dynamical information beyond the static structure is needed when T0.10.16em0exΩP. These quantitative comparisons help to establish QMC as a viable technique to calculate κ at moderate temperatures in the range of T=0.1--10.16em0exΩP of relevance to the study of accreting neutron stars. This finding is especially important because QMC is the only viable technique so far for calculating κ in multicomponent systems at low temperatures.