Abstract
Strongly correlated systems are often associated with an underlying quantum critical point which governs their behavior in the finite temperature phase diagram. Their thermodynamical and transport properties arise from critical fluctuations and follow universal scaling laws. Here, we develop a microscopic theory of thermal transport in the quantum critical regime expressed in terms of a thermal sum rule and an effective scattering time. We explicitly compute the characteristic scaling functions in a quantum critical model system, the unitary Fermi gas. Moreover, we derive an exact thermal sum rule for heat and energy currents and evaluate it numerically using the nonperturbative Luttinger-Ward approach. For the thermal scattering times we find a simple quantum critical scaling form. Together, the sum rule and the scattering time determine the heat conductivity, thermal diffusivity, Prandtl number and sound diffusivity from high temperatures down into the quantum critical regime. The results provide a quantitative description of recent sound attenuation measurements in ultracold Fermi gases.
Highlights
Thermal transport caused by temperature gradients is ubiquitous in nature and typically occurs in a diffusive manner
Transport in the quantum critical regime (QCR) above the quantum critical point (QCP) may be analyzed in terms of critical fluctuations where decay and scattering rates typically scale linearly with temperature according to a Planckian law τ −1 ∝ kBT /h [5,6,7], a behavior which has been observed recently in the thermal diffusivity of near optimally doped cuprates
We have found that transport scattering times τκ and τη in the quantum critical regime follow a remarkably simple scaling law, which extends to the vicinity of the superfluid transition where pairing fluctuations become dominant
Summary
Thermal transport caused by temperature gradients is ubiquitous in nature and typically occurs in a diffusive manner. A calculation of the corresponding thermal conductivity κ and the associated thermal diffusion constant DT = κ/cp is often based on a kinetic theory description like the Boltzmann equation This works well, e.g., in metals at low temperature and allows one to understand the origin of universal laws like the Lorenz ratio L = κ/σ T → L0 = π 2kB2/3e2 between the thermal and the electrical conductivity σ as predicted by Wiedemann and Franz. Developing a microscopic theory for thermal transport in non-Fermi liquids has been a major challenge for many years. It has been approached using a number of different techniques like the memory function formalism [4]. Transport in the quantum critical regime (QCR) above the QCP may be analyzed in terms of critical fluctuations where decay and scattering rates typically scale linearly with temperature according to a Planckian law τ −1 ∝ kBT /h [5,6,7], a behavior which has been observed recently in the thermal diffusivity of near optimally doped cuprates
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
