Transport properties of a spinon Fermi surface coupled to a U(1) gauge field

With the organic compound $\kappa \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\text{−}{\mathrm{Cu}}_2{\left(\mathrm{C}\mathrm{N}\right)}_3$ in mind, we consider a spin liquid system where a spinon Fermi surface is coupled to a U(1) gauge field. Using the nonequilibrium Green’s function formalism, we derive the quantum Boltzmann equation for this system. In this system, however, one cannot a priori assume the existence of Landau quasiparticles. We show that even without this assumption, one can still derive a linearized equation for a generalized distribution function. We show that the divergence of the effective mass and of the finite temperature self-energy do not enter these transport coefficients and thus they are well defined. Moreover, using a variational method, we calculate the temperature dependence of the spin resistivity and thermal conductivity of this system.