Computing Transport Coefficients of Many-Body Hamiltonians by Equilibrium Averages*

DC transport coefficients of most strongly interacting Hamiltonians demand insurmountable computational challenges, e.g. large system sizes, long real-time evolution, and poorly controlled analytic continuation of quantum Monte Carlo data. In contrast, continued fractions expansions and the use of our new formulas for Hall-type resistivities, require only computations of equilbrium averages. These are amenable to well controlled methods, e.g. imaginary-time quantum Monte Carlo, high temperature series, and variational wavefunctions. We review continued fractions dynamical conductivity and Hall and Thermal Hall coeffiicents calculations for the Bose and Fermi Hubbard models, and the disordered Heisenberg chain.