Quantum Transport Theory of Strongly Correlated Matter

Abstract

Kubo formulas for electric and thermal magneto-conductivities are generally notoriously costly to compute in strong scattering regime where Boltzmann equation and Hall conductivity proxies exceed their validity. This seminar cover three recently developed approaches which can significantly simplify such calculations.1. Degeneracy-projected polarization (DPP) formulas for Hall-type conductivities, which reduce the Kubo formulas to on-shell expressions with significantly less matrix elements. The DPP formulas reduce to Berry curvature integral formulas for perfectly periodic models. 2. Continued fraction (CF) representation of dynamical longitudinal conductivities. The calculations produce a set of thermodynamic averages, which can be controllably extrapolated using their mathematical relations to low and high frequency conductivity asymptotics.3. Hall-type coefficients summation formulas, which are constructed from thermodynamic expectation values of static operators.The thermodynamic formulas (2 and 3) are derived in the operator Hilbert space formalism, which avoids the opacity and high computational cost of the Hamiltonian eigenspectrum. The coefficients can be computed d by well established imaginary-time Monte Carlo sampling, high temperature expansion, traces of operator products, and variational wavefunctions at low temperatures. The power of approaches 1–3 is demonstrated by their application to strongly interacting n models of lattice electrons and bosons. The calculations clarify the far-reaching influence of strong many-body interactions on metallic transport near Mott insulators. Future directions for these approaches are discussed.