Maximum entropy analytic continuation for frequency-dependent transport coefficients with non-positive spectral weight

Abstract

The computation of transport coefficients, even in linear response, is a major challenge for theoretical methods that rely on analytic continuation of correlations functions obtained numerically in Matsubara space. While maximum entropy methods can be used for certain correlation functions, this is not possible in general, important examples being the Seebeck, Hall, Nernst and Reggi-Leduc coefficients. Indeed, positivity of the spectral weight on the positive real-frequency axis is not guaranteed in these cases. The spectral weight can even be complex in the presence of broken time-reversal symmetry. Various workarounds, such as the neglect of vertex corrections or the study of the infinite frequency or Kelvin limits have been proposed. Here, we show that one can define auxiliary response functions that allow to extract the desired real-frequency susceptibilities from maximum entropy methods in the most general multiorbital cases with no particular symmetry. As a benchmark case, we study the longitudinal thermoelectric response and corresponding Onsager coefficient in the single-band two-dimensional Hubbard model treated with dynamical mean-field theory (DMFT) and continuous-time quantum Monte Carlo (CTQMC). We thereby extend to transport coefficients the maximum entropy analytic continuation with auxiliary functions (MaxEntAux method), developed for the study of the superconducting pairing dynamics of correlated materials.

12 pages, 8 figures

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• Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation
• The Wiedemann-Franz law in doped Mott insulators without quasiparticles
• Minimal Pole Representation and Controlled Analytic Continuation of Matsubara Response Functions
• Minimal pole representation and analytic continuation of matrix-valued correlation functions
• Stochastic pole expansion method
• Numerical approaches for calculating the low-field dc Hall coefficient of the doped Hubbard model
• Barycentric rational function approximation made simple: A fast analytic continuation method for Matsubara Green's functions
• Intrinsic Thermal Hall Effect in Mott Insulators