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

A. Reymbaut, A.-M. Gagnon, D. Bergeron, and A.-M. S. Tremblay
Phys. Rev. B 95, 121104(R) – Published 13 March 2017
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Abstract

The computation of transport coefficients, even in linear response, is a major challenge for theoretical methods that rely on analytic continuation of correlation 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 one 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 and continuous-time quantum Monte Carlo. We thereby extend the maximum entropy analytic continuation with auxiliary functions (MaxEntAux method), developed for the study of the superconducting pairing dynamics of correlated materials, to transport coefficients.

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  • Received 6 December 2016
  • Revised 17 February 2017

DOI:https://doi.org/10.1103/PhysRevB.95.121104

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Reymbaut1, A.-M. Gagnon1, D. Bergeron1, and A.-M. S. Tremblay1,2

  • 1Département de Physique and Institut Quantique, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1
  • 2Canadian Institute for Advanced Research, Toronto, Ontario, Canada M5G 1Z8

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Issue

Vol. 95, Iss. 12 — 15 March 2017

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