arXiv subjects

D. Bergeron

Publications and source records attributed to D. Bergeron.

3 recordsLinked to original sources

arXiv2017

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

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.

cond-mat.str-el↗

arXiv2015

Maximum Entropy Analytic Continuation for Spectral Functions with Non-Positive Spectral Weight

Information about the pairing mechanism for superconductivity is contained in the spectral weight for the anomalous (Gorkov) Green function. In the most general case, this spectral weight can change sign on the positive real axis or even be complex in the presence of broken time-reversal symmetry. This renders impossible the direct analytic continuation with Maximum Entropy methods of numerical results obtained for the anomalous Green function either in Matsubara frequency or in imaginary time. Here we show that one can define auxiliary Green functions that allow one to extract the anomalous spectral weight in the most general multi-orbital spin-singlet or triplet cases with no particular symmetry. As a simple example, we treat the case of lead in Eliashberg theory: Maximum Entropy analytic continuation with auxiliary Green functions (MaxEntAux) allows us to recover spectral functions that change sign on the positive real axis. The approach can be extended to transport quantities.

cond-mat.supr-con↗

arXiv2012

Extended quantum criticality of low-dimensional superconductors near a spin-density-wave instability

We use the renormalization group method to study the normal state of quasi-one-dimensional superconductors nearby a spin-density-wave instability. On the basis of one-loop scattering amplitudes for the quasi-one-dimensional electron gas, the integration of the renormalization group equations for the two-loop single particle Matsubara self-energy leads to a nonFermi-liquid temperature downturn of the momentum-resolved quasi-particle weight over most part of the Fermi surface. The amplitude of the downturn correlates with the entire instability line for superconductivity, defining an extended quantum critical region of the phase diagram as a function of nesting deviations of the Fermi surface. One also extracts the downward renormalization of interchain hopping amplitudes at arbitrary low temperature in the normal phase. By means of analytical continuation of the Matsubara self-energy, one-particle spectral functions are obtained with respect to both energy and temperature and their anomalous features analyzed in connection with the sequence of instability lines of the phase diagram. The quasi-particle scattering rate is found to develop an unusual temperature dependence, which is best described by the superimposition of a linear and quadratic $T$ dependences. The nonFermi-liquid linear-$T$ component correlates with the temperature scale $T_c$ of the superconducting instability over an extended range of nesting deviations, whereas its anisotropy along the Fermi surface is predicted to parallel the momentum profile of a d-wave pairing gap on the Fermi surface. We examine the implications of our results for low dimensional unconventional superconductors, in particular the Bechgaard salts series of quasi-1D organic conductors, but also the pnictide and cuprate superconductors where several common features are observed.

cond-mat.str-el↗