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Description
The optical conductivity of systems with strong interactions is one of the most studied quantities experimentally, yet its computation from microscopic models remains challenging. In the context of linear response theory and of the Kubo formula for conductivity, this difficulty is embedded in the momentum and energy dependence of the electron self-energy and of the vertex corrections. One popular approach to treat the former is the use of Dynamical Mean-Field Theory (DMFT), the resulting self-energy however is purely local and the associated vertex correction in the conductivity vanishes. Multiple studies have shown that these vertex corrections are extremely relevant [1] in the two-dimensional Hubbard model, especially close to half-filling [2].
In this work, we present a study of the optical conductivity using Algorithmic Matsubara Integration [3] (AMI) which allows for the evaluation of diagrammatic series up to a fixed order. Contrary to other popular numerical techniques based on diagrammatic expansions such as Diagrammatic Quantum Monte-Carlo, the evaluation of the Matsubara summations is done analytically for every diagram. In particular, this allows us to evaluate the series directly on the real frequency axis, without relying on analytic continuation tools such as maximum entropy or Pade approximant.
The resulting optical conductivity is obtained at different temperatures at the leading order and its non-trivial frequency dependence is analyzed through the lens of an extended Drude model by introducing a frequency-dependent scattering time and mass enhancement. We recover the linear temperature dependence of the dc resistivity that has been observed in previous work [4,5]. Additionally, we show that the optical conductivity presents a regime of power-law scaling at intermediate frequencies. This scaling satisfies a "Planckian"-like behaviour similar to the one expected in the strange metal regime of non-fermi liquids [6] and reported in experiments [7]. We extend the analysis to include vertex corrections as well as study the effect of doping away from the half-filled case.
[1] A. Vranić et al., Physical Review B 102 (2020).
[2] A. Mu, Z. Sun, and A. J. Millis, arXiv e-prints (2022), arXiv:2205.09217.
[3] H. Elazab, B. McNiven, and J. LeBlanc, Computer Physics Communications 280, 108469 (2022).
[4] E. W. Huang, R. Sheppard, B. Moritz, and T. P. Devereaux, Science 366, 987 (2019).
[5] J. Vucicevic, S. Predin, and M. Ferrero, arXiv e-prints , arXiv:2208.04047 (2022).
[6] P. T. Dumitrescu, N. Wentzell, A. Georges, and O. Parcollet, Physical Review B 105 (2022).
[7] B. Michon, C. Berthod, C. W. Rischau, A. Ataei, L. Chen, S. Komiya, S. Ono, L. Taillefer, D. Van Der Marel, and A. Georges, arXiv:2205.04030v1.
