Spectral moment sum rules for strongly correlated electrons in time-dependent electric fields

Abstract

We derive exact operator average expressions for the first two spectral moments of nonequilibrium Green's functions for the Falicov-Kimball model and the Hubbard model in the presence of a spatially uniform, time-dependent electric field. The moments are similar to the well-known moments in equilibrium, but we extend those results to systems in arbitrary time-dependent electric fields. Moment sum rules can be employed to estimate the accuracy of numerical calculations; we compare our theoretical results to numerical calculations for the nonequilibrium dynamical mean-field theory solution of the Falicov-Kimball model at half-filling.

Nonlinear Response of Strongly Correlated Materials to Large Electric Fields

“…These relations follow from the definition of the Green's functions and the anticommutation properties of the Fermionic operators. Similarly, the first two derivatives of the Green's functions, which are equivalent to the first two moments of the spectral function, (i.e., multiplying the density of states by one or two powers of frequency and then integrating over frequency) also can be determined exactly [11] . We use these results as a benchmark of the accuracy of the calculation.…”

Femtosecond Electron Imaging and Spectroscopy

“…The moment sum rules have already been derived in equilibrium (Kornilovitch, 2002;R€ osch et al, 2007), but they actually hold true, unchanged, in nonequilibrium as well (Turkowski & Freericks, 2006;Turkowski & Freericks, 2008;Freericks & Turkowski, 2009;Freericks et al, 2013). With these sum rules, one can understand how the electron-phonon interaction responds to nonequilibrium driving and how different response functions will behave.…”

“…Unlike in the case of the Hubbard or Falicov-Kimball model, where the sum rules relate to constants or simple expectation values (Turkowski & Freericks, 2006;Turkowski & Freericks, 2008;Freericks & Turkowski, 2009), one can see here that one needs to know things like the average phonon coordinate and its fluctuations in order to find the moments. We will discuss this further later in this paper.…”

Nonequilibrium spectral moment sum rules of the Holstein-Hubbard model

“…It is, of course, also necessary to examine the extent of agreement with the literature. Consistency of the zeroth − second order results is apparent throughout the relevant body of work [21][22][23][24][25][26][27]30 . For the 3rd order results, verification is more complicated as Eqs.…”