Thef-electron spectrum of the spinless Falicov-Kimball model in large dimensions

Brandt, U.; Urbánek, Miroslav

doi:10.1007/bf01318160

Cited by 45 publications

(75 citation statements)

References 7 publications

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“…We use the Kadanoff-Baym-Keldysh approach to calculate the real-time Green's function because there is no simple way of performing the analytical continuation of the Matsubara frequency Green's function to the real axis [7]. We are interested in the retarded Green's function, so we consider the greater Green's function for positive time t > 0…”

Section: Real-time Green's Functionsmentioning

confidence: 99%

“…The first representation (2.30) was originally used by Brandt and Urbanek [7] and improved by Zlatić et al [9] and Freericks, Turkowski and Zlatić [10] …”

Section: Real-time Green's Functionsmentioning

confidence: 99%

“…This problem was first investigated by Brandt and Urbanek [7] and by Janis [8]. The numerical approach of Brandt and Urbanek was extended by Zlatić et al [9] and Freericks, Turkowski and Zlatić [10][11][12] within the original Brandt-Urbanek framework.…”

Section: Introductionmentioning

confidence: 99%

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F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach

Shvaika¹,

Freericks²

2008

Condens. Matter Phys.

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We derive an alternative representation for the f -electron spectral function of the Falicov-Kimball model from the original one proposed by Brandt and Urbanek. In the new representation, all calculations are restricted to the real time axis, allowing us to go to arbitrarily low temperatures. The general formula for the retarded Green's function involves two determinants of continuous matrix operators that have the Toeplitz form. By employing the Wiener-Hopf sum equation approach and Szegö's theorem, we can derive exact analytic formulas for the large-time limits of the Green's function; we illustrate this for cases when the logarithm of characteristic function (which defines the continuous Toeplitz matrix) does and does not wind around the origin. We show how accurate these asymptotic formulas are to the exact solutions found from extrapolating matrix calculations to the zero discretization size limit.

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Section: Real-time Green's Functionsmentioning

confidence: 99%

“…The first representation (2.30) was originally used by Brandt and Urbanek [7] and improved by Zlatić et al [9] and Freericks, Turkowski and Zlatić [10] …”

Section: Real-time Green's Functionsmentioning

confidence: 99%

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F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach

Shvaika¹,

Freericks²

2008

Condens. Matter Phys.

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“…Their theoretical formulation evaluated the case of a spatially uniform, but time dependent scalar potential, which unfortunately does not correspond to any electric field. More recently, a generalization of the Brandt-Urbanek solution 8 for the localized electron spectral function allows for an exact numerical solution of the nonequilibrium problem for the Falicov-Kimball model 9 within the DMFT framework. The procedure works directly in time by discretizing the continuous matrix operators and solving the nonlinear equations by iterating matrix operations on the discretized operators.…”

Section: Introductionmentioning

confidence: 99%

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

Turkowski

Freericks

2006

Phys. Rev. B

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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.

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“…The formalism for solving the conduction-electron Green's function was worked out by Brandt and Mielsch [3]. Brandt and Urbanek [4] describe how to calculate the f -electron spectral function using the Keldysh technique to directly determine the greater Green's function (along the Keldysh contour) and then Fourier transforming to real frequency (see also [5] The contour runs from 0 to t, then back from t to 0 and finally goes along the imaginary axis down to −iβ. When we discretize the matrix operator over the Keldysh contour, we evaluate the integrals via a rectangular (midpoint) summation.…”

mentioning

confidence: 99%

f-Electron spectral function near a quantum critical point

Freericks

Turkowski

Zlatič

2005

Physica B: Condensed Matter

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We calculate the f -electron spectral function using a Keldysh formalism for the Falicov-Kimball model in infinite dimensions. We study the region close to the quantum critical point on both the hypercubic and Bethe lattices.Key words: f -electron, spectral function, Falicov-Kimball modelThe Falicov-Kimball model [1] involves conduction electrons, which are free to move through the lattice, and f -electrons which are immobile. The two electrons interact with each other by a Coulomb interaction (of strength U ) when they are located at the same lattice site. The Hamiltonian is (at half filling)where c † i (ci) creates (destroys) a conduction electron at site i, f † i (fi) creates (destroys) a localized electron at site i, and t * is the hopping integral [2]. The symbol Z represents the number of nearest neighbors, and ij denotes a sum over all nearest neighbor pairs. The formalism for solving the conduction-electron Green's function was worked out by Brandt and Mielsch [3]. Brandt and Urbanek [4] describe how to calculate the f -electron spectral function using the Keldysh technique to directly determine the greater Green's function (along the Keldysh contour) and then Fourier transforming to real frequency (see also The contour runs from 0 to t, then back from t to 0 and finally goes along the imaginary axis down to −iβ. When we discretize the matrix operator over the Keldysh contour, we evaluate the integrals via a rectangular (midpoint) summation. We typically use no more than 2500 time steps on the contour.of the formalism). The greater Green's function is defined to bewith f (t) = exp(itHimp)f exp(−itHimp) and the evolution operator is given byThe subscript imp denotes the use of the impurity Hamiltonian (no hopping) with the evolution operator corresponding to the dynamical mean field [3] λ(ω) (the dynamical mean field mimics the hopping of conduction electrons onto and off of a given site; it is adjusted so that the impurity conduction-electron Green's function equals the local lattice Green's function). The

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Thef-electron spectrum of the spinless Falicov-Kimball model in large dimensions

Cited by 45 publications

References 7 publications

F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach

F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach

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

f-Electron spectral function near a quantum critical point

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