Nonlinear Response of Strongly Correlated Materials to Large Electric Fields

Freericks, J. K.; Turkowski, Volodymyr; Zlatič, V.

doi:10.1109/hpcmp-ugc.2006.52

Cited by 8 publications

(14 citation statements)

References 15 publications

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“…In the infinitedimensional case, the nonequilibrium properties of the Hubbard 13,14 and Falicov-Kimball 15 models were studied by using second-order perturbation theory in U within DMFT. Recently, the Falicov-Kimball model was solved exactly 16,17,18,19,20,21 in the presence of a homogeneous time-dependent electric field and in the case of a sudden change in the interaction strength U. 22 In these papers, the nonequilibrium generalization of the DMFT approximation was proposed, which allows one to obtain the numerical solution of the nonequilibrium problem for the Falicov-Kimball model.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium sum rules for the retarded self-energy of strongly correlated electrons

Turkowski

Freericks

2008

Phys. Rev. B

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We derive the first two moment sum rules of the conduction electron retarded self-energy for both the Falicov-Kimball model and the Hubbard model coupled to an external spatially uniform and time-dependent electric field (this derivation also extends the known nonequilibrium moment sum rules for the Green's functions to the third moment). These sum rules are used to further test the accuracy of nonequilibrium solutions to the many-body problem; for example, we illustrate how well the self-energy sum rules are satisfied for the Falicov-Kimball model in infinite dimensions and placed in a uniform electric field turned on at time t = 0. In general, the self-energy sum rules are satisfied to a significantly higher accuracy than the Green's functions sum rules.

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Section: Introductionmentioning

confidence: 99%

Nonequilibrium sum rules for the retarded self-energy of strongly correlated electrons

Turkowski

Freericks

2008

Phys. Rev. B

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“…In order to solve these equations we adopt the discretization method which was employed by Freericks et al in solving the NEDMFT equations. 20,27 We discretize the time variables with step ∆t for real time t and ∆τ for imaginary time τ . As a result the real time domain is divided into L points, and the imaginary time domain β is divided into M points.…”

Section: Self-consistent Perturbation Theorymentioning

confidence: 99%

“…Nevertheless, it was shown that the discretization approach is an efficient way to solve the nonequilibrium Green function equations. 20,27 Note that the Kadanoff-Baym-Wagner equations (12)- (16) …”

Section: Self-consistent Perturbation Theorymentioning

confidence: 99%

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Initial correlations in a nonequilibrium Falicov-Kimball model

Tran

2008

Phys. Rev. B

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The Keldysh boundary problem in a nonequilibrium Falicov-Kimball model in infinite dimensions is studied within the truncated and self-consistent perturbation theories, and the dynamical meanfield theory. Within the model the system is started in equilibrium, and later a uniform electric field is turned on. The Kadanoff-Baym-Wagner equations for the nonequilibrium Green functions are derived, and numerically solved. The contributions of initial correlations are studied by monitoring the system evolution. It is found that the initial correlations are essential for establishing full electron correlations of the system and independent on the starting time of preparing the system in equilibrium. By examining the contributions of the initial correlations to the electric current and the double occupation, we find that the contributions are small in relation to the total value of those physical quantities when the interaction is weak, and significantly increase when the interaction is strong. The neglect of initial correlations may cause artifacts in the nonequilibrium properties of the system, especially in the strong interaction case.

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“…Details of the formalism and of the numerical calculations will be given elsewhere (preliminary discussions can be found in [17,24]). But we can briefly describe the numerical procedure.…”

Section: Nonlinear Peltier Effectmentioning

confidence: 99%

Nonlinear Peltier effect and the nonequilibrium Jonson-Mahan theorem

Freericks¹,

Zlatic²

2006

Condens. Matter Phys.

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We generalize the many-body formalism for the Peltier effect to the nonlinear/nonequilibrium regime corresponding to large amplitude (spatially uniform but time-dependent) electric fields. We find a relationship between the expectation values for the charge current and for the part of the heat current that reduces to the Jonson-Mahan theorem in the linear-response regime. The nonlinear-response Peltier effect has an extra term in the heat current that is related to Joule heating (we are unable to fully analyze this term). The formalism holds in all dimensions and for arbitrary many-body systems that have local interactions. We illustrate it for the Falicov-Kimball, Hubbard, and periodic Anderson models.

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Nonlinear Response of Strongly Correlated Materials to Large Electric Fields

Cited by 8 publications

References 15 publications

Nonequilibrium sum rules for the retarded self-energy of strongly correlated electrons

Nonequilibrium sum rules for the retarded self-energy of strongly correlated electrons

Initial correlations in a nonequilibrium Falicov-Kimball model

Nonlinear Peltier effect and the nonequilibrium Jonson-Mahan theorem

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