Erratum: Spectral moment sum rules for strongly correlated electrons in time-dependent electric fields [Phys. Rev. B<b>73</b>, 075108 (2006)]

Turkowski, Volodymyr; Freericks, J. K.

doi:10.1103/physrevb.73.209902

Cited by 26 publications

(49 citation statements)

References 9 publications

(14 reference statements)

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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%

“…But the situation is not hopeless, as we quickly learn when we recall that a derivative of the Green's function with respect to t rel , brings down commutators of the creation and annihilation operators with the Hamiltonian. This analysis was carried out for both the first and second derivatives in order to determine the first two moments of the spectral function in [17]. It is also related to the fact that one can determine the expectation value of the Hamiltonian from the Green's function, because of the special form for the equation of motion of the Green's function and how it relates to the Hamiltonian.…”

Section: Nonequilibrium Formalism For the Many-body Problemmentioning

confidence: 99%

“…The accuracy of the calculations can be tested by comparing with moment sum rules for the lowest few moments of the Green's function, as detailed in [17]. The zeroth, first, and second moments of the local retarded Green's function can be found from the interaction, the chemical potential, and the fillings.…”

Section: Nonlinear Peltier Effectmentioning

confidence: 99%

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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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“…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%

Section: Nonequilibrium Formalism For the Many-body Problemmentioning

confidence: 99%

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Nonlinear Peltier effect and the nonequilibrium Jonson-Mahan theorem

Freericks¹,

Zlatic²

2006

Condens. Matter Phys.

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“…[40] Figure 2 shows the power delivered to the system by the pump pulse as well as the time-dependent total energy for the systems discussed in Fig deviations near time 0/t * (near the center of the pulse) where the power (and instantaneous current) changes rapidly. The offset simply reflects the initial energy in equilibrium.…”

mentioning

confidence: 99%

Electron-Mediated Relaxation Following Ultrafast Pumping of Strongly Correlated Materials: Model Evidence of a Correlation-Tuned Crossover between Thermal and Nonthermal States

et al. 2013

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We examine electron-electron mediated relaxation following excitation of a correlated system by an ultrafast electric field pump pulse. The results reveal a dichotomy in the temporal evolution as one tunes through a Mott metal-to-insulator transition: in the metallic regime relaxation can be characterized by evolution toward a steady-state electronic distribution well described by Fermi-Dirac statistics with an increased effective temperature; however, in the insulating regime this quasithermal paradigm breaks down with relaxation toward a nonthermal state with a more complicated electronic distribution that does not vary monotonically as a function of energy. We characterize the behavior by studying changes in the energy, photoemission response, and electronic distribution as functions of time. Qualitatively these results should be observable on short enough time scales that the electrons behave like an isolated system not in contact with additional degrees of freedom which can act as a thermal bath. Importantly, proper modeling used to analyze experimental findings should account for this behavior, especially when using strong driving fields or studying materials whose physics may manifest the effects of strong correlations. -6, 8-10, 12-18] On sufficiently short time scales, the initial recovery in these systems following an ultrafast pump pulse should be dominated by electron-electron scattering which on its own can drive the system into a new steady-state. Conventional analysis has been based on a quasithermal paradigm ("hot electron" or multi-temperature models); [19,20] however, there have been few tests of the validity of its underlying assumptions as a function of the strength of electronic correlations, [21] in particular as one tunes between the two regimes of a metal-to-insulator transition (MIT). [22] The MIT driven by electronic correlations usually is accompanied by a number of interesting ordering phenomena among the spin, charge, and orbital degrees of freedom in a material. An understanding of the key physics which leads to these emergent phases is often at the heart of pump-probe experiments in condensed matter systems, including high-T c cuprate superconductors, [23] nickelates, manganites, ruthenates, vanadates, [22] and even organic materials. [24][25][26] A number of experimental parameters can be used to tune across the MIT including doping and chemical substitution, pressure, and applied fields. What can be learned about the underlying physics leading to these phases as a function of these key parameters requires an understanding of the proper paradigm in which to ask the relevant questions and conduct analysis of experimental data. This is in addition to what can be learned by tuning the interaction parameters of model systems simulated in fermionic or bosonic cold atom mixtures and performing the experimental equivalent of time-resolved, pump-probe measurements. [27][28][29] In this Letter we discuss the evolution of an electronic system described in equilibrium by a simple Hamiltoni...

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“…However, if one numerically calculates the sum rule of higher-order moments, a deviation from the exact value may appear due to numerical derivative calculations from discretized points. 29 The possible deviation of the sum rule of higher order moment does not necessarily mean an inaccuracy of the Green function. It relates to the finite value of ∆t which may be not small enough for performing numerical derivative calculations.…”

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confidence: 99%

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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Erratum: Spectral moment sum rules for strongly correlated electrons in time-dependent electric fields [Phys. Rev. B73, 075108 (2006)]

Cited by 26 publications

References 9 publications

Nonlinear Peltier effect and the nonequilibrium Jonson-Mahan theorem

Nonlinear Peltier effect and the nonequilibrium Jonson-Mahan theorem

Electron-Mediated Relaxation Following Ultrafast Pumping of Strongly Correlated Materials: Model Evidence of a Correlation-Tuned Crossover between Thermal and Nonthermal States

Initial correlations in a nonequilibrium Falicov-Kimball model

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