Answer to the Comments by H. P. Furth

Schmidt, G.

doi:10.1063/1.1706405

Cited by 31 publications

(55 citation statements)

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“…The generalized Hubbard model for the correlated system at hand, U = 0, in the non-equilibrium, Eq. (1), is numerically solved by means of a single-site Dynamical Mean Field Theory (DMFT) [38,39,40,41,42,43,44,45,46,47,48,49,50,51,52]. As explained in section 2.1 the expansion into Floquet modes in combination with the proper Keldysh description implements the external time dependent classical driving field, and couples it to the quantum many body system.…”

Section: Numerical Solutions: Dynamical Mean Field Theory In the Non-mentioning

confidence: 99%

“…It has been shown by [41] that the coupling of an electromagnetic field modulation to the onsite electronic density n i = c † i,σ c i,σ alone as an effect in the unlimited three dimensional translationally invariant system, can be gauged away. The effect for this type of coupling can be absorbed in an overall shift of the local potential while no additional dispersion is reflecting any induced functional dynamics of the system.…”

Section: Numerical Solutions: Dynamical Mean Field Theory In the Non-mentioning

confidence: 99%

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Evolution of Floquet topological quantum states in driven semiconductors

Lubatsch

Frank

2019

Eur. Phys. J. B

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Spatially uniform excitations can induce Floquet topological bandstructures within insulators which have equal characteristics to those of topological insulators. Going beyond we demonstrate in this article the evolution of Floquet topological quantum states for electromagnetically driven semiconductor bulk matter. We show the direct physical impact of the mathematical precision of the Floquet-Keldysh theory when we solve the driven system of a generalized Hubbard model with our framework of dynamical mean field theory (DMFT) in the non-equilibrium. We explain the physical consequences of the topological non-equilibrium effects in our results for correlated sysems with impact on optoelectronic applications. PACS. 71.10.-w Theories and models of many-electron systems -42.50.Hz Strong-field excitation of optical transitions in quantum systems; multi-photon processes; dynamic Stark shift -74.40+ Fluctuations -03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations -72.20.Ht High-field and nonlinear effects -89.75.-k Complex systems arXiv:1909.06922v1 [cond-mat.str-el]

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Section: Numerical Solutions: Dynamical Mean Field Theory In the Non-mentioning

confidence: 99%

Section: Numerical Solutions: Dynamical Mean Field Theory In the Non-mentioning

confidence: 99%

Evolution of Floquet topological quantum states in driven semiconductors

Lubatsch

Frank

2019

Eur. Phys. J. B

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“…Since the correlated lattice problem cannot be solved exactly we have to resort to an approximate scheme for calculating the self-energy Σ mn (ω, k || ). To this end, we use dynamical mean field theory [32][33][34] (DMFT) in its generalization to the periodically driven systems [13][14][15] . Within DMFT one neglects the k || -dependence of the self-energy, Σ mn (ω, k || ) ≈ Σ mn (ω), which allows one to calculate the approximate self-energy by the solution of a self consistently determined impurity-problem.…”

Section: Floquet Dmftmentioning

confidence: 99%

“…As we have seen above, the Floquet DMFT equations lead to a periodically time-dependent bath for the impurity problem which makes the latter hard to solve. In the literature, the Floquet-DMFT impurity problem is treated with low order perturbative expansions that work directly in the time domain 13,15,[36][37][38][39][40][41] , for example IPT. While this is numerically possible to carry out quite easily, the drawbacks of such solvers is of course their limitation to certain parameter regimes, in the interaction and/or hybridization strength, There is also a limited error control when such solvers are applied to new situations where no benchmarks are available.…”

Section: Floquet-diagonal Self Energymentioning

confidence: 99%

“…In order to explore properties of the system in a steady state with the period associated with the frequency of the electric field, we employ a Floquet plus DMFT [13][14][15] approach, whereby the recently introduced auxiliary master equation approach (AMEA) [16][17][18][19] is used as impurity solver. For simplicity, we restrict the self energy to be diagonal in the Floquet index.…”

Section: Introductionmentioning

confidence: 99%

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Impact ionization processes in the steady state of a driven Mott-insulating layer coupled to metallic leads

et al. 2018

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We study a simple model of photovoltaic energy harvesting across a Mott insulating gap consisting of a correlated layer connected to two metallic leads held at different chemical potentials. We address in particular the issue of impact ionization, whereby a particle photoexcited to the high-energy part of the upper Hubbard band uses its extra energy to produce a second particle-hole excitation. We find a drastic increase of the photocurrent upon entering the frequency regime where impact ionization is possible. At large values of the Mott gap, where impact ionization is energetically not allowed, we observe a suppression of the current and a piling up of charge in the high-energy part of the upper Hubbard band.Our study is based on a Floquet dynamical mean field theory treatment of the steady state with the so-called auxiliary master equation approach as impurity solver. We verify that an additional approximation, taking the self-energy diagonal in the Floquet indices, is appropriate for the parameter range we are considering.

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Solving real time evolution problems by constructing excitation operators

Wang

2012

AIP Advances

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In this paper we study the time evolution of an observable in the interacting fermion systems driven out of equilibrium. We present a method for solving the Heisenberg equations of motion by constructing excitation operators which are defined as the operators Â satisfying [ Ĥ , Â ] =λ Â . It is demonstrated how an excitation operator and its excitation energy λ can be calculated. By an appropriate supposition of the form of Â we turn the problem into the one of diagonalizing a series of matrices whose dimension depends linearly on the size of the system. We perform this method to calculate the evolution of the creation operator in a toy model Hamiltonian which is inspired by the Hubbard model and the nonequilibrium current through the single impurity Anderson model. This method is beyond the traditional perturbation theory in Keldysh-Green's function formalism, because the excitation energy λ is modified by the interaction and it will appear in the exponent in the function of time

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Answer to the Comments by H. P. Furth

Cited by 31 publications

References 1 publication

Evolution of Floquet topological quantum states in driven semiconductors

Evolution of Floquet topological quantum states in driven semiconductors

Impact ionization processes in the steady state of a driven Mott-insulating layer coupled to metallic leads

Solving real time evolution problems by constructing excitation operators

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