Time-Dependent Mean Field Theory for Quench Dynamics in Correlated Electron Systems

Schiró, Marco; Fabrizio, Michele

doi:10.1103/physrevlett.105.076401

Cited by 198 publications

(325 citation statements)

References 31 publications

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“…In several studies presented in the literature it was shown that a number of quantum isolated systems with short-range interactions reach a stationary state [17,18,20,21,30], while some fully-connected models [33,35,54] and some mean-field approximations to models with short-range interactions [55][56][57] keep a nonstationary behavior. For the isolated quantum Ising chain a stationary state is indeed reached after the quench and we will therefore focus on this relatively simple case.…”

Section: B Dynamic Correlations and Response Functionsmentioning

confidence: 99%

“…However, their asymptotic stationary state should nonetheless be described by the so-called generalized Gibbs ensemble (GGE) in which each conserved quantity is characterized by a generally different effective temperature [17][18][19][20][21][22][23]. On the other hand, other works [24][25][26][27][28][29][30][31][32][33][34][35] have shown (or at least argued) that this scenario could actually be significantly richer.…”

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Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

2012

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Fluctuation-dissipation relations, i.e., the relation between two-time correlation and linear response functions, were successfully used to search for signs of equilibration and to identify effective temperatures in the non-equilibrium behavior of a number of macroscopic classical and quantum systems in contact with thermal baths. Among the most relevant cases in which the effective temperatures thus defined were shown to have a thermodynamic meaning one finds the stationary dynamics of driven super-cooled liquids and vortex glasses, and the relaxation of glasses. Whether and under which conditions an effective thermal behavior can be found in quantum isolated many-body systems after a global quench is a question of current interest. We propose to study the possible emergence of thermal behavior long after the quench by studying fluctuation-dissipation relations in which (possibly time-or frequency-dependent) parameters replace the equilibrium temperature. If thermalization within the Gibbs ensemble eventually occurs these parameters should be constant and equal for all pairs of observables in "partial" or "mutual" equilibrium. We analyze these relations in the paradigmatic quantum system, i.e., the quantum Ising chain, in the stationary regime after a quench of the transverse field. The lack of thermalization to a Gibbs ensemble becomes apparent within this approach. Contents

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Section: B Dynamic Correlations and Response Functionsmentioning

confidence: 99%

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confidence: 99%

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

2012

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“…Again, in higher dimensions, appropriate approximations are necessary, such as a time-dependent Monte-Carlo method [52], time-dependent dynamical mean field theory [53][54][55][56][57], the Gutzwiller ansatz for fermions [58][59][60], the flow equation method [9,10,61,62], or effective quasi-particle methods [63].…”

Section: Introductionmentioning

confidence: 99%

Equilibration and prethermalization in the Bose-Hubbard and Fermi-Hubbard models

et al. 2014

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“…We now turn to the 2D square lattice. The spreading of correlations in dimension higher than one constitutes an almost unexplored land where only mean-field methods have been applied so far [21][22][23][24][25][26]. The latter are reliable only in the unphysical limits of large lattice connectivity or large internal "flavor" degeneracy.…”

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Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids

et al. 2014

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We study the spreading of density-density correlations in Bose-Hubbard models after a quench of the interaction strength, using time-dependent variational Monte Carlo simulations. It gives access to unprecedented long propagation times and to dimensions higher than one. In both one and two dimensions, we find ballistic lightcone spreading of correlations and extract accurate values of the light-cone velocity in the superfluid regime. We show that the spreading of correlations is generally supersonic, with a light-cone propagating faster than sound modes but slower than the maximum group velocity of density excitations, except at the Mott transition, where all the characteristic velocities are equal. Further, we show that in two dimensions the correlation spreading is highly anisotropic and presents nontrivial interference effects.

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Time-Dependent Mean Field Theory for Quench Dynamics in Correlated Electron Systems

Cited by 198 publications

References 31 publications

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

Equilibration and prethermalization in the Bose-Hubbard and Fermi-Hubbard models

Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids

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