Interplay of charge and spin dynamics after an interaction quench in the Hubbard model

Abstract

We investigate the unitary dynamics following a sudden increase ∆U > 0 of repulsion in the paramagnetic sector of the half-filled Hubbard model on a Bethe lattice, by means of a variational approach that combines a Gutzwiller wavefunction with a partial Schrieffer-Wolff transformation, both defined through time-dependent variational parameters. Besides recovering at ∆Uc the known dynamical transition linked to the equilibrium Mott transition, we find pronounced dynamical anomaly at larger ∆U * > ∆Uc manifested in a singular behaviour of the long-time average of double occupancy. Although the real-time dynamics of the variational parameters at ∆U * strongly resembles the one at ∆Uc, careful frequency spectrum analysis suggests a dynamical crossover, instead of a dynamical transition, separating regions of a different behaviour of the spin-exchange.Pump-probe time-resolved spectroscopy is growing in importance as a tool for studying and manipulating correlated materials [1]. On one hand it gives access to new enlightening information about the dynamical properties of those materials, beyond reach of conventional spectroscopy. In addition, it provides a very efficient tool to drive phase transitions on ultra-short time scales, and concurrently investigate them in the time domain. There are cases where the photo-induced phases are actually those observed at thermal equilibrium upon heating, like for instance in photo-excited VO 2 [2]. This might be suggestive of a quasi-thermal pathway, though that is not generically the case, even in the same VO 2 [3]. Indeed, there are evidences of photo-induced hidden phases that are absent at equilibrium [4,5], as well as of remarkable non-thermal transient properties [6,7].At first sight it might seem unsurprising to observe non-thermal behaviour in correlated electron systems, which are complex materials with several competing phases and many actors playing a role. In reality, even the simplest among all models of correlated electrons, i.e. the single-band Hubbard model where the complexity of real materials is reduced just to the competition between the on-site repulsion U and the nearest-neighbour hopping t, shows puzzling and still controversial non-thermal behaviour. In a seminal work [8], Eckstein, Kollar and Werner discovered by time-dependent dynamical meanfield theory (t-DMFT) that the unitary evolution of the half-filled Hubbard model in an infinitely coordinated Bethe lattice after a sudden increase of the repulsion U from the initial U 0 = 0 to a final U f > 0 displays a sharp crossover at U f = U c , which, within the relativelyshort numerically-affordable simulation times, resembles a genuine dynamical transition. Such an interpretation was however contrasted by the observation that, if one assumes thermalisation, the temperature that corresponds to the energy supplied by the quench U = 0 → U c is well above the second-order critical endpoint of the Motttransition line in the T vs. U equilibrium phase diagram [8]. The same dynamical crossover was later found, stil...

Realistic estimates of superconducting properties for the cuprates: reciprocal-space diagrammatic expansion combined with variational approach

“…by using the t-J-U model in the same scheme [29]. Similar scenario and an alternative rationalization for the t-J-U-model extensions is provided by the recently proposed [59,60] adaptive canonical transformation as applied to the pure Hubbard Hamiltonian. A detailed analysis of such an involved model with the k-DE-GWF is beyond our present computational capabilities.…”

Resonant Thermalization of Periodically Driven Strongly Correlated Electrons

“…To gain an analytical insight into the Floquet prethermalization and the resonant thermalization we use a Floquet Schrieffer-Wolff transformation [67][68][69]. This conveniently describes the strong coupling regime, where doublon excitations are suppressed because of the large average interaction, thus preventing the system from absorbing energy unless the frequency of the drive is resonant with the doublon energy.…”

Universal collective modes from strong electronic correlations: Modified $1/\mathcal{N}_f$ theory with application to high-$T_c$ cuprates

“…78,79 An extension of this concept by means of adaptive canonical transformation has been proposed recently. 80,81 The VWF+1/N f and GA+RPA methods are similar in the sense that both are a dynamical extension of the variational wave function, but the realization of this goal is achieved in different manner. VWF+1/N f is a path-integral method applicable at finite-temperature, whereas GA+RPA is a T = 0 formalism based on the equations of motion for the density-matrix.…”