Crossover from adiabatic to sudden interaction quenches in the Hubbard model: prethermalization and non-equilibrium dynamics

Abstract

The recent experimental implementation of condensed matter models in optical lattices has motivated research on their nonequilibrium behavior. Predictions on the dynamics of superconductors following a sudden quench of the pairing interaction have been made based on the effective BCS Hamiltonian; however, their experimental verification requires the preparation of a suitable excited state of the Hubbard model along a twofold constraint: (i) a sufficiently nonadiabatic ramping scheme is essential to excite the nonequilibrium dynamics, and (ii) overheating beyond the critical temperature of superconductivity must be avoided. For commonly discussed interaction ramps there is no clear separation of the corresponding energy scales. Here we show that the matching of both conditions is simplified by the intrinsic relaxation behavior of ultracold fermionic systems: For the particular example of a linear ramp we examine the transient regime of prethermalization [M. Moeckel and S. Kehrein, Phys. Rev. Lett. 100, 175702 (2008)] under the crossover from sudden to adiabatic switching using Keldysh perturbation theory. A real-time analysis of the momentum distribution exhibits a temporal separation of an early energy relaxation and its later thermalization by scattering events. For long but finite ramping times this separation can be large. In the prethermalization regime the momentum distribution resembles a zero temperature Fermi liquid as the energy inserted by the ramp remains located in high energy modes. Thus ultracold fermions prove robust to heating which simplifies the observation of nonequilibrium BCS dynamics in optical lattices.

Time evolution during and after finite-time quantum quenches in Luttinger liquids

“…Defining a n (t) = u n (t) + v n (t) [we stress that (36) and (37) are no longer valid] and taking the second derivative we obtain…”

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

“…Let us stress that the Néel state (63) is only the lowest-order approximation of the real ground state of the Heisenberg model (62), there are quantum spin fluctuations of order O(1/Z). These quantum spin fluctuations do not vanish in the limit J → 0 since J only appears in the overall pre-factor in front of the Heisenberg Hamiltonian (62) while the internal structure remains the same.…”

“…consistent with the Heisenberg Hamiltonian (62). In analogy to the n µnν -correlator in the bosonic case, one has to go to second order O(1/Z 2 ) in order to calculate these quantities.…”

“…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].…”

Linear ramps of interaction in the fermionic Hubbard model

“…The crossover from adiabatic to sudden quench regimes and in particular the scaling of the excitation energy with the ramp time τ has been studied in the Falikov Kimball model by non equilibrium DMFT 34 . For what concerns the Hubbard model, (1) the problem has been tackled in the perturbative small U f regime and arbitrary ramp-time using Keldysh perturbation theory 35 , and in the non-perturbative regime but short ramp times by non equilibrium DMFT in combination with CTQMC 29 . Here we will make use of the mean field theory plus fluctuations we have developed for the sudden quench case to address the problem of ramps and we will compare with the results available whenever this is possible.…”