Real-time evolution for weak interaction quenches in quantum systems

Abstract

Motivated by recent experiments in ultracold atomic gases that explore the nonequilibrium dynamics of interacting quantum many-body systems, we investigate the nonequilibrium properties of a Fermi liquid. We apply an interaction quench within the Fermi liquid phase of the Hubbard model by switching on a weak interaction suddenly; then we follow the real-time dynamics of the momentum distribution by a systematic expansion in the interaction strength based on the flow equation method [1]. In this paper we derive our main results, namely the applicability of a quasiparticle description, the observation of a new type of quasi-stationary nonequilibrium Fermi liquid like state and a delayed thermalization of the momentum distribution. We explain the physical origin of the delayed relaxation as a consequence of phase space constraints in fermionic many-body systems. This brings about a close relation to similar behavior of one-particle systems which we illustrate by a discussion of the squeezed oscillator; we generalize to an extended class of systems with discrete energy spectra and point out the generic character of the nonequilibrium Fermi liquid results for weak interaction quenches. Both for discrete and continuous systems we observe that particular nonequilibrium expectation values are twice as large as their corresponding analogues in equilibrium. For a Fermi liquid, this shows up as an increased correlation-induced reduction of the quasiparticle residue in nonequilibrium.

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

“…2). This factor of two has already been found elsewhere in the context of standard time-dependent and timeindependent perturbation theory, see also [10]. This is incompatible with the small Boltzmann factors e −βU/2 = O(1/Z) and would require a comparably large effective temperature…”

“…With the definitions (8) and the time-evolution for the single-site density matrix (A1), we find for the two-point correlation functions (10). The equations (9) and ( …”

“…One of the major unsolved questions (or rather a set of questions) is the problem of thermalization of isolated quantum systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In one version, this question can be posed in the following way: Given an interacting quantum many-body system on an infinite lattice in a globally excited state, do all observables involving a finite number of lattice sites settle down to a value which is consistent with a thermal state described by a suitable temperature?…”

“…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].…”

Nonequilibrium transport theory of the singlet-triplet transition: Perturbative approach

“…Although theoretical physicists devoted a lot of effort to design methods that are able to tackle these difficulties, so far none of the proposed methods proved to be entirely successful in describing strongly interacting non-equilibrium systems: Monte Carlo methods are presently unable to reach the required precision, 20,21 Bethe Ansatz methods can be used for a few models only, and are still in an experimental stage, [22][23][24] and perturbative renormalization group methods can only reach a particular region of the parameter space. [25][26][27][28] Maybe numerical renormalization group methods are currently the most reliable techniques to study these non-equilibrium systems, 24,29,30 however, they scale very badly with the number of states involved, and to compute the transport through just two levels in the presence of interaction seems to be numerically too demanding.…”