Quantum quenches in the Hubbard model: Time-dependent mean-field theory and the role of quantum fluctuations

Abstract

We study the non equilibrium dynamics in the fermionic Hubbard model after a sudden change of the interaction strength. To this scope, we introduce a time dependent variational approach in the spirit of the Gutzwiller ansatz. At the saddle-point approximation, we find at half filling a sharp transition between two different regimes of small and large coherent oscillations, separated by a critical line of quenches where the system is found to relax. Any finite doping washes out the transition, leaving aside just a sharp crossover. In order to investigate the role of quantum fluctuations, we map the model onto an auxiliary Quantum Ising Model in a transverse field coupled to free fermionic quasiparticles. Remarkably, the Gutzwiller approximation turns out to correspond to the mean field decoupling of this model in the limit of infinite coordination lattices. The advantage is that we can go beyond mean field and include gaussian fluctuations around the non equilibrium mean field dynamics. Unlike at equilibrium, we find that quantum fluctuations become massless and eventually unstable before the mean field dynamical critical line, which suggests they could even alter qualitatively the mean field scenario.

Linear ramps of interaction in the fermionic Hubbard model

“…, 2 electrons. Then assuming a time independent Slater determinant as well as an homogeneous and non magnetic wave function 33 we can further simplify the dynamical equations. At half filling the classical mean-field dynamics for the double occupancy D(t) and its conjugate variable φ(t) readṡ …”

“…In particular, by using the time dependent Gutzwiller approach we have recently developed 16,33 , we will study linear ramps of the Hubbard interaction across the Mott transition. The paper is structured as follows.…”

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

“…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].…”

Analysis of Particle Transfer for Periodic Lattice Modulation in Three Dimensional Optical Lattice

“…The GW wave function is extended straightforwardly to the time-dependent case simply by making the variational parameter time-dependent [6,7]:…”