Quantum Quench and Prethermalization Dynamics in a Two-Dimensional Fermi Gas with Long-Range Interactions

We study the effect of suddenly turning on a long-range interaction in a spinless Fermi gas in two dimensions. The short- to intermediate-time dynamics is described using the method of bosonization of the Fermi surface. The space-time dependence of the nonequilibrium fermion density matrix as well as the evolution after the quench of the discontinuity at the Fermi momentum of the momentum distribution are computed. We find that the asymptotic state predicted by bosonization is consistent with the existence of a prethermalization plateau, which is also predicted by a perturbative approach in terms of the fermionic degrees of freedom. The bosonized representation, however, explicitly allows for the construction of the generalized Gibbs ensemble describing the prethermalized state.

Figure 1

Discontinuity of the zero-temperature momentum distribution at the Fermi momentum, $Z^{\mathrm{neq}}(t)$, as a function of time $t$ for several values of $g=f_0\sqrt{k_F{q}_c}/(2{\pi }^2{v}_F)$. $Z^{\mathrm{neq}}(t)$ exhibits a Gaussian decay at short times. Asymptotically, it saturates to a finite value $Z^{\mathrm{st}}\simeq (Z^{\mathrm{eq}}{)}^2$ (horizontal lines) in the stationary (prethermalized) state. Inset: $\ln [Z^{\mathrm{neq}}(t)/Z^{\mathrm{st}}]$ showing that $\ln Z^{\mathrm{neq}}(t)\sim t^{-1}$ asymptotically.