Dynamical Correlation of the Post-quench Non-thermal Equilibrium State

Abstract

After a quantum quench, the integrable system is expected to relax to a non-thermal equilibrium state (NTES) whose local properties are believed to be governed by a generalized Gibbs ensemble (GGE). Combining quench action and the form factor approach, we compute the field-field correlation in the NTES produced by an interaction quench of the Lieb-Liniger model. The spectral distribution is shown to be qualitatively different from that of a thermal equilibrium state (TES): a new dispersion branch appears whose microscopic mechanism can be traced to the algebraic decaying tail for the root density distribution function, and indicates the existence of a broader family of NTES featuring similar spectral property.

Figures (8)

• Figure 1: The rescaled root density distribution $\rho(\lambda)/\rho(0)$ are shown for TES and NTES of different values of $c$. The solid line and symbol reresent the results of NTES and TES, respectively.
• Figure 2: The logarithm of 1BDCF in NTES and TES in the momentum-energy plane. The momentum and energy are measured in units of Fermi momentum $k_F = \pi N/L$ and Fermi energy, respectively. From top to bottom, the interaction varies from weak $c=0.1$, medium $c=1$ to strong $c=5$; the corresponding system size is $N=L=80$, $30$ and $12$; the temperature of TES takes $T=0.13$, $1.15$ and $6.36$, respectively. The sum rules, c.f. Eq. \ref{['sumrule']}, of (a) to (f) are 99.99%, 99.99%, 99.99%, 99.97%, 99.72%, and 99.99%, respectively.
• Figure 3: The 1st line shows the QN configuration for a sample of the NTES where the solid and hollow ball represents the particle and hole, respectively; following two lines demonstrate how the intermediate states are produced by a combination of generalized p-h excitations. The bottom plot shows the most spectral distribution resulted from above two categories of intermediate states produced by corresponding types of excitations.
• Figure 4: Plot of function $\tilde{g}_1(k,\omega)$ with argument $\omega$ for several different momenta. The results for TES and NTES are respectively represented by solid and dashed lines. The interaction strength $c$ takes $0.1$, $1$, and $5$ from top to bottom.
• Figure :