Universal work statistics in quenched gapless quantum systems

Abstract

We study the universality of work statistics performed during a quench in gapless quantum systems. We show that the cumulants of work scale separately in the fast and slow quench regimes, following a power law analogous to the universal scaling in the Kibble-Zurek mechanism for topological defect formation in phase transition. As an example, we analyze the nonequilibrium dynamics of a quenched Heisenberg XXZ chain at its critical gapless state using the bosonization picture, resulting in a Tomonaga-Luttinger liquid. The analytical scaling is in agreement with the exact numerical calculation for the fast and slow quench regimes. In finite systems, the characteristic function display an oscillatory pattern which disappears in the thermodynamic limit. This study is particularly useful for understanding the thermodynamics of adiabatic quantum computation.

Figures (1)

• Figure 1: Renormalized cumulants $(\kappa_n)_\text{f,s}$ (absolute values) with respect to the (a) fast and (b) slow quench values as a function of the quench duration $\tau_Q$ (in units of $J^{-1}$). (a) Symbols represent exact numerics of a $N=12$ XXZ chain with $\Delta_\text{f}=0.1$. Solid lines are the analytical results in thermodynamic limit ($N=400$) fitted with UV cutoff $\alpha=3.51$. Dashed line indicates finite size analytical $\kappa_1$. Inset: Real value of the full CFW for $N=(4,8,12)$ with $\alpha=(3.05,2.76,2.72)$ in linear-log plot. For slow quenches, the plateaus are approached according to power law $\tau_Q^{-2}$. The solid line represent the thermodynamic limit value. (b) The same data with (a) albeit renormalized with the adiabatic values (plateaus of the inset). Dashed line is the finite size analytical result of $\kappa_1$. Solid lines connecting the symbols are added to aid the eyes.