Work done and irreversible entropy production in a suddenly quenched quantum spin chain with asymmetrical excitation spectra

In this paper, we extend the studies on the emergent thermodynamics in a quenched quantum Ising chain (QIC) [R. Dorner, J. Goold, C. Cormick, M. Paternostro, and V. Vedral, Phys. Rev. Lett. 109, 160601 (2012)] to a more general quantum spin chain with asymmetrical excitation spectra. We verify that the Jarzynski and Tasaki-Crooks relations are still tenable in this system. As an example, we discuss the behaviors of the work done and irreversible entropy production induced by a sudden quenching in the anisotropic XY chain in a transverse field with the XZY-YZX type of three-site interactions. Different from the QIC, this system has the phase transitions not only between two gapped phases, but also between gapped (or gapless) and gapless phases at zero temperature. We discuss the effects of quantum phase transitions on the work done and irreversible entropy production at low temperature.

Figure 1

The phase diagram at zero temperature for the XY chain with the XZY-YZX type of three-site interaction in a transverse field for $\alpha =0.5$. The horizontal dashed line corresponds to $\gamma =0.7$ and the vertical dashed line corresponds to $h=0.5$.

Figure 2

(a)$\frac{\langle w\rangle }{\Delta h}$ and (b)$\frac{\Delta s_{\text{irr}}}{\Delta h}$ as functions of $h$ for $\Delta h=0.01,\gamma =0.7,\alpha =0.5$, and $N=1000$. The solid, dashed, and dotted lines correspond to $\beta =100,50,10$, respectively.

Figure 3

(a)$\frac{\langle w\rangle }{\Delta \gamma }$ and (b)$\frac{\Delta s_{\text{irr}}}{\Delta \gamma }$ as functions of $\gamma$ for $\Delta \gamma =0.01,h=0.5,\alpha =0.5$, and $N=1000$. The solid, dashed, and dotted lines correspond to $\beta =100,50,10$, respectively.

Figure 4

The phase diagram at zero temperature for the XY chain with the XZY-YZX type of three-site interaction in a transverse field for $h=0$. The horizontal dashed line corresponds to $\gamma =0$.

Figure 5

(a)$\frac{\langle w\rangle }{\Delta \alpha }$ and (b)$\frac{\Delta s_{\text{irr}}}{\Delta \alpha }$ as functions of $\alpha$ for $\Delta \alpha =0.01,\gamma =0,h=0$, and $N=1000$. The solid, dashed, and dotted lines correspond to $\beta =100,50,10$, respectively.

Figure 6

$\frac{\Delta s_{\text{irr}}}{\Delta \gamma }$ as a function of $\gamma$ for $\Delta \gamma =0.3,h=0.5,\alpha =0.5$, and $N=1000$. The solid, dashed, and dotted lines correspond to $\beta =100,50,10$, respectively.