How order melts after quantum quenches

Injecting a sufficiently large energy density into an isolated many-particle system prepared in a state with long-range order will lead to the melting of the order over time. Detailed information about this process can be derived from the quantum mechanical probability distribution of the order parameter. We study this process for the paradigmatic case of the spin-1/2 Heisenberg XXZ chain. We determine the full quantum mechanical distribution function of the staggered subsystem magnetization as a function of time after a quantum quench from the classical Néel state. We establish the existence of an interesting regime at intermediate times that is characterized by a very broad probability distribution. Based on our findings we propose a simple general physical picture of how long-range order melts.

Figure 1

Density plot of ${\tilde{P}}_{\ell }(m,t)$ with $m\in [-\ell /2,\ell /2]$ and $t\in [0,12]$ for a subsystem size $\ell =15$, after a quench from the Néel state $\left|{\mathrm{GS}}_{\infty }^{+}\right.〉$ to $\mathrm{\Delta }=0$, 1, 2, 3. The solid line represents the expectation value $\overline{m}\left(t\right)$, and the dashed lines are the standard deviation from the average, namely $\overline{m}\left(t\right)\pm \sigma \left(t\right)$.

Figure 2

Snapshots of the rescaled PDF in Fig. 1 at fixed times $t=2$, 12. The numerical data (symbols/dashed lines) are compared to the Gaussian approximation (4) (solid lines).

Figure 3

${\tilde{P}}_{\ell }(m,t)$ for $\ell =20$ at times $t=0.2$, 0.5, and 1 after a quench from the classical Néel state to a Heisenberg chain with $\mathrm{\Delta }=3$. Lines are obtained by the self-consistent fermionic mean-field approximation and the symbols are iTEBD results.

Figure 4

Density plot of the PDF for the XXZ chain at finite temperature $1/\beta$ for subsystem size $\ell =50$ and $\mathrm{\Delta }=4$ (left panel); $\mathrm{\Delta }=1$ (right panel).

Figure 5

Weights ${\tilde{P}}_{\ell }(m,t)$ for $\ell =10$ and a quench from the classical Néel state to a Heisenberg chain with $\mathrm{\Delta }=6$. We observe a linear growth (decrease) in time of the weights for $m=-\ell /2$ ($m=\ell /2$), indicating that the symmetrization of the PDF is driven by ballistic propagation of quasiparticles.