Dynamical quantum phase transitions in the quantum Potts chain

We analyze the dynamics of the return amplitude following a sudden quench in the three-state quantum Potts chain. For quenches crossing the quantum critical point from the paramagnetic to the ferromagnetic phase, the corresponding rate function is nonanalytic at critical times and behaves linearly in their vicinity. In particular, we find no indication of a link between the time evolution close to the critical times and the scaling properties of the quantum critical point in the Potts chain.

Figure 1

Rate function $l\left(t\right)$ defined in Eq. (3) for a quench from the PM to the FM phase in the three-state quantum Potts chain. $l\left(t\right)$ characterizes the overlap with the initial state in the thermodynamic limit. The DMRG data agree well with the analytic result (11) obtained for the trivial quench $f_0=\infty$ to $f_1=0$. The rate function shows nonanalytic behavior (kinks) at the critical times $t^{*}$.

Figure 2

The rate function $l\left(t\right)$ of Fig. 1 close to the first critical time $t^{*}$. The behavior is always linear, $l\left(t\right)\propto |t-t^{*}|$. For comparison, we also show the naive expectation predicted by Eq. (4) with $d/y=5/6$.

Figure 3

Rate function $l\left(t\right)$ for a quench starting from a fully polarized FM state to the Potts chain with final parameters $J_1$ and $f$ (see text). For the trivial quench to $J_1=0,l\left(t\right)$ is analytic at all times [see also Eq. (14)]. For finite $J_1$, nonanalyticities (kinks) develop for large enough times.