Fig. 4: Self-normal and biorthogonal DQPTs during a quench between distinct topological phases in the PT-symmetry-broken region.

Loschmidt rate of LR(t) as a function of time in non-unitary QWs with self-normal bases (a) and with biorthogonal bases (b), respectively. DTOPs of ν(t) as a function of time in non-unitary QWs for c with self-normal bases and d biorthogonal bases, respectively. In all panels, l = 0.5, \(\xi =\arccos (1/\alpha )\) and \(\alpha =(1+\sqrt{1-l})/\left(2\root{4}\of{1-l}\right)\). The initial state of the QWs is \(\left\vert x=0\right\rangle \otimes \left\vert {\psi }_{-}^{i}\right\rangle\) of \({\hat{U}}^{i}\) with the coin parameters \(({\theta }_{1}^{i}=\pi /4,{\theta }_{2}^{i}=-\pi /2)\) and the QWs are governed by the final Floquet operator \({\hat{U}}^{f}\) with \(({\theta }_{1}^{f}=-\pi /2,{\theta }_{2}^{f}=(\pi -\xi )/2)\). All quantities are unitless