For the random-bond quantum N-state Potts chain, the Loschmidt rate function keeps a sharp time-dependent phase transition, usually a linear cusp and sometimes a logarithmic divergence, with continuous disorder forcing a universal large-time plateau.
The calculation can thus be done for L = ∞ by computing the leading eigenvalue of the transfer matrix of the homogeneous chain
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Dynamical Quantum Phase Transition of the Quantum $N$-state Potts Chain with Quenched Disorder
For the random-bond quantum N-state Potts chain, the Loschmidt rate function keeps a sharp time-dependent phase transition, usually a linear cusp and sometimes a logarithmic divergence, with continuous disorder forcing a universal large-time plateau.