# Dynamical Quantum Phase Transition of the Quantum $N$-state Potts Chain with Quenched Disorder

## TL;DR

This paper analyzes the dynamical quantum phase transition in a disordered quantum Potts chain using exact renormalization group methods, revealing how disorder influences the sharpness and nature of the transition.

## Contribution

It provides an exact analysis of the Loschmidt amplitude in a disordered quantum Potts chain, showing the persistence of sharp phase transitions and classifying the effects of different bond distributions.

## Key findings

- Phase transition remains sharp under disorder.
- Pure model's linear-cusp transition persists with typical disorder.
- Special discrete disorder causes logarithmic divergences.

## Abstract

We present an exact renormalization group analysis of the Loschmidt amplitude of the quantum $N$-state Potts chain with random quench-disordered nearest neighbor bonds, under the extreme dynamical quantum quench. We prove that the phase transition of the Loschmidt rate function remains sharp in general. For typical bond distributions, the phase transition is found to be a linear-cusp, as in the pure model. For some special discrete bond distributions, however, the rate function exhibits logarithmic divergences. These singularities are due to the competition between the non-critical dynamical phases of the pure model, which is very different from how disorder affects equilibrium phase transitions. In addition, due to the periodicity of the complex exponential function, all continuous bond distributions result in rate functions which converge to a universal value at large time.