# Boundaries and unphysical fixed points in Dynamical Quantum Phase Transitions

## TL;DR

This paper investigates how boundary conditions influence dynamical quantum phase transitions (DQPT) and reveals the presence of unphysical fixed points affecting the nature of these transitions in quantum spin models.

## Contribution

It demonstrates that boundary effects can suppress bulk DQPTs and identifies unphysical RG fixed points through exact analysis of quantum Ising and Potts models.

## Key findings

- Boundary conditions can completely suppress bulk DQPTs.
- Unphysical fixed points are involved in DQPTs.
- DQPTs in the Potts chain relate to period-2 fixed points.

## Abstract

We show that dynamic quantum phase transitions (DQPT) in many situations involve renormalization group (RG) fixed points that are unphysical in the context of thermal phase transitions. In such cases, boundary conditions are shown to become relevant to the extent of even completely suppressing the bulk transitions. We establish these by performing exact RG analysis of the quantum Ising model on scale-invariant lattices of different dimensions, and by analyzing the zeros of the Loschmidt amplitude. Further corroboration of boundaries affecting the bulk transition comes from the three-state quantum Potts chain, for which we also show that the DQPT corresponds to a pair of period-2 fixed points.