# Dynamical Quantum Phase Transition and Quasi Particle Excitation

## TL;DR

This paper investigates the relationship between dynamical quantum phase transitions and equilibrium phase transitions, demonstrating through exactly solvable models that the connection is not universal and identifying conditions for DPTs to occur independently of equilibrium critical points.

## Contribution

The study provides analytical evidence that dynamical phase transitions are not always linked to equilibrium phase transitions, challenging previous assumptions and clarifying conditions for their occurrence.

## Key findings

- DPTs can occur without crossing equilibrium critical points.
- The connection between DPTs and EPTs is not universal.
- Analytical analysis of the extended XY and compass models supports these conclusions.

## Abstract

Dynamical phase transitions (DPTs) are signaled by the non-analytical time evolution of the dynamical free energy after quenching some global parameters in quantum systems. The dynamical free energy is calculated from the overlap between the initial and the time evolved states (Loschmidt amplitude). In a recent study it was suggested that DPTs are related to the equilibrium phase transitions (EPTs) (M. Heyl et al., Phys. Rev. Lett. \textbf{110}, 135704 (2013)). We here study an exactly solvable model, the extended $XY$ model, the Loschmidt amplitude of which provides a counterexample. We show analytically that the connection between the DPTs and the EPTs does not hold generally. Analysing also the general compass model as a second example, assists us to propound the physical condition under which the DPT occurs without crossing the equilibrium critical point, and also no DPT by crossing the equilibrium critical point.