# Dynamical quantum phase transitions on cross-stitch flat band networks

## TL;DR

This paper analyzes dynamical quantum phase transitions in cross-stitch flat band networks following sudden changes in inter-cell hopping, revealing critical times where phase transitions occur and discussing potential experimental observations.

## Contribution

It provides analytical expressions for Loschmidt echo zeros during quenches in cross-stitch flat band networks, highlighting novel dynamical quantum phase transition phenomena.

## Key findings

- Loschmidt echo exhibits zeros at critical times during $J=0$ to $J
eq0$ quenches.
- In certain quenches, the Loschmidt echo remains unity despite state changes.
- Numerical simulations support analytical results and potential ultracold atom experiments are discussed.

## Abstract

We study the quench dynamics on cross-stitch flat band networks by a sudden change of the inter-cell hopping strength $J$. For quench processes with $J$ changing as $J=0\rightarrow J\neq0$, we give the analytical expression to the Loschmidt echo which possesses a series of zero points at critical times $t^{*}$, indicating where the dynamical quantum phase transitions occur. We further study the converse quench process with $J\neq0\rightarrow J=0$, and find a non-trivial example that the pre-quench quantum state is not an eigenstate of the post-quench Hamiltonian, whereas the Loschmidt echo $\mathcal{L}(t)\equiv1$ during this process. For both situations, these results are also illustrated numerically. Finally, we give a brief discussion on the observation of these predictions in the system of ultracold atoms in optical lattices.