Dynamical quantum phase transitions on cross-stitch flat band networks

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 $J=0\to J\ne 0$, we give the analytical expression to the Loschmidt echo which possesses a series of zero points at critical times $t^{\ast }$, indicating where the dynamical quantum phase transitions occur. We further study the converse quench process with $J\ne 0\to J=0$, 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 $\mathcal{L}(t)\equiv 1$ 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.

5 pages, 4 figures

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Cited by in corpus (2)

• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
• Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications