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.

arXiv comment5 pages, 4 figures

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• Exploring Dynamical Phase Transitions in the XY Chain through Linear Quench: Early and Long-term Perspectives
• Aperiodic dynamical quantum phase transitions in multi-band Bloch Hamiltonian and its origin
• Dynamical quantum phase transitions in Stark quantum spin chains
• Geometry effect of the dynamical quantum phase transitions at finite temperatures
• Critical Exponent of Dynamical Quantum Phase Transition in One-Dimensional Bose-Hubbard Model in the Strong Interacting Limit