Theory of Dynamical Phase Transitions in Quantum Systems with Symmetry-Breaking Eigenstates

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We present a theory for the two kinds of dynamical quantum phase transitions, termed DPT-I and DPT-II, based on a minimal set of symmetry assumptions. In the special case of collective systems with infinite -range interactions, both are triggered by excited-state quantum phase transitions. For quenches below the critical energy, the existence of an additional conserved charge, identifying the corresponding phase, allows for a nonzero value of the dynamical order parameter characterizing DPTs-I, and precludes the main mechanism giving rise to nonanalyticities in the return probability, trademark of DPTs-II. We propose a statistical ensemble describing the long-time averages of order parameters in DPTs-I, and provide a theoretical proof for the incompatibility of the main mechanism for DPTs-II with the presence of this additional conserved charge. Our results are numerically illustrated in the fully connected transverse-field Ising model, which exhibits both kinds of dynamical phase transitions. Finally, we discuss the applicability of our theory to systems with finite-range interactions, where the phenomenology of excited-state quantum phase transitions is absent. We illustrate our findings by means of numerical calculations with experi-mentally relevant initial states.
© 2023 American Physical Society. We gratefully acknowledge discussions with P. Pérez-Fernández and J. Dukelsky. A. L. C. is also thankful toJ. Novotny, P. Stransky, and P. Cejnar for discussions and their hospitality at Charles University, Prague, when this work was at an advanced stage. This work has been supported by the Spanish Grant No. PGC-2018-094180-B-I00 funded by Ministerio de Ciencia e Innovación/Agencia Estatal de Investigación MCIN/AEI/10.13039/501100011033 and FEDER"A Way of Making Europe."A. L. C. acknowledges financial support from"la Caixa"Foundation (ID 100010434) through the fellowship LCF/BQ/DR21/11880024.
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