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This research provides a rigorous theoretical framework distinguishing between local order parameter transitions and global return rates in dynamical quantum phase transitions (DQPT). By decomposing stabilizer returns into costs from support loss and destructive interference, the study clarifies how discrete phase space scales dictate the information requirements for defining these non-equilibrium phenomena. These insights are critical for advancing our understanding of non-analyticities in quantum dynamics without relying on quasiprobability negativity.
Phase space anatomy of dynamical quantum phase transitions
arXiv:2609.24636v1 Announce Type: new Abstract: Dynamical quantum phase transitions (DQPT) are commonly defined either by the behavior of a late-time order parameter or by nonanalyticities in a quantum state's return rate. We show that discrete phase space fundamentally separates these two notions by the scale of information they require. An order parameter transition is determined by a local reduced state, requiring no quasiprobability negativity. In contrast, general global returns can contain information absent from every proper reduced state. For stabilizer returns, we derive an exact decomposition of the rate into distinct costs from loss of support and destructive quantum interference. Dynamics of a qutrit Potts chain show that selective cancellation can reverse the ranking of competing block returns and delay their exchange. An exact control also exhibits a thermodynamic return cusp with zero negativity at the crossing. The existence of a return singularity and the role of interference in selecting its branches are therefore distinct physical questions.
Abstract:Dynamical quantum phase transitions (DQPT) are commonly defined either by the behavior of a late-time order parameter or by nonanalyticities in a quantum state's return rate. We show that discrete phase space fundamentally separates these two notions by the scale of information they require. An order parameter transition is determined by a local reduced state, requiring no quasiprobability negativity. In contrast, general global returns can contain information absent from every proper reduced state. For stabilizer returns, we derive an exact decomposition of the rate into distinct costs from loss of support and destructive quantum interference. Dynamics of a qutrit Potts chain show that selective cancellation can reverse the ranking of competing block returns and delay their exchange. An exact control also exhibits a thermodynamic return cusp with zero negativity at the crossing. The existence of a return singularity and the role of interference in selecting its branches are therefore distinct physical questions.
arXiv:2609.24636 [quant-ph]
(or arXiv:2609.24636v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.24636 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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