Quantum state texture of dynamical criticality

@misc{celeri2026quantum,
  title = {{Quantum state texture of dynamical criticality}},
  author = {Lucas C. Céleri and Krissia Zawadzki and Ivan Medina and Diogo O. Soares-Pinto},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.04161},
  eprint = {2605.04161},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.04161},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Quantum state texture of dynamical criticality
AU  - Lucas C. Céleri
AU  - Krissia Zawadzki
AU  - Ivan Medina
AU  - Diogo O. Soares-Pinto
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2605.04161
UR  - https://arxiv.org/abs/2605.04161
AB  - We investigate the role of quantum state texture in dynamical quantum phase transitions by establishing a direct connection between critical nonequilibrium dynamics and the recently introduced notion of rugosity, a measure of quantum state texture. Considering a generic quench protocol, we analyze both standard formulations of dynamical quantum phase transitions. For type-I transitions, characterized through the long-time behavior of a dynamical order parameter, we show that the time-averaged rugosity, evaluated in the eigenbasis of the pre-quench Hamiltonian, exhibits an order-parameter-like behavior across the transition. In the Lipkin-Meshkov-Glick model, this behavior is traced back to the underlying semiclassical structure, where crossing the excited-state quantum phase transition separatrix controls the redistribution of the quantum state over the pre-quench energy basis. We further demonstrate that the response function associated with the time-averaged rugosity develops a pronounced critical peak whose maximum grows algebraically with the system size, providing quantitative finite-size evidence of its sensitivity to the dynamical critical point. For type-II transitions, characterized by nonanalyticities in the Loschmidt rate function, we establish an exact connection with rugosity. For a suitable choice of basis, the rate function is exactly given by the density of rugosity, establishing a model-independent equivalence. Moreover, we show that even in physically motivated bases, such as the pre-quench energy eigenbasis, rugosity provides clear signatures of dynamical criticality. Our results establish rugosity as a sensitive probe of dynamical quantum phase transitions while highlighting its role as a basis-dependent measure of quantum state texture, thereby providing an information-theoretic perspective on nonequilibrium quantum critical phenomena.
ER  -