4.6 Article

Entanglement and precession in two-dimensional dynamical quantum phase transitions

Journal

PHYSICAL REVIEW B
Volume 105, Issue 16, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.105.165149

Keywords

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Funding

  1. European Research Council (ERC) under the European Union [850899]
  2. Institute of Science and Technology (IST) Austria
  3. European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant [754411]
  4. European Research Council (ERC) [850899] Funding Source: European Research Council (ERC)

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This paper investigates the dynamical quantum phase transitions (DQPTs) in two-dimensional systems by considering semi-infinite ladders of varying width. The concepts of precession (pDQPTs) and entanglement (eDQPTs) DQPTs are extended and studied in this context. The phenomenology of pDQPTs and eDQPTs in square lattices show similar characteristics to the one-dimensional case, while honeycomb lattices with an odd number of nearest neighbors exhibit beyond one-dimensional classification.
Nonanalytic points in the return probability of a quantum state as a function of time, known as dynamical quantum phase transitions (DQPTs), have received great attention in recent years, but the understanding of their mechanism is still incomplete. In our recent work [Phys. Rev. Lett. 126, 040602 (2021)], we demonstrated that one-dimensional DQPTs can be produced by two distinct mechanisms, namely semiclassical precession and entanglement generation, leading to the definition of precession (pDQPTs) and entanglement (eDQPTs) dynamical quantum phase transitions. In this manuscript, we extend and investigate the notion of p-and eDQPTs in two-dimensional systems by considering semi-infinite ladders of varying width. For square lattices, we find that pDQPTs and eDQPTs persist and are characterized by similar phenomenology as in 1D: pDQPTs are associated with a magnetization sign change and a wide entanglement gap, while eDQPTs correspond to suppressed local observables and avoided crossings in the entanglement spectrum. However, DQPTs show higher sensitivity to the ladder width and other details, challenging the extrapolation to the thermodynamic limit especially for eDQPTs. Moving to honeycomb lattices, we also demonstrate that lattices with an odd number of nearest neighbors give rise to phenomenologies beyond the one-dimensional classification.

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