Out-of-Time-Ordered Crystals and Fragmentation

Abstract

Quantum many-body models with both Hilbert space fragmentation and non-stationarity have recently been identified. Hilbert space fragmentation does not immediately imply non-stationarity. However, strictly local dynamical symmetries directly imply non-stationarity. It is demonstrated here that these symmetries are equivalent to local fragmentation into spatially localized blocks. Using strictly local dynamical symmetries, a lower bound is given here for persistent oscillations of generalised out-of-time-ordered correlation functions (OTOCs). A novel notion of genuinely manybody continuous time translation symmetry breaking is provided by demanding non-trivial spatial modulation of the Fourier transform of the OTOC. Such non-trivial spatial-temporal dynamics stems from a perpetual backflow of quantum scrambling. Here we call systems with time-translation symmetry breaking in the OTOC, OTO crystals. This breaking cannot be realised by systems with a single effective degree of freedom (e.g. spin precession). Furthermore, the breaking is stable to all local unitary and dissipative perturbations. An XYZ Creutz ladder is presented as an example.

Long-time dynamics in quantum spin lattices: ergodicity and hydrodynamic projections at all frequencies and wavelengths

“…Thus hydrodynamics can be applied in the neighbourhood of any value (ω, k) in the frequencywavelength plane. This shows that recent ideas on dynamical symmetries [16][17][18][19][20] can be extended to the hydrodynamic regime of correlation functions.…”

“…Almost-everywhere ergodicity with nonzero frequency and/or wavelength rigorously forbids sustained oscillatory behaviours, over extended regions, for correlations of local operators and OTOC such as A(x, t)B c and [A(x, t), B] 2 . Recent results have established lower bounds on localised persistent oscillations (on the ray v = 0) using "strictly local dynamical symmetries" [17,19,20]. We find that such symmetries may only exist on a set of rays v of measure zero: for infinitely-many rays as near as desired to 0, there is no such oscillation.…”

Quantum Information Scrambling in Quantum Many-body Scarred Systems

“…In this sense, the periodic revival behaviors of OTOCs in quantum many-body scarred systems are pretty similar to the dynamics in time crystals [86,[96][97][98]: the ZZ-OTOC dynamics for the |Z 2 initial state is an analogue to the time crystals without perturbations; while the XZ-OTOCs for |Z 2 and ZZ-OTOCs for general initial states within the scarred subspace correspond to the perturbed time crystals, which will exhibit certain robustness and maintain the synchronized oscillations. This topic might need deeper understanding and more powerful techniques to deal with, so that is expected to inspire in-depth analytical studies in future.…”

“…Conclusions and discussions.-In summary, we have numerically calculated the information scrambling dynamics in quantum many-body scarred systems, and found a new paradigm (a linear light cone and periodic oscillations inside the light cone) intrinsically different from the previously studied ETH or MBL cases. Analytical explanations based on perturbation-type calculations are provided [65], yet we expect this work to inspire subsequent in-depth analytical studies, from the perspectives such as Hilbert space fragmentation [46,47,[84][85][86], connections to the classical OTOC and chaos theory [32-34, 65, 87, 88], robustness of scarred eigenstates under perturbations [50][51][52][53][54], black hole physics [89,90], and information scrambling dynamics in other many-body scarred systems [13]. The two criteria, OTOCs and Holevo information, support each other and have been demonstrated to have measurable signatures with current experimental technologies.…”

Exact bistability and time pseudo-crystallization of driven-dissipative fermionic lattices

“…Such semi-local symmetry operators have been studied recently in the context of generalized hydrodynamic corrections in quadratic and integrable models where their existence was associated with the topological nature of the models [30]. These new kinds of dynamical symmetries should be distinguished from both local extensive [28,[96][97][98] and strictly local ones [99][100][101] Topology likely plays a role in our model as it is intimately related to the Kitaev chain. We emphasize, that in the model studied here there is no obvious transformation that would allow mapping the semi-local dynamical symmetry into a semi-local non-Abelian symmetry while preserving the spatial locality of H.…”