Out-of-Time-Ordered Crystals and Fragmentation

Is a spontaneous perpetual reversal of the arrow of time possible? The out-of-time-ordered correlator (OTOC) is a standard measure of irreversibility, quantum scrambling, and the arrow of time. The question may be thus formulated more precisely and conveniently: can spatially ordered perpetual OTOC oscillations exist in many-body systems? Here we give a rigorous lower bound on the amplitude of OTOC oscillations in terms of a strictly local dynamical algebra allowing for identification of systems that are out-of-time-ordered (OTO) crystals. While OTOC oscillations are possible for few-body systems, due to the spatial order requirement OTO crystals cannot be achieved by effective single or few body dynamics, e.g., a pendulum or a condensate. Rather they signal perpetual motion of quantum scrambling. It is likewise shown that if a Hamiltonian satisfies this novel algebra, it has an exponentially large number of local invariant subspaces, i.e., Hilbert space fragmentation. Crucially, the algebra, and hence the OTO crystal, are stable to local unitary and dissipative perturbations. A Creutz ladder is shown to be an OTO crystal, which thus perpetually reverses its arrow of time.

Automated summary

This study examines the possibility of spontaneous perpetual reversal of the arrow of time and investigates the existence of perpetual out-of-time-ordered correlator (OTOC) oscillations in many-body systems. The researchers provide a rigorous lower bound for the amplitude of OTOC oscillations and identify systems that exhibit out-of-time-ordered (OTO) crystals through a strictly local dynamical algebra. Additionally, the study demonstrates that a Hamiltonian satisfying this algebra possesses a large number of local invariant subspaces and remains stable under local unitary and dissipative perturbations. The Creutz ladder is shown to be an OTO crystal capable of perpetually reversing the arrow of time.