Out-of-Time-Ordered Crystals and Fragmentation

TL;DR

This paper introduces the concept of out-of-time-ordered (OTO) crystals, systems with perpetual OTOC oscillations indicating a form of quantum scrambling that reverses the arrow of time, and demonstrates their stability and existence in specific models.

Contribution

It provides a rigorous lower bound on OTOC oscillations, characterizes OTO crystals via a local dynamical algebra, and shows their stability and realization in models like the Creutz ladder.

Findings

OTOC oscillations can be bounded and characterized by a local algebra.

OTO crystals exhibit perpetual quantum scrambling and time-reversal features.

The Creutz ladder exemplifies an OTO crystal with stable, perpetual oscillations.

Abstract

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.