Long-time properties of generic Floquet systems are approximately periodic with the driving period
arXiv:2309.05641 · doi:10.1088/1367-2630/ad5eb1
Abstract
A Floquet quantum system is governed by a Hamiltonian that is periodic in time. Consider the space of piecewise time-independent Floquet systems with (geometrically) local interactions. We prove that for all but a measure zero set of systems in this space, starting from a random product state, many properties (including expectation values of observables and the entanglement entropy of a macroscopically large subsystem) at long times are approximately periodic with the same period as the Hamiltonian. Thus, in almost every Floquet system of arbitrarily large but finite size, discrete time-crystalline behavior does not persist to strictly infinite time.
v2: published version
References in corpus (16)
- Thermalization and its mechanism for generic isolated quantum systems
- Equilibrium states of generic quantum systems subject to periodic driving
- Many-body localization in periodically driven systems
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
- Periodically driven ergodic and many-body localized quantum systems
- A Sharp Fannes-type Inequality for the von Neumann Entropy
- Avalanches and many-body resonances in many-body localized systems
- Colloquium: Quantum and Classical Discrete Time Crystals
- Can we study the many-body localisation transition?
- Comment on "Quantum Time Crystals": a new paradigm or just another proposal of perpetuum mobile?
- Markovian baths and quantum avalanches
- A Brief History of Time Crystals
- Statistical Mechanics of Floquet Quantum Matter: Exact and Emergent Conservation Laws
- Extensive entropy from unitary evolution
- Adding boundary terms to Anderson localized Hamiltonians leads to unbounded growth of entanglement