Unscrambling the physics of out-of-time-order correlators

Sergey Syzranov, Victor Galitski

Samudra Sur, Diptiman Sen

The out-of-time-order correlator (OTOC) measures the propagation and scrambling of local quantum information. For the transverse field Ising model with open boundaries, the local operator ${\ensuremath{\sigma}}^{x}$ shows an interesting picture of the ground state OTOC where the local information alternately gets scrambled and then ``unscrambled'' upon reflection at the ends. Earlier discussions of OTOCs did not explain the physical processes responsible for such scrambling and unscrambling. We explicitly show that in the paramagnetic phase, the scrambling and unscrambling is due to the scattering of a pair of low-energy spin-flip excitations, and extend it to incorporate integrability-breaking interactions. In the ferromagnetic phase these are explained by the motion of a domain-wall excitation, and we find that unscrambling survives up to moderate values of interactions. Thus, in different limits of the system parameters, we provide a simple understanding of the OTOCs, including the unscrambling, in terms of the low-energy excitations like spin flips or domain walls. We mention a system where our results can be experimentally tested.

Somsubhra Ghosh, Indranil Paul, K. Sengupta

The occurrence of prethermal Hilbert space fragmentation (HSF) in periodically driven quantum systems has its roots in the emergence of additional, approximate, kinetic constraints at special driving frequencies. Here, the authors show that the out-of-time-ordered correlators (OTOCs) of a driven fermion chain with open boundary condition exhibit a signature of such HSF. At the special drive frequencies where such prethermal HSF occurs, the OTOCs display periodic unscrambling of information, which provides a yet unexplored, experimentally testable, marker for prethermal fragmentation.

Adam Smith

Jochen Braumüller, Amir H. Karamlou, Yariv Yanay +13 more

Bryce Kobrin, Schuster, Thomas, Maxwell Block +4 more

We introduce a novel protocol, which enables Heisenberg-limited quantum-enhanced sensing using the dynamics of any interacting many-body Hamiltonian. Our approach - dubbed butterfly metrology - utilizes a single application of forward and reverse time evolution to produce a coherent superposition of a "scrambled" and "unscrambled" quantum state. In this way, we create metrologically-useful long-range entanglement from generic local quantum interactions. The sensitivity of butterfly metrology is given by a sum of local out-of-time-order correlators (OTOCs) - the prototypical diagnostic of quantum information scrambling. Our approach broadens the landscape of platforms capable of performing quantum-enhanced metrology; as an example, we provide detailed blueprints and numerical studies demonstrating a route to scalable quantum-enhanced sensing in ensembles of solid-state spin defects.