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**From**: Janos Asboth <asboth.janos AT wigner.mta.hu>**To**: seminar AT szfki.hu, fizinfo AT lists.kfki.hu**Subject**: [Fizinfo] Wigner Kvantumoptika Szeminárium - május 31, Rakovszky Tibor**Date**: Mon, 29 May 2017 08:40:10 +0200**Authentication-results**: smtp0.kfki.hu (amavisd-new); dkim=pass (1024-bit key) reason="pass (just generated, assumed good)" header.d=wigner.mta.hu

Operator hydrodynamics, OTOCs, and entanglement growth in systems without

conservation laws

*Rakovszky Tibor*

TU München

vendéglátó: Asbóth János

2017. 05. 31. szerda, 10:00, MTA Wigner FK SZFI, I. épület 1. emeleti

Tanácsterem

The scrambling of quantum information and so-called 'many-body quantum

chaos' are the subject of much recent study from the perspective of lattice

Hamiltonians (i.e. spin chains), quantum field theory and holography. A

quantity of interest, proposed to measure such quantum chaotic effects, is

the out-of-time-order correlator (OTOC), which exhibits an analogue of the

classical Lyapunov exponent in certain systems, such as large N field

theories and the Sachdev-Ye-Kitaev model. Much less is known about the

spreading of quantum information in lattice systems with locally bounded

Hilbert spaces and local interactions. Here we investigate this question in

one-dimensional spin chains evolving under random local unitary circuits

and prove a number of exact results on the behavior of OTOCs and the growth

of entanglement in this setting. These results follow from the observation

that the spreading of operators in random circuits is described by a

"hydrodynamical'' equation of motion, despite the fact that random unitary

circuits do not have locally conserved quantities (e.g., no conserved

energy). In this hydrodynamic picture quantum information travels in a

front with a `butterfly velocity' that is smaller than the light cone

velocity of the system, while the front itself broadens diffusively in

time. The OTOC increases sharply after the arrival of the light cone, but

we do not observe a prolonged exponential regime for any fixed Lyapunov

exponent. We find that the diffusive broadening of the front also has

important consequences for entanglement growth, leading to an entanglement

velocity that can be significantly smaller than the butterfly velocity. We

conjecture that the hydrodynamical description captures certain universal

properties of more generic ergodic systems and support this by verifying

numerically that the diffusive broadening of the operator wavefront also

holds in a more traditional non-random Floquet spin-chain. We also compare

our results to Clifford circuits, which have less rich hydrodynamics and

consequently trivial OTOC behavior, but which can nevertheless exhibit

linear entanglement growth and thermalization.

Minden érdeklődőt szívesen látunk!

Asbóth János

szfi-seminar AT wigner.mta.hu

**[Fizinfo] Wigner Kvantumoptika Szeminárium - május 31, Rakovszky Tibor**,*Janos Asboth, 05/29/2017*

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