ELFT HÍRADÓ

[Janos Asboth <asboth.janos AT 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