Speaker
Vedika Khemani
(Harvard)
Description
I will discuss the “scrambling” of local quantum
information in chaotic quantum many-body systems in the
presence of a locally conserved quantity like charge or
energy that moves diffusively. The interplay between
conservation laws and scrambling sheds light on the
mechanism by which unitary quantum dynamics, which is
reversible, gives rise to diffusive hydrodynamics, which is
a dissipative process. Our results are obtained by
examining the dynamics of operator spreading under unitary
time evolution in a random quantum circuit model that is
constrained to have a conservation law. We find that a
generic spreading operator spreads ballistically with a
front that moves at a “butterfly speed”, but develops a
power law “tail” behind its leading ballistic front due to
the slow dynamics of the conserved component of the
operator. This structure implies that the out-of-time-order
commutator (OTOC) between two initially spatially separated
operators grows sharply upon the arrival of the ballistic
front but, in contrast to systems with no conservation laws,
it develops a diffusive tail and approaches its asymptotic
late-time value only as a power of time instead of
exponentially. I will also present these results within an
effective hydrodynamic description which contains multiple
coupled diffusion equations.
