23,917 research outputs found
Out-of-Time-Order Correlation at a Quantum Phase Transition
In this paper we numerically calculate the out-of-time-order correlation
functions in the one-dimensional Bose-Hubbard model. Our study is motivated by
the conjecture that a system with Lyapunov exponent saturating the upper bound
will have a holographic dual to a black hole at finite
temperature. We further conjecture that for a many-body quantum system with a
quantum phase transition, the Lyapunov exponent will have a peak in the quantum
critical region where there exists an emergent conformal symmetry and is absent
of well-defined quasi-particles. With the help of a relation between the
R\'enyi entropy and the out-of-time-order correlation function, we argue that
the out-of-time-order correlation function of the Bose-Hubbard model will also
exhibit an exponential behavior at the scrambling time. By fitting the
numerical results with an exponential function, we extract the Lyapunov
exponents in the one-dimensional Bose-Hubbard model across the quantum critical
regime at finite temperature. Our results on the Bose-Hubbard model support the
conjecture. We also compute the butterfly velocity and propose how the echo
type measurement of this correlator in the cold atom realizations of the
Bose-Hubbard model without inverting the Hamiltonian.Comment: 7 pages, 6 figures, published versio
Out-of-Time-Order Correlation for Many-Body Localization
In this paper we first compute the out-of-time-order correlators (OTOC) for
both a phenomenological model and a random-field XXZ model in the many-body
localized phase. We show that the OTOC decreases in power law in a many-body
localized system at the scrambling time. We also find that the OTOC can also be
used to distinguish a many-body localized phase from an Anderson localized
phase, while a normal correlator cannot. Furthermore, we prove an exact theorem
that relates the growth of the second R\'enyi entropy in the quench dynamics to
the decay of the OTOC in equilibrium. This theorem works for a generic quantum
system. We discuss various implications of this theorem.Comment: 6 pages, 3 figures, published versio
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