Absence of operator growth for average equal-time observables in
charge-conserved sectors of the Sachdev-Ye-Kitaev model
- URL: http://arxiv.org/abs/2210.02427v2
- Date: Tue, 21 Mar 2023 17:48:53 GMT
- Title: Absence of operator growth for average equal-time observables in
charge-conserved sectors of the Sachdev-Ye-Kitaev model
- Authors: Alessio Paviglianiti and Soumik Bandyopadhyay and Philipp Uhrich and
Philipp Hauke
- Abstract summary: Quantum scrambling plays an important role in understanding thermalization in closed quantum systems.
We show that scrambling is absent for disorder-averaged expectation values of observables.
We develop a cumulant expansion approach to approximate the evolution of equal-time observables.
- Score: 11.353329565587574
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum scrambling plays an important role in understanding thermalization in
closed quantum systems. By this effect, quantum information spreads throughout
the system and becomes hidden in the form of non-local correlations.
Alternatively, it can be described in terms of the increase in complexity and
spatial support of operators in the Heisenberg picture, a phenomenon known as
operator growth. In this work, we study the disordered fully-connected
Sachdev-Ye-Kitaev (SYK) model, and we demonstrate that scrambling is absent for
disorder-averaged expectation values of observables. In detail, we adopt a
formalism typical of open quantum systems to show that, on average and within
charge-conserved sectors, operators evolve in a relatively simple way which is
governed by their operator size. This feature only affects single-time
correlation functions, and in particular it does not hold for out-of-time-order
correlators, which are well-known to show scrambling behavior. Making use of
these findings, we develop a cumulant expansion approach to approximate the
evolution of equal-time observables. We employ this scheme to obtain analytic
results that apply to arbitrary system size, and we benchmark its effectiveness
by exact numerics. Our findings shed light on the structure of the dynamics of
observables in the SYK model, and provide an approximate numerical description
that overcomes the limitation to small systems of standard methods.
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