We study quantum many-body systems with a global U(1) conservation law, focusing on a theory of $N$ interacting fermions with charge conservation, or $N$ interacting spins with one conserved component of total spin. We define an effective operator size at finite chemical potential through suitably regularized out-of-time-ordered correlation functions. The growth rate of this density-dependent operator size vanishes algebraically with charge density; hence we obtain new bounds on Lyapunov exponents and butterfly velocities in charged systems at a given density, which are parametrically stronger than any Lieb-Robinson bound. We argue that the density dependence of our bound on the Lyapunov exponent is saturated in the charged Sachdev-Ye-Kitaev model. We also study random automaton quantum circuits and Brownian Sachdev-Ye-Kitaev models, each of which exhibit a different density dependence for the Lyapunov exponent, and explain the discrepancy. We propose that our results are a cartoon for understanding Planckian-limited energy-conserving dynamics at finite temperature.
Cited by 3
Chunxiao Liu et al., Non-unitary dynamics of Sachdev-Ye-Kitaev chain
SciPost Phys. 10, 048 (2021) [Crossref]
Jason Iaconis et al., Measurement-induced phase transitions in quantum automaton circuits
Phys. Rev. B 102, 224311 (2020) [Crossref]
Chao Yin et al., Quantum operator growth bounds for kicked tops and semiclassical spin chains
Phys. Rev. A 103, 042414 (2021) [Crossref]