Abstract
In this paper, we study non-equilibrium dynamics induced by a sudden quench of strongly correlated Hamiltonians with all-to-all interactions. By relying on a Sachdev-Ye-Kitaev (SYK)-based quench protocol, we show that the time evolution of simple spin-spin correlation functions is highly sensitive to the degree of k-locality of the corresponding operators, once an appropriate set of fundamental fields is identified. By tracking the time-evolution of specific spin-spin correlation functions and their decay, we argue that it is possible to distinguish between operator-hopping and operator growth dynamics; the latter being a hallmark of quantum chaos in many-body quantum systems. Such an observation, in turn, could constitute a promising tool to probe the emergence of chaotic behavior, rather accessible in state-of-the-art quench setups.
Highlights
We focus on quench protocols realized by means of a paradigmatic example of dynamical system equipped with all-to-all interactions, that is, the Sachdev-Ye-Kitaev (SYK) model [50,51,52]
Under the specific protocol where the quench Hamiltonian takes the form of SYK models, with different values of q, we investigate the dynamics of different spin correlation functions in 1D lattice spin systems
We have investigated whether quantum chaos, and operator growth, can be revealed by performing quantum quench protocols on systems defined over spin lattices
Summary
The study of strongly correlated quantum systems dates back to the early stages of quantum mechanics, and it still represents one of the most intriguing and challenging subjects of research [1,2,3,4,5,6,7]. Under the specific protocol where the quench Hamiltonian takes the form of SYK models, with different values of q, we investigate the dynamics of different spin correlation functions in 1D lattice spin systems We argue that these correlators, which, in general, can be accessed by state-ofthe-art quench experiments by exploiting local imaging of quantum gas microscopes [57], contain useful information on the operator dynamics. We start by presenting a seeming paradox, that is, that the time evolution of some spin-spin correlation functions, when a spin chain model is perturbed by a quantum quench, are dramatically affected by performing a simple rotation of an external constant magnetic field This issue is explained, understanding that this simple rotation deeply changes the operator size of the operators studied in the quench.
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