Signatures of quantum chaos transition in short spin chains

¹ Departamento de Física “J. J. Giambiagi” and IFIBA, FCEyN, Universidad de Buenos Aires 1428 Buenos Aires, Argentina
² Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata and CONICET - 7600 Mar del Plata, Argentina
³ Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 F-67000 Strasbourg, France

Received: 5 May 2020
Accepted: 17 June 2020

Abstract

The non-integrability of quantum systems, often associated with chaotic behavior, is a concept typically applied to cases with a high-dimensional Hilbert space. Among different indicators signaling this behavior, the study of the long-time oscillations of the Out-of-Time Ordered Correlator (OTOC) appears as a versatile tool, that can be adapted to the case of systems with a small number of degrees of freedom. Using such an approach, we consider the oscillations observed after the scrambling time in the measurement of OTOCs of local operators for an Ising spin chain on a nuclear magnetic resonance quantum simulator (Li J. et al., Phys. Rev. X, 7 (2017) 031011). We show that the systematic of the OTOC oscillations describes qualitatively well, in a chain with only 4 spins, the integrability-to-chaos transition inherited from the infinite chain.