Abstract
Out-of-time-ordered correlators (OTOCs) have been proposed as a probe of chaos in quantum mechanics, on the basis of their short-time exponential growth found in some particular setups. However, it has been seen that this behavior is not universal. Therefore, we query other quantum chaos manifestations arising from the OTOCs, and we thus study their long-time behavior in systems of completely different nature: quantum maps, which are the simplest chaotic one-body system, and spin chains, which are many-body systems without a classical limit. It is shown that studying the long-time regime of the OTOCs it is possible to detect and gauge the transition between integrability and chaos, and we benchmark the transition with other indicators of quantum chaos based on the spectra and the eigenstates of the systems considered. For systems with a classical analog, we show that the proposed OTOC indicators have a very high accuracy that allow us to detect subtle features along the integrability-to-chaos transition.
Highlights
The original Bohr-Sommerfeld formulation of quantum mechanics addressed integrable classical systems, with as many conserved quantities as degrees of freedom
We start by presenting numerical studies of the of-time-ordered correlators (OTOCs) in the long-time regime using a one-body system
The OTOC is a quantity that has recently drawn attention since it has been suggested as a measure of quantum chaos, and because of possible implications in studies of highenergy physics, many-body localization, quantum information scrambling, and thermalization
Summary
The original Bohr-Sommerfeld formulation of quantum mechanics addressed integrable classical systems, with as many conserved quantities as degrees of freedom. Einstein’s 1917 observation that such a quantization scheme remained extremely limited (as integrability is a singularity among dynamical systems) remained relatively unnoticed until the late 1950s, probably due to the success of the Schrödinger equation [1,2]. The quantization of chaotic systems, as well as the understanding of the consequences of classical chaos on quantum observables such as the level statistics, developed in the 1970s and 1980s [3,4], provided the connection of quantum mechanics with fully chaotic systems, which constitute another singularity within the ensemble of dynamical systems. The connection of classical and quantum properties in the generic case of mixed systems, away from the two previously mentioned singularities, remains, comparatively, less understood and more difficult to quantify. In multidimensional and many-body systems the “no-man’s land” between the two singular behaviors is difficult to avoid
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