# Out-of-Time-Order Correlators in One-Dimensional XY model

## TL;DR

This paper investigates how out-of-time-order correlators (OTOC) behave in the one-dimensional XY model, revealing how parameters like anisotropy and magnetic field influence chaos spreading, and analyzing temporal decay patterns and temperature effects.

## Contribution

It provides a detailed analysis of OTOC dynamics in the XY model, including the dependence of butterfly speed on model parameters and the behavior of local and nonlocal operators over time.

## Key findings

- Butterfly speed depends on anisotropy and magnetic field parameters.
- Wavefront of chaos spreading follows a positive universal form.
- Local OTOC decays as power law t^{-1}, nonlocal operators show complex decay patterns.

## Abstract

Out-of-time-order correlators (OTOC) are considered to be a promising tool to characterize chaos in quantum systems. In this paper we study OTOC in XY model. With the presence of anisotropic parameter $\gamma$ and external magnetic field $\lambda$ in the Hamiltonian, we mainly focus on their influences on OTOC in thermodynamical limit. We find that the butterfly speed $v_B$ is dependent of these two parameters, and the recent conjectured universal form which characterizes the wavefront of chaos spreading are proved to be positive with varying $v_B$ in different phases of XY model. Moreover, we also study the behaviors of OTOC with fixed location, and we find that the early-time part fully agrees with the results derived from Hausdorff-Baker-Campbell expansion. The long-time part is studied either, while in the local case $C(t)$ decay as power law $t^{-1}$, $|F(t)|$ with nonlocal operators show quite interesting and nontrivial power law decay corresponding to different choices of operators and models. At last, we observe temperature dependence for OTOC with local operators at ($\gamma=0, \lambda=1$), and divergent behavior with low temperature for nonlocal operator case at late time.