Quantum Liang Information Flow vs. Out-of-Time-Order Correlators as Chaos Diagnostics in the Mixed-Field Ising Chain

TL;DR

This paper compares Quantum Liang Information Flow (QLIF) and out-of-time-order correlators (OTOC) as tools to diagnose quantum chaos in a mixed-field Ising chain, revealing their different sensitivities and regimes of effectiveness.

Contribution

It demonstrates that QLIF can serve as a late-time chaos indicator and complements OTOC, with unique dependence on initial states and growth behaviors.

Findings

QLIF's early-time growth is identical for integrable and chaotic regimes.

Time-integrated QLIF grows linearly in chaotic systems, indicating thermalization.

QLIF's sensitivity varies greatly with initial states, spanning four orders of magnitude.

Abstract

We systematically compare Quantum Liang Information Flow (QLIF) a recently proposed causal information measure with the out-of-time-order correlator (OTOC) as diagnostics of quantum chaos in the one-dimensional mixed-field Ising chain. Using exact diagonalization and MPS-TEBD, we show that the early-time power-law growth and wavefront propagation velocity of QLIF are identical for integrable and chaotic parameters, being controlled solely by the local Hamiltonian structure. The QLIF signal strength depends sensitively on the initial state, spanning four orders of magnitude across product states, ground state eigenstate evolution, and quantum quench protocols. We identify the time-integrated QLIF as a late-time chaos diagnostic: it grows linearly (monotonically) in chaotic systems, reflecting irreversible thermalization, while saturating or oscillating in integrable systems, reflecting reversible quasiparticle dynamics. These findings establish QLIF as a complementary probe to OTOC, with distinct optimal operating regimes.