Universal Hypothesis of Autocorrelation Function from Krylov Complexity

Abstract

In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the autocorrelation function. In particular, we focus on a particular kind of operator complexity called the Krylov complexity. We find that a set of Lanczos coefficients $\{b_n\}$ computed for determining the Krylov complexity can reveal the universal behaviors of autocorrelations, which are otherwise impossible. When the time axis is scaled by $b_1$, different autocorrelation functions obey a universal function form at short time. We further propose a characteristic parameter deduced from $\{b_n\}$ that can largely determine the behavior of autocorrelations at the intermediate time. This parameter can also largely determine whether the autocorrelation function oscillates or monotonically decays in time. We present numerical evidences and physical intuitions to support these universal hypotheses of autocorrelations. We emphasize that these universal behaviors are held across different operators and different physical systems.

5 pages, 3 figures

References in corpus (4)

• Krylov complexity from integrability to chaos
• Krylov Localization and suppression of complexity
• Probing quantum scars and weak ergodicity-breaking through quantum complexity
• Operator growth in the transverse-field Ising spin chain with integrability-breaking longitudinal field

Cited by in corpus (8)

• Quantum Dynamics in Krylov Space: Methods and Applications
• Krylov complexity and Trotter transitions in unitary circuit dynamics
• Emergent Universal Quench Dynamics in Randomly Interacting Spin Models
• Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
• Estimation of equilibration time scales from nested fraction approximations
• Evidence for simple "arrow of time functions" in closed chaotic quantum systems
• Universal Aspects of High-Temperature Relaxation Dynamics in Random Spin Models
• Hybrid Brownian SYK-Hubbard Model: from Spectral Function to Quantum Chaos