2026-04-13 カリフォルニア大学アーバイン校（UCI）
A quantum state portrayed as a large collection of dots. As information spreads through the system from left to right, complexity increases and with it the potential for quantum scrambling. Rishik Perugu and Thomas Scaffidi / UC Irvine
＜関連情報＞
- https://news.uci.edu/2026/04/13/uc-irvine-physicists-discover-method-to-reverse-quantum-scrambling/
- https://journals.aps.org/prl/abstract/10.1103/bt23-4y1t
演算子成長ダイナミクスにおけるクリロフ巻きと創発的コヒーレンス Krylov Winding and Emergent Coherence in Operator Growth Dynamics
Rishik Perugu, Bryce Kobrin, Michael O. Flynn, and Thomas Scaffidi
Physical Review Letters Published: 13 April, 2026
DOI: https://doi.org/10.1103/bt23-4y1t
Abstract
The operator wave function provides a fine-grained description of quantum chaos and of the irreversible growth of simple operators into increasingly complex ones. Remarkably, at finite temperature, this wave function can acquire a phase that increases linearly with the operator’s size, a phenomenon called size winding. Although size winding occurs naturally in a holographic setting, the emergence of a coherent phase in a scrambled operator remains mysterious from the standpoint of a thermalizing quantum many-body system. In this work, we elucidate this phenomenon by introducing the related concept of Krylov winding, whereby the operator wave function acquires a phase that winds linearly with the Krylov index. We show that Krylov winding is a generic feature of quantum chaotic systems and is a direct consequence of the universal operator growth bound hypothesis. It gives rise to size winding under two additional conditions: (i) a low-rank mapping between the Krylov and size bases, which ensures phase alignment among operators of the same size, and (ii) the saturation of the “chaos-operator growth” bound λL≤2α (with λL the Lyapunov exponent and α the growth rate), which ensures a linear phase dependence on size. For systems that do not saturate this bound, with ℎ= λL/2α <1, the winding with Pauli size ℓ becomes superlinear, behaving as ℓ1/ℎ. We illustrate these results with two classes of microscopic models: the Sachdev-Ye-Kitaev (SYK) model and its variants, and a disordered -local spin model.
