2025/09/29 by Perugu, Rishik, Kobrin, Bryce, Flynn, Michael O. +1
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2509.25331
The operator wavefunction 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 wavefunction can acquire a phase that increases linearly with the size of operator, 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 wavefunction has a phase which winds linearly with the Krylov index. We argue that Krylov winding is a generic feature of quantum chaotic systems. 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 ≤ 2 α (with λL the Lyapunov exponent and α the growth rate), which ensures a linear phase dependence on size. For systems which 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 microscopic models: the Sachdev-Ye-Kitaev (SYK) model and a disordered k-local spin model.