Operator Size Distribution in Large $N$ Quantum Mechanics of Majorana Fermions

Abstract

Under the Heisenberg evolution in chaotic quantum systems, initially simple operators evolve into complicated ones and ultimately cover the whole operator space. We study the growth of the operator ``size'' in this process, which is related to the out-of-time-order correlator (OTOC). We derive the full time evolution of the size distribution in large $N$ quantum mechanics of Majorana fermions. As examples, we apply the formalism to the Brownian SYK model (infinite temperature) and the large $q$ SYK model (finite temperature).

arXiv comment14 pages, 4 figures

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• Scheme to Detect the Strong-to-weak Symmetry Breaking via Randomized Measurements
• Scrambling Transition in Free Fermion Systems Induced by a Single Impurity
• Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
• Revealing quantum operator scrambling via measuring Holevo information on digital quantum simulators
• Krylov Winding and Emergent Coherence in Operator Growth Dynamics