Chaos, Entanglement and Measurement: Field-Theoretic Perspectives on Quantum Information Dynamics

TL;DR

This paper develops theoretical tools to analyze quantum information dynamics, scrambling, and measurement effects in many-body systems, with a focus on the SYK model and related field theories.

Contribution

It introduces a field-theoretic framework for understanding measurement and scrambling in SYK models, including analytic control of randomness and a nonlinear sigma model for weak measurements.

Findings

Quantified pseudorandomness and scrambling times in Brownian SYK.

Derived a nonlinear sigma model capturing measurement back-action.

Identified features of measurement-only SYK clusters and their potential infinite-randomness behavior.

Abstract

This work develops tools to understand how quantum information spreads, scrambles, and is reshaped by measurements in many-body systems. First, I study scrambling and pseudorandomness in the Brownian Sachdev-Ye-Kitaev (SYK) model, quantifying pseudorandomness using unitary k-designs and frame potentials. Using Keldysh path integrals with replicas and disorder averaging, I obtain analytic control of the approach to randomness, identify collective modes that delay convergence to Haar-like behavior, and estimate design times as functions of model parameters, clarifying links between scrambling, complexity growth, and random-circuit phenomenology. Second, I construct a field theory for weakly measured SYK clusters. Starting from a system-ancilla description and a continuum monitoring limit, and using fermionic coherent states with replicas and disorder averaging, I derive a nonlinear sigma model that captures measurement back-action and the competition between interaction-induced scrambling and information extraction, predicting characteristic crossover scales and response signatures that distinguish weak monitoring from fully unitary evolution. Third, I develop a strong-disorder renormalization group for measurement-only SYK clusters, based on the SO(2n) replica algebra and Dasgupta-Ma decimation rules. The flow shows features reminiscent of infinite-randomness behavior, but an order-of-limits subtlety renders the leading recursions non-robust, so the analytic evidence for an infinite-randomness fixed point is inconclusive, even though the average second Renyi entropy displays logarithmic scaling. Together, these results provide a unified language to diagnose when many-body dynamics generate operational randomness and how measurements redirect that flow.