Infinite-randomness criticality in monitored quantum dynamics with static disorder

TL;DR

This paper investigates a measurement-induced phase transition in monitored quantum circuits with spatial disorder, revealing an infinite-randomness critical point characterized by unusual entanglement scaling and dynamical properties.

Contribution

It introduces the concept of infinite-randomness criticality in monitored quantum dynamics with static disorder, supported by numerical evidence and theoretical arguments.

Findings

Entanglement scales as √ℓ at criticality

Dynamical critical exponent z = ∞

Presence of Griffiths phases with varying exponents

Abstract

We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in their entanglement structure, but the nature of the critical point differs drastically from the case with constant measurement rate. In particular, at the critical measurement rate, we find that the entanglement of a subsystem of size $\ell$ scales as $S \sim \sqrt{\ell}$; moreover, the dynamical critical exponent $z = \infty$. The MIPT is flanked by Griffiths phases with continuously varying dynamical exponents. We argue for this infinite-randomness scenario on general grounds and present numerical evidence that it captures some features of the universal critical properties of MIPT using large-scale simulations of Clifford circuits. These findings demonstrate that the relevance and irrelevance of perturbations to the MIPT can naturally be interpreted using a powerful heuristic known as the Harris criterion.