Measurement-Induced Phase Transition in a Disordered XX Spin Chain: A Real-Space Renormalization Group Study

TL;DR

This paper studies a disordered XX spin chain under random measurements, revealing new non-Hermitian fixed points and phase transitions using a novel real-space renormalization group approach.

Contribution

It introduces an RSRG-X method for open quantum systems with measurements, uncovering new critical behavior due to non-unitarity in disordered spin chains.

Findings

Identification of a new class of strongly disordered fixed points

Mapping monitored chains to non-Hermitian spin ladders

Revealing measurement-induced phase transitions in disordered systems

Abstract

Spin chains with quenched disorder exhibit rich critical behavior, often captured by real-space renormalization group (RSRG) techniques. However, the physics of such systems in the presence of random measurements (i.e., non-Hermitian dephasing) remains largely unexplored. The interplay between measurements and unitary dynamics gives rise to novel phases and phase transitions in monitored quantum systems. In this work, we investigate the disordered XX spin chain subject to stochastic local measurements in the $X$ and $Y$ bases. By mapping the monitored chain to a non-Hermitian spin ladder with complex couplings, we propose an RSRG-for-excited-states (RSRG-X) approach for this open-system setting. Our analysis reveals a new class of strongly disordered fixed points that emerge due to non-unitarity, broadening the landscape of critical phenomena accessible via RSRG.