The measurement-induced phase transition in strongly disordered spin chains

TL;DR

This paper studies how local measurements affect the phase transition in strongly disordered spin chains, revealing a measurement-induced transition from localized to volume-law entangled phases with specific scaling behaviors.

Contribution

It demonstrates that any non-zero measurement rate destabilizes MBL regimes, inducing a volume-law phase and characterizes the critical measurement rate's dependence on disorder and operator overlap.

Findings

Measurement rate $p_c$ is exponentially small in disorder strength $W$ and operator overlap.

Volume-law phase saturation time scales linearly with system size $L$.

Prethermal and MBL regimes exhibit exponentially slow saturation at zero measurement rate.

Abstract

We investigate the dynamics of strongly disordered spin chains in the presence of random local measurements. By studying the transverse-field Ising model with a site-dependent random longitudinal field and an effective $l$-bit many-body localized Hamiltonian, we show that the prethermal and MBL regimes are unstable to local measurements along any direction. Any non-zero measurement density induces a volume-law entangled phase with a subsequent phase transition into an area-law state as the measurement rate is further increased. The critical measurement rate $p_c$, where the transition occurs, is exponentially small in the strength of disorder $W$ and the average overlap between the measurement operator and the local integrals of motion $O$ as $p_c \sim \exp[-\alpha W/(1-O^2)]$. In the measurement-induced volume-law phase, the saturation time scales as $t_s \sim L $, contrasting the exponentially slow saturation $t_s \sim e^{aL}$ in the prethermal and MBL regimes at $p = 0$.