Measurement-induced criticality in extended and long-range unitary circuits

TL;DR

This paper investigates how the range of interactions in monitored Clifford circuits influences measurement-induced phase transitions, revealing different universality classes and critical behaviors depending on interaction distribution.

Contribution

It demonstrates that the interaction range determines the universality class of measurement-induced transitions in Clifford circuits, with a continuous change for power-law distributed interactions.

Findings

Cluster gates exhibit a transition similar to short-range circuits.

Power-law interactions lead to a non-conformal critical line.

Entanglement scaling varies from volume-law to area-law depending on parameters.

Abstract

We explore the dynamical phases of unitary Clifford circuits with variable-range interactions, coupled to a monitoring environment. We investigate two classes of models, distinguished by the action of the unitary gates, which either are organized in clusters of finite-range two-body gates, or are pair-wise interactions randomly distributed throughout the system with a power-law distribution. We find the range of the interactions plays a key role in characterizing both phases and their measurement-induced transitions. For the cluster unitary gates we find a transition between a phase with volume-law scaling of the entanglement entropy and a phase with area-law entanglement entropy. Our results indicate that the universality class of the phase transition is compatible to that of short range hybrid Clifford circuits. Oppositely, in the case of power-law distributed gates, we find the universality class of the phase transition changes continuously with the parameter controlling the range of interactions. In particular, for intermediate values of the control parameter, we find a non-conformal critical line which separates a phase with volume-law scaling of the entanglement entropy from one with sub-extensive scaling. Within this region, we find the entanglement entropy and the logarithmic negativity present a cross-over from a phase with algebraic growth of entanglement with system size, and an area-law phase.