Triviality of quantum trajectories close to a directed percolation transition

TL;DR

This paper investigates the distinct quantum phase transitions in monitored quantum circuits, demonstrating that entanglement and absorbing state transitions are separate phenomena, with their relationship depending on the local Hilbert space dimension.

Contribution

The work analytically and numerically distinguishes measurement-induced entanglement and absorbing state transitions, introducing Effective Tensor Networks to analyze their critical properties.

Findings

Entanglement transition occurs before the absorbing state transition.

Transitions are only coincident at infinite local Hilbert-space dimension.

Numerical simulations confirm the analytical predictions and finite-size effects.

Abstract

We study quantum circuits consisting of unitary gates, projective measurements, and control operations that steer the system towards a pure absorbing state. Two types of phase transition occur as the rate of these control operations is increased: a measurement-induced entanglement transition, and a directed percolation transition into the absorbing state (taken here to be a product state). In this work we show analytically that these transitions are generically distinct, with the quantum trajectories becoming disentangled before the absorbing state transition is reached, and we analyze their critical properties. We introduce a simple class of models where the measurements in each quantum trajectory define an Effective Tensor Network (ETN) -- a subgraph of the initial spacetime graph where nontrivial time evolution takes place. By analyzing the entanglement properties of the ETN, we show that the entanglement and absorbing-state transitions coincide only in the limit of infinite local Hilbert-space dimension. Focusing on a Clifford model which allows numerical simulations for large system sizes, we verify our predictions and study the finite-size crossover between the two transitions at large local Hilbert space dimension. We give evidence that the entanglement transition is governed by the same fixed point as in hybrid circuits without feedback.