Critical behaviors of magic and participation entropy at measurement induced phase transitions

TL;DR

This paper investigates the critical behavior of participation and stabilizer entropy in non-unitary quantum circuits, revealing logarithmic entanglement scaling and critical slowing down at phase transition points.

Contribution

It introduces large-scale matrix product state simulations to analyze critical regimes and identifies universal slow dynamics in participation and stabilizer entropy near phase transitions.

Findings

Participation and stabilizer entropy show critical slowing down with linear saturation time.

Logarithmic entanglement scaling observed along the critical line.

Similar slow dynamical behavior found in Clifford circuits at critical points.

Abstract

We study the participation and stabilizer entropy of non-unitary quantum circuit dynamics, focusing on the critical line that separates the low-entanglement spin-glass phase and the paramagnetic phase. Along this critical line, the entanglement has a logarithmic scaling, which enables us to access the critical regime using large-scale matrix product state simulations with modest bond dimension. We find that both the participation entropy and stabilizer entropy exhibit critical slowing down: their saturation time scales linearly with the system size, in stark contrast to purely unitary dynamics, where saturation occurs on logarithmic time scales. In addition, we study bipartite participation and stabilizer mutual information, and find that it shows similar scaling behavior to the entanglement entropy. Finally, by analyzing the participation entropy of several paradigmatic Clifford circuits, we identify similar slow dynamical behavior near their respective critical points.