We study the critical properties of random quantum circuits with a
U(1) symmetry subject to local projective measurements that explicitly break this symmetry. We find that, at the measurement-induced phase transition, symmetry-breaking measurements act as a relevant perturbation at large scales, leading to the same universal critical properties as the corresponding monitored random circuit with non-symmetric unitary dynamics. In particular, we consider monitored
U(1)-symmetric Haar-random circuits in the limit of large local Hilbert-space dimension, where the trajectory-averaged entanglement entropy can be exactly obtained in terms of a classical statistical mechanics model. In this model, the charge associated with the conservation law follows a symmetric simple exclusion process, in which symmetry-breaking measurements correspond to disordered defects that create and destroy charges. We prove that the charge correlation length remains finite for any measurement rate, ruling out a charge-sharpening transition, in contrast to the case of symmetry-preserving measurements. We further support our predictions at finite local Hilbert-space dimension through numerical finite-size scaling analyses of the entanglement transition in monitored
U(1)-symmetric Haar and stabilizer random circuits.
We study the critical properties of random quantum circuits with a
U(1) symmetry subject to local projective measurements that explicitly break this symmetry. We find that, at the measurement-induced phase transition, symmetry-breaking measurements act as a relevant perturbation at large scales, leading to the same universal critical properties as the corresponding monitored random circuit with non-symmetric unitary dynamics. In particular, we consider monitored
U(1)-symmetric Haar-random circuits in the limit of large local Hilbert-space dimension, where the trajectory-averaged entanglement entropy can be exactly obtained in terms of a classical statistical mechanics model. In this model, the charge associated with the conservation law follows a symmetric simple exclusion process, in which symmetry-breaking measurements correspond to disordered defects that create and destroy charges. We prove that the charge correlation length remains finite for any measurement rate, ruling out a charge-sharpening transition, in contrast to the case of symmetry-preserving measurements. We further support our predictions at finite local Hilbert-space dimension through numerical finite-size scaling analyses of the entanglement transition in monitored
U(1)-symmetric Haar and stabilizer random circuits.
The interplay of unitary evolution and projective measurements is a modern interest in the study of many-body entanglement. On the one hand, the competition between these two processes leads to the recently discovered measurement-induced phase transition (MIPT). On the other hand, measurement-based quantum computation (MBQC) is a well-known computational paradigm where measurements simulate unitary evolution by utilizing the entanglement of special resources such as the two-dimensional (2D) cluster state. The entanglement properties enabling MBQC may be attributed to symmetry-protected topological (SPT) orders, particularly subsystem-symmetry-protected topological (SSPT) orders. It was recently found that the one-dimensional cluster state may be associated with an SPT phase in random circuits respecting a global ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry, and furthermore that all phase transitions in this scenario belong to the same universality class. As resources with greater computational power feature greater symmetry, it is fruitful to investigate further any relationship between levels of symmetry in MIPTs and MBQC. In this paper we investigate MIPTs on a torus with three levels of symmetry-respecting unitary evolution interspersed by measurements. Although we find two area-law phases and one volume-law phase with distinct entanglement structures for each ensemble, the phase transition from the volume-law phase to the area-law phase associated with the 2D SSPT cluster state has variable correlation length exponent $\ensuremath{\nu}$. Whereas $\ensuremath{\nu}\ensuremath{\approx}0.90$ for unconstrained Clifford unitaries and $\ensuremath{\nu}\ensuremath{\approx}0.83$ for globally symmetric Cliffords, subsystem-symmetric Cliffords feature a much smaller value $\ensuremath{\nu}\ensuremath{\approx}0.38$. We discuss how these distinct $\ensuremath{\nu}$'s quantify spacetime response scales where quantum information is manipulated by single-qubit measurements as in MBQC.