A mean-field description of strong-to-weak symmetry breaking in the monitored Bose-Hubbard model

Abstract

Strong-to-weak spontaneous symmetry breaking has emerged as a novel form of ordering in monitored and open quantum systems, yet its characterization has so far primarily relied on nonlocal diagnostics. Here, we develop a Gutzwiller mean-field framework for monitored bosonic lattice systems, enabling the direct simulation of stochastic measurement dynamics in three spatial dimensions. Applying this approach to the monitored Bose-Hubbard model with local density measurements and Lindbladian dissipation, we identify strong-to-weak symmetry breaking through a trajectory-averaged local order parameter. We find that this local order parameter becomes critical near the critical measurement strength as the charge-sharpening transition. Both transitions exhibit a dynamical exponent $z=2$ in the dilute limit with a correlation length $ν\simeq 0.6$, comparable to that of the charge-sharpening transition, suggesting that the two phenomena may originate from a common underlying critical point. Our work shows a local characterization of strong-to-weak symmetry breaking, reveals its connection to charge sharpening, and provides concrete predictions for future experiments on the monitored Bose-Hubbard model.