Strong-to-weak symmetry breaking in monitored dipole conserving quantum circuits

In monitored quantum circuits with conserved charge and dipole moment we investigate non-equilibrium phases, that exhibit either strong symmetries on the level of individual quantum states or weak symmetries on the level of the ensemble.

These phases are revealed through circuit- and measurement-averaged correlation functions acting on multiple copies of the density matrix but remain hidden in (multiple copies of) the averaged density matrix itself. In 1+1D, any nonzero measurement rate enforces strong charge symmetry, while a transition between weak and strong dipole symmetry occurs at a finite measurement rate. In 2+1D, we argue that a rich hierarchy of transitions arises for charge and dipole.

Our work on monitored circuits with unconventional symmetries furthers the understanding of the rich landscape of non-equilibrium phases of matter.