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

TL;DR

This paper investigates how monitored quantum circuits with charge and dipole conservation exhibit phases where global charges can be either easily or hard to learn from local measurements, revealing a complex phase diagram with symmetry-breaking phenomena.

Contribution

It introduces a detailed phase diagram of monitored dipole-conserving quantum circuits, highlighting the spontaneous breaking of strong symmetries to weak symmetries and their information-theoretic implications.

Findings

Charge is always easy to learn in 1D.

Dipole moment can be either easy or hard to learn in 1D.

In 2D, measurement rate controls phases where both charges are easy or hard to learn.

Abstract

We explore the information-theoretic phases of monitored quantum circuits subject to dynamics that conserves both charge and dipole moment, as well as measurements of the local charge density. Explicitly, both charge and dipole-moment conservation are strong symmetries, but under the dynamics they can be spontaneously broken to weak symmetries: this spontaneous symmetry breaking has an information-theoretic interpretation in terms of whether one can learn global charges from local measurements. We find a rich phase diagram: in one spatial dimension, charge is always easy to learn, while dipole moment can be either easy or hard. In two dimensions, we find three phases: for frequent measurements, both charge and dipole moment are easy to learn; as the measurement rate is decreased, first dipole moment and then charge become hard. In two dimensions, the low-measurement phase is an exotic critical phase with anisotropic spacetime scaling, analogous to a smectic liquid crystal.