Continuous symmetry breaking of low-dimensional systems driven by inhomogeneous oscillatory driving forces

Abstract: The driving forces of chiral active particles and deformations of cells are often modeled by spatially inhomogeneous but temporally periodic driving forces. Such inhomogeneous oscillatory driving forces have only recently been proposed in the context of active matter, and their effects on the systems are not yet fully understood. In this work, we theoretically study the impact of spatially inhomogeneous oscillatory driving forces on continuous symmetry breaking. We first analyze the linear model for the soft modes in the ordered phase to derive the lower critical dimension of the model, and then analyze the spherical model to investigate more detailed phase behaviors. Interestingly, our analysis reveals that symmetry breaking occurs even in one and two dimensions, where the Hohenberg--Mermin--Wagner theorem prohibits continuous symmetry breaking in equilibrium. Furthermore, fluctuations of conserved quantities, such as density, are anomalously suppressed in the long-wavelength, {\it i.e.}, show hyperuniformity.