Multiversality and Unnecessary Criticality in One Dimension

Abstract: We present microscopic models of spin ladders which exhibit continuous critical surfaces whose properties and existence, unusually, cannot be inferred from those of the flanking phases. These models exhibit either multiversality' -- the presence of different universality classes over finite regions of a critical surface separating two distinct phases -- or its close cousin,unnecessary criticality'-- the presence of a stable critical surface within a single, possibly trivial, phase. We elucidate these properties using Abelian bosonization and density-matrix renormalization-group simulations, and attempt to distill the key ingredients required to generalize these considerations.