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.

6+23 pages, 4+17 figures (main + supplementary material). v2: minor changes to main text, expanded supplementary materials, close to published version

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• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• "Deconfined" quantum critical points
• Intrinsically Gapless Topological Phases
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Cited by in corpus (11)

• Symmetry-Enriched Criticality in a Coupled Spin-Ladder
• Pivoting through the chiral-clock family
• Classical origins of Landau-incompatible transitions
• Dirac spin liquid as an "unnecessary" quantum critical point on square lattice antiferromagnets
• Charge pumps, boundary modes, and the necessity of unnecessary criticality
• Spectral Form Factors of Topological Phases
• Exploring quantum criticality and ergodicity-breaking dynamics in spin-1 Kitaev chains via single-ion anisotropies
• Terminable Transitions in a Topological Fermionic Ladder
• From $G_2$ to $SO(8)$: Emergence and reminiscence of supersymmetry and triality
• Unnecessary quantum criticality in $SU(3)$ kagome magnets
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice