Potential Flow of Renormalization Group in Quasi-One-Dimensional Systems

Abstract

We address the issue why the phase diagrams for quasi-one-dimensional systems are rather simple, while the renormalization group equations behind the scene are non-linear and messy looking. The puzzle is answered in two steps -- we first demonstrate that the complicated coupled flow equations are simply described by a potential $V(h_i)$, in an appropriate basis for the interaction couplings $h_i$. The renormalization-group potential is explicitly constructed by introducing the Majorana fermion representation. The existence of the potential prevents chaotic behaviors and other exotic possibilities such as limit cycles. Once the potential is obtained, the ultimate fate of the flows are described by a special set of fixed-ray solutions and the phase diagram is determined by Abelian bosonization. Extension to strong coupling regime and comparison with the Zamolodchikov c-theorem are discussed at the end.

Minor changes, final version to appear in Phys. Rev. B

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Cited by in corpus (10)

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• Scaling Theory of ${\mathbb{Z}}_2$ Topological Invariants
• Competing Orders and Hidden Duality Symmetries in Two-leg Spin Ladder Systems
• Duality approach to one-dimensional degenerate electronic systems
• Bipairing and the Stripe Phase in 4-Leg Ladders
• Phase diagrams of the metallic zigzag carbon nanotube
• Dynamical symmetry enlargement in metallic zigzag carbon nanotubes
• One-dimensional physics in transition-metal nanowires: Renormalization group and bosonization analysis
• Influence of electron-phonon coupling on low temperature phases of metallic single-wall carbon nanotubes