Paths for Z_k parafermionic models
P. Jacob, P. Mathieu
TL;DR
This paper establishes a bijection between two types of lattice paths, linking RSOS paths and parafermionic states, thereby providing a new combinatorial understanding of Z_k parafermionic models.
Contribution
It introduces a simple bijection connecting Bressoud lattice paths and RSOS paths, clarifying the structure of Z_k parafermionic modules.
Findings
Bijection between Bressoud lattice paths and RSOS paths
Correspondence between paths and parafermionic states
Enhanced combinatorial understanding of Z_k models
Abstract
We present a simple bijection between restricted (Bressoud) lattice paths and RSOS paths in regime II. Both types of paths describe states in Z_k parafermionic irreducible modules. The bijection implies a direct correspondence between a RSOS path and a parafermionic state in a quasi-particle basis.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Physics of Superconductivity and Magnetism · Advanced Condensed Matter Physics