Fused Potts Models

Abstract

Generalizing the mapping between the Potts model with nearest neighbor interaction and six vertex model, we build a family of "fused Potts models" related to the spin $k/2$ ${\mathrm{U}}_q\mathrm{su}(2)$ invariant vertex model and quantum spin chain. These Potts model have still variables taking values $1,\dots ,Q$ ($\sqrt{Q}=q+q^{-1}$) but they have a set of complicated multi spin interactions. The general technique to compute these interactions, the resulting lattice geometry, symmetries, and the detailed examples of $k=2,3$ are given. For $Q>4$ spontaneous magnetizations are computed on the integrable first order phase transition line, generalizing Baxter's results for $k=1$. For $Q\le 4$, we discuss the full phase diagram of the spin one ($k=2$) anisotropic and ${\mathrm{U}}_q\mathrm{su}(2)$ invariant quantum spin chain (it reduces in the limit $Q=4$ ($q=1$) to the much studied phase diagram of the isotropic spin one quantum chain). Several critical lines and massless phases are exhibited. The appropriate generalization of the Valence Bond State method of Affleck et al. is worked out.

60 pages and 39 figures, uuencoded, tar, compressed Latex files, YCTP-P44-92,USC-93-013

Cited by in corpus (15)

• Enlarged symmetry algebras of spin chains, loop models, and S-matrices
• Anyonic quantum spin chains: Spin-1 generalizations and topological stability
• Indecomposability parameters in chiral Logarithmic Conformal Field Theory
• Continuum limit and symmetries of the periodic gl(1|1) spin chain
• Hecke algebraic approach to the reflection equation for spin chains
• Exact S-matrices for supersymmetric sigma models and the Potts model
• The Temperley-Lieb algebra and its generalizations in the Potts and XXZ models
• Associative algebraic approach to logarithmic CFT in the bulk: the continuum limit of the gl(1|1) periodic spin chain, Howe duality and the interchiral algebra
• Lattice W-algebras and logarithmic CFTs
• Entanglement in valence-bond-solid states on symmetric graphs
• Ground state energy and mass gap of a generalised quantum spin ladder
• The Bubble Algebra: Structure of a Two-Colour Temperley-Lieb Algebra
• Elaborating the phase diagram of spin-1 anyonic chains
• Integrability in anyonic quantum spin chains via a composite height model
• $U_q[OSp(3|2)]$ quantum chains with quantum group invariant boundaries