Fundamental Models on the Lattice

Jacques H. H. Perk, Fa Yueh Wu, X. N. Wu

The authors consider the O(2) gauge transformation for a two-state vertex model on a lattice, and derive its fundamental algebraic invariants, the minimal set of homogeneous polynomials of the vertex weights which are invariant under O(2) transformations. Explicit expressions of the fundamental invariants are given for symmetric vertex models on lattices with coordination number p=2, 3, 4, 5, 6, generalising p=3 results obtained previously from more elaborate considerations.

Hector J. de Vega, Esther Lopes

Kazuhiro Hikami, Rei Inoue

We investigate the integrable structure of the quantum Volterra model, which is a discretization of the Korteweg–de Vries equation. Based on Sklyanin's method we derive the Baxter equation, and then clarify a role of the “fundamental transfer matrix”. We show that the fundamental transfer matrix also generates the integrals of motion for a lattice analogue of the sine–Gordon system.

William A. Schwalm, Brian Moritz, Mizuho K. Schwalm +1 more

Zohar Nussinov

We prove that in short range Klein spin models on general lattices, all ground states are of the dimer type- each fundamental plaquette must host at least one singlet. These ground states are known to rigorously exhibit high dimensional fractionalization. When combined with a recent theorem, this establishes that Klein spin models exhibit topological order on the pyrochlore and checkerboard lattices.

R. J. Baxter