Quasi-Particles in the Chiral Potts Model

Abstract

We study the quasi-particle spectrum of the integrable three-state chiral Potts chain in the massive phase by combining a numerical study of the zeroes of associated transfer matrix eigenvalues with the exact results of the ferromagnetic three-state Potts chain and the three-state superintegrable chiral Potts model. We find that the spectrum is described in terms of quasi-particles with momenta restricted only to segments of the Brillouin zone 0 ≤ P ≤ 2π where the boundaries of the segments depend on the chiral angles of the model. 5/94

Excitation spectrum and correlation functions of theZ3 chiral Potts quantum spin chain

“…2 we start considering the simple situation which occurs for a small value of λ, here in particular λ = 0.1, and a self-dual choice of the chiral angles φ = ϕ = π 4 well below the superintegrable line. The single-particle dispersion curves can be determined with high precision: the N = 12 finite-size value for E 1 (P ) agrees to better than 10 −4 with the value given by formula (7). Also the agreement in E 2 (P ) between N = 12 and perturbation theory is better than 10 −3 over the whole range of P .…”

“…2 (see Fig. 1) we have also noticed that for large λ the third order formula (7) does not describe the dispersion curve around the minimum.…”

“…Of course, we have to use the doubled Brillouin zone for P . In the perturbation formula (7) the first term to spoil the form ( 16) is the term ∼ λ 2 cos (2P − 2φ 3 ). For the parameters chosen in Fig.…”

“…We have noticed in [10] that in the high-temperature limit, the dispersion curve of the Q = 1-particle has its minimum at P min = Reφ/3, as it is obvious from the term of first order in λ of E 1 (P ), see eq. (7). The value of P min decreases with increasing λ: e.g.…”

A Critical Ising Model on the Labyrinth

“…On the other hand, numerous series of solvable vertex models [2,3] and IRF (Interaction-Round-a-Face) models [2,4] have been constructed. Furthermore, the so-called chiral Potts models [5,6] attracted a lot of interest, mainly due to the existence of superintegrable cases [5] (see also [7] and references therein) and applications to 3D systems [8].…”