The TBA, the Gross-Neveu Model, and Polyacetylene

We summarize recent work showing how the Thermodynamic Bethe Ansatz may be used to study the finite-density first-order phase transition in the Gross-Neveu model. The application to trans-polyacetylene is discussed, and the significance of the results is addressed. In this contribution, rather than simply repeat what is contained in the literature, we should like to attempt to place this work in context, and to emphasize those points that are either the most novel or the most inviting of further investigation. Details of calculation can be found in the published references (Chodos and Minakata 1994, 1997). This work brings together three disparate elements: the Gross-Neveu (GN) model, the thermodynamic Bethe Ansatz (TBA), and the phenomenology of polyacetylene ((CH)x). Polyacetylene is essentially a linear chain which comes in two forms, dubbed trans and cis. The trans form, which is the more stable, has a doublydegenerate ground state. It is this circumstance that allows for the existence of topological excitations, or solitons, and these lead in turn to a rich phenomenology. An excellent review of polyacetylene and other similar polymers is the article in Reviews of Modern Physics by Heeger, Kivelson, Schrieffer and Su (1988). It was realized long ago, by Takayama, Lin-liu and Maki (1980) and by Campbell and Bishop (1982), that in the continuum limit, and in an approximation that ignores the dynamics of the lattice vibrations, the insulatormetal transition in polyacetylene can be described by the N = 2 Gross-Neveu model, i.e. by the Lagrangian density L = ψ̄i 6 δψ − gσψ̄ψ − 1