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arXiv:hep-th/9712210 · Nuclear Physics B

Non-local Thirring model at finite temperature

M. V. Manías, Carlos Naón, Marta L. Trobo

Published Aug 1, 1998• 8 citations
arXivHTMLPDF
DOI
10.1016/s0550-3213(98)00394-0

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Using the path-integral bosonization procedure at Finite Temperature we study the equivalence between a massive Thirring model with non-local interaction between currents (NLMT) and a non-local extension of the sine-Gordon theory (NLSG). To this end we make a perturbative expansion in the mass parameter of the NLMT model and in the cosine term of the NLSG theory in order to obtain explicit expressions for the corresponding partition functions. We conclude that for certain relationship between NLMT and NLSG potentials both the fermionic and bosonic expansions are equal term by term. This result constitutes a generalization of Coleman's equivalence at T=0, when considering a Thirring model with bilocal potentials in the interaction term at Finite Temperature. The study of this model is relevant in connection with the physics of strongly correlated systems in one spatial dimension. Indeed, in the language of many-body non-relativistic systems, the relativistic mass term can be shown to represent the introduction of backward-scattering effects.
We study, through path-integral methods, an extension of the massive Thirring model in which the interaction between currents is non-local. By examining the mass expansion of the partition function we show that this non-local massive Thirring model is equivalent to a certain non-local extension of the sine-Gordon theory. Thus, we establish a non-local generalization of the well known Coleman's equivalence. We also discuss some possible applications of this result in the context of one-dimensional strongly correlated systems and finite-size quantum field theories.
The thermodynamics of the massive Thirring model is discussed with the help of the Bethe Ansatz approach in a way different from Fowler and Zotos (1982). In particular a finite Debye cut-off is introduced to investigate effects of the lattice discreteness. The specific heat seems to have a structure as a sum of the Debye-type specific heat and a 'soliton' peak, when the authors take into account the relation of the massive Thirring model to the quantum sine-Gordon model. The finite temperature excitations are calculated. The excitation energy proposed by Fowler and Zotos is shown to have significance which is insensitive to the way of formulation.