Non-local Thirring model with backward and umklapp interactions

V FERNÁNDEZ; C IUCCI; C NAÓN

NUCLEAR PHYSICS B

ELSEVIER SCIENCE BV

Año: 2002 vol. 636 p. 514 - 528

0550-3213

We extend a non-local and non-covariant version of the Thirring model in order to describe amany-body system with backward and umklapp scattering processes. We express the vacuum tovacuum functional in terms of a non-trivial fermionic determinant. Using path-integral methods wefind a bosonic representation for this determinant which allows us to obtain an effective action forthe collective excitations of the system. By introducing a non-local version of the self-consistentharmonic approximation, we get an expression for the gap of the charge-density excitations asfunctional of arbitrary electron–electron potentials. As an example we also consider the case of anon-contact umklapp interaction.