Functional Bosonization of Non-Relativistic Fermions in $(2+1)$ Dimensions

Details Functional Bosonization of Non-Relativistic Fermions in $(2+1)$ Dimensions Functional Bosonization of Non-Relativistic Fermions in $(2+1)$ Dimensions

1999-07-13

arxiv.org/abs/cond-mat/9907193v4

Int.J.Mod.Phys.A15:4655-4680,2000

Physics

Condensed Matter

Strongly Correlated Electrons

26 Pages, LaTeX, Final version to appear in International Journal of Modern Physics A

Scientific paper

10.1142/S0217751X00002032

We analyze the universality of the bosonization rules in non-relativistic fermionic systems in $(2+1)d$. We show that, in the case of linear fermionic dispersion relations, a general fermionic theory can be mapped into a gauge theory in such a way that the fermionic density maps into a magnetic flux and the fermionic current maps into a transverse electric field. These are universal rules in the sense that they remain valid whatever the interaction considered. We also show that these rules are universal in the case of non-linear dispersion relations provided we consider only density-density interactions. We apply the functional bosonization formalism to a non-relativistic and non-local massive Thirring-like model and evaluate the spectrum of collective excitations in several limits. In the large mass limit, we are able to exactly calculate this spectrum for arbitrary density-density and current-current interactions. We also analyze the massless case and show that it has no collective excitations for any density-density potential in the Gaussian approximation. Moreover, the presence of current interactions may induce a gapless mode with a linear dispersion relation.

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