Abstract
We calculate the fermion Green function and particle-hole susceptibilities for a degenerate two-dimensional fermion system with a singular gauge interaction. We show that this is a strong-coupling problem, with no small parameter other than the fermion spin degeneracy N. We consider two interactions, one arising in the context of the t-J model and the other in the theory of half-filled Landau level. For the fermion self-energy we show that the qualitative behavior found in the leading order of perturbation theory is preserved to all orders in the interaction. The susceptibility at a general wave vector Q≠2 retains the Fermi-liquid form. However, the 2 susceptibility either diverges as T→0 or remains finite but with nonanalytic wave-vector, frequency, and temperature dependence. We express our results in the language of recently discussed scaling theories, give the fixed-point action, and show that at this fixed point the fermion-gauge-field interaction is marginal in d=2, but irrelevant at low energies in d≥2.
- Received 3 June 1994
DOI:https://doi.org/10.1103/PhysRevB.50.14048
©1994 American Physical Society