On the low energy properies of fermions with singular interactions

TL;DR

This paper analyzes the low-energy properties of two-dimensional fermions with singular gauge interactions, revealing strong coupling behavior, non-Fermi liquid susceptibilities, and fixed-point characteristics relevant to condensed matter systems.

Contribution

It provides a nonperturbative analysis of fermion Green functions and susceptibilities in singular gauge fields, clarifying their behavior at all orders and identifying the fixed-point nature of the interaction.

Findings

Fermion self energy behavior is preserved beyond leading order.

The susceptibility at wavevector not equal to 2p_F remains Fermi-liquid like.

The 2p_F susceptibility diverges or shows nonanalytic behavior at low temperatures.

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 in contrast to previous claims that the qualitative behavior found in the leading order of perturbation theory is preserved to all orders in the interaction. The susceptibility $\chi_Q$ at a general wavevector $\bf{Q} \neq 2\bf{p_F}$ retains the fermi-liquid form. However the $2p_F$ susceptibility $\chi_{2p_F}$ either diverges as $T -> 0$ or remains finite but with nonanalytic wavevector, 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 $d \ge 2$.