LOW-DENSITY REPULSIVE FERMI GAS IN 2 DIMENSIONS - BOUND-PAIR EXCITATIONS AND FERMI-LIQUID BEHAVIOR

We study the dilute-gas expansion for a two-dimensional Fermi system with arbitrary short-range repulsive interactions. In contrast with the three-dimensional case, we find an unusual pole in the vertex part in the particle-particle channel, for all center-of-mass momenta q < 2k(F). We show that this represents an excitation consisting of bound hole pairs, which disperses down to zero energy at q = 2k(F). We study the effect of these bound states on the single-particle self-energy and find that the quasiparticles are well defined. Thus in the low-density regime, there is no breakdown of Fermi-liquid theory. In the Appendix we discuss the two-particle phase shift in the dilute Fermi gas, its connection with bound states, and the analogy with the potential scattering phase shift.