Truncation of a Two-Dimensional Fermi Surface due to Quasiparticle Gap Formation at the Saddle Points

We study a two-dimensional Fermi liquid with a Fermi surface containing the saddle points $(\pi ,0\mathrm{})$ and $(0,\pi )$. Including Cooper and Peierls channel contributions leads to a one-loop renormalization group flow to strong coupling for short range repulsive interactions. In a certain parameter range the characteristics of the fixed point, opening of a spin and charge gap, and dominant pairing correlations are similar to those of a two-leg ladder at half-filling. We argue that an increase of the electron density leads to a truncation of the Fermi surface to only four disconnected arcs.