Fermi Surface Phenomena in the (2+1)d Four-Fermi Model

Details Fermi Surface Phenomena in the (2+1)d Four-Fermi Model Fermi Surface Phenomena in the (2+1)d Four-Fermi Model

2003-02-26

arxiv.org/abs/hep-lat/0302021v1

Phys.Rev. D68 (2003) 016005

Physics

High Energy Physics

High Energy Physics - Lattice

33 pages, 16 figures

Scientific paper

10.1103/PhysRevD.68.016005

We study the Gross-Neveu model in 2+1 dimensions with a baryon chemical potential mu using both analytical and numerical methods. For mu greater than a critical value the model is chirally symmetric and has a Fermi surface with Fermi momentum ~mu. We have calculated the particle interaction in medium due to scalar meson exchange to leading order in 1/N, where N is the number of flavors, in the hard dense loop approach. The result has been used to calculate the relation between mu and the Fermi momentum and velocity in the resulting Fermi liquid to O(1/N). Simulation results from a 32^2x48 lattice for fermion and meson dispersion relations and meson wavefunctions are then presented, showing qualitative and in some cases quantitative agreement with analytic predictions. In particular, the simulations show clear evidence for the in-medium modification of the scalar propagator, oscillatory behaviour in the wavefunction consistent with a sharp Fermi surface, and tentative evidence for a massless pole in the vector meson channel resembling zero sound.

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