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

Abstract

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.

arXiv comment33 pages, 16 figures

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Cited by in corpus (17)

• Deconfinement in dense 2-color QCD
• Updating the Phase Diagram of the Gross-Neveu Model in 2+1 Dimensions
• Finite size effects in the Gross-Neveu model with isospin chemical potential
• Numerical Portrait of a Relativistic BCS Gapped Superfluid
• Lattice QCD at finite T and μ
• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions $1\le d<3$
• Collective excitations in a superfluid of color-flavor locked quark matter
• Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
• Review of Vector Condensation at High Chemical Potential
• The magnetized (2+1)-dimensional Gross-Neveu model at finite density
• Zero Lattice Sound
• Monte Carlo Study of Strongly-Interacting Degenerate Fermions: a Model for Voltage-Biased Bilayer Graphene
• Order from disorder in lattice QCD at high density
• High Density Effective Theory Confronts the Fermi Liquid
• Hadron Wavefunctions as a Probe of a Two Color Baryonic Medium
• Can we study Quark Matter in the Quenched Approximation?