Vector Meson at Non - Zero Baryon Density and Zero Sound

We present simulation results of the (2 + 1)d four-fermion model with a baryon chemical potential µ. We examine temporal correlation functions of the vector me-son, and find evidence of phonon-like behavior characterised by a linear dispersion relation in the long wavelength limit. We also discuss the consistency of our numerical results with analytical solutions to the Boltzmann equation corresponding to zero sound. We argue that our results provide the first evidence for a collective excitation in a lattice simulation. We study the (2 + 1)d Gross-Neveu (GN) model with a Z 2 chiral symmetry describing N f flavors of self-interacting fermions, with continuum lagrangian L = ¯ ψ(∂ / + µγ 0)ψ − g 2 2N f (¯ ψψ) 2. (1) As µ is increased, the model exhibits a sharp first-order transition at a critical µ c from a phase where a fermion mass m f is dynamically generated but baryon density n B = ¯ ψγ 0 ψ vanishes to one where m f = 0 and n B ∝ µ 2 [1]. The main new feature emerging for µ > µ c is the existence of a new scale, the Fermi momentum k F. Since the lowest energy excitations of the ground state have | k| ≈ k F , measurements of Euclidean timeslice correlators with k = 0 are mandatory. If certain conditions are fulfilled, such as an effective interaction between quasiparticles which is both short-ranged and repulsive, then there is a massless bosonic excitation in the spectrum as T → 0. Carrying zero baryon number, it is a phonon, ie. a quantum of a collective excitation