Critical Behaviour in the Dense Planar NJL Model

TL;DR

This study uses Monte Carlo simulations to explore the critical behavior and fermionic properties of a 2+1D NJL model, revealing a critical system with no superfluidity and a sharp Fermi surface.

Contribution

It provides the first detailed analysis of diquark condensate scaling and fermionic dispersion in the dense planar NJL model, highlighting critical phenomena without superfluidity.

Findings

Diquark condensate vanishes linearly in vacuum

Power-law scaling indicates a critical system at high density

Fermionic excitations show a sharp Fermi surface

Abstract

We present results of a Monte Carlo simulation of a 2+1 dimensional Nambu - Jona-Lasinio model including diquark source terms. A diquark condensate <qq> is measured as a function of source strength j. In the vacuum phase <qq> vanishes linearly with j as expected, but simulations in a region with non-zero baryon density suggest a power-law scaling and hence a critical system for all mu > mu_c. There is no diquark condensation signalling superfluidity. Comparisons are drawn with known results in two dimensional theories, and with the pseudogap phase in cuprate superconductors. We also measure the dispersion relation E(k) for fermionic excitations, and find results consistent with a sharp Fermi surface. Any superfluid gap Delta is constrained to be much less than the constituent quark mass scale Sigma_0.