The U(1) Gross-Neveu Model at Non-Zero Chemical Potential

TL;DR

This study investigates the U(1) Gross-Neveu model at non-zero chemical potential using analytical and computational methods, revealing symmetry breaking and restoration phenomena relevant to lattice QCD.

Contribution

It combines $1/N_f$ expansion and computer simulations to analyze phase transitions in the model at finite chemical potential, providing new insights into chiral symmetry behavior.

Findings

Critical chemical potential close to the lightest fermion mass.

Rapid increase in pion screening mass beyond critical point.

Insights relevant to lattice QCD at non-zero chemical potential.

Abstract

The four-fermi model with continuous chiral symmetry is studied in three dimensions at non-zero chemical potential $\mu$ using both the $1/N_f$ expansion and computer simulations. For strong coupling this model spontaneously breaks its U(1) chiral symmetry at zero chemical potential and the Goldstone mechanism is realized through massless pions. The computer simulation predicts a critical chemical potential $\mu_c$ close to the lightest fermion mass in the model. As $\mu$ is increased beyond $\mu_c$, the pion screening mass increases rapidly from zero to a nonvanishing value indicating symmetry restoration. Some lessons are drawn relevant to lattice QCD simulations at non-zero $\mu$.