Critical behavior in the dense planar Nambu--Jona-Lasinio model

Area of Science:

• Quantum Chromodynamics (QCD)
• Condensed Matter Physics
• High-Energy Physics

Background:

• The Nambu-Jona-Lasinio (NJL) model is a effective field theory used to study the low-energy properties of Quantum Chromodynamics.
• Understanding the phase structure of strongly interacting matter at finite baryon density is crucial for nuclear physics and astrophysics.

Purpose of the Study:

• To investigate the behavior of the diquark condensate and fermionic excitations in a (2+1)-dimensional NJL model at nonzero baryon density using Monte Carlo simulations.
• To explore the possibility of a critical system and superfluidity in this model.
• To compare the findings with the pseudogap phase in cuprate superconductors.

Main Methods:

• Monte Carlo simulation of a (2+1)-dimensional Nambu-Jona-Lasinio model.
• Analysis of the diquark condensate as a function of the diquark source j.
• Measurement of the dispersion relation E(k) for fermionic excitations.

Main Results:

• In the vacuum phase, the diquark condensate vanishes linearly with the diquark source j.
• At nonzero baryon density (mu > mu(c)), simulations suggest a power-law scaling proportional to j(alpha), indicating a critical system.
• No signal for superfluidity was observed.
• The dispersion relation E(k) is consistent with a sharp Fermi surface.
• Any energy gap Delta is significantly smaller than the constituent quark mass scale Sigma(0).

Conclusions:

• The (2+1)-dimensional NJL model exhibits critical behavior at nonzero baryon density, distinct from the vacuum phase.
• The absence of superfluidity and the presence of a sharp Fermi surface provide insights into the nature of strongly interacting matter.
• The findings offer a theoretical framework for understanding phenomena like the pseudogap phase in cuprate superconductors.