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Inhomogeneous Phase of the Chiral Gross-Neveu Model.

Riccardo Ciccone1, Lorenzo Di Pietro2, Marco Serone1

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Physical Review Letters
|August 26, 2022
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The chiral spiral phase in the 2D chiral Gross-Neveu model is shown to persist at finite N and zero temperature for any positive chemical potential. This inhomogeneous phase, characterized by a spatially periodic chiral condensate, is robust across different model parameters.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • High Energy Physics

Background:

  • The 2D chiral Gross-Neveu model is a fundamental model in quantum field theory.
  • Previous studies suggested a
  • chiral spiral
  • phase in the large N limit at finite chemical potential.
  • The stability of this phase at finite N and zero temperature was not fully established.

Purpose of the Study:

  • To investigate the persistence of the chiral spiral phase in the 2D chiral Gross-Neveu model at finite N and T=0.
  • To analyze the influence of a U(1) fermion number chemical potential (μ) on the model's ground state.
  • To provide a simplified explanation for the emergence of the inhomogeneous phase.

Main Methods:

  • Nonabelian bosonization to relate the Gross-Neveu model to a Wess-Zumino-Witten model.
  • Analysis of current-current interactions in the bosonized theory.
  • Direct diagrammatic computation to rederive the phase diagram.

Main Results:

  • The chiral spiral configuration is confirmed to persist at finite N and T=0 for all μ > 0.
  • Nonabelian bosonization offers a surprisingly simple description of the inhomogeneous phase.
  • Diagrammatic computations successfully reproduce the known phase diagram for the large N limit.

Conclusions:

  • The chiral spiral phase is a robust feature of the 2D chiral Gross-Neveu model under various conditions.
  • The nonabelian bosonization approach provides valuable insights into the model's complex behavior.
  • The findings contribute to a deeper understanding of phase transitions and ground states in quantum field theories.