Chiral density waves in the NJL${}_2$ model with quark number and isospin chemical potentials

Abstract

We investigate the phase portrait of the (1+1)-dimensional massless two-flavored NJL${}_2$ model containing a quark number chemical potential $\mu$ and an isospin chemical potential ${\mu }_I$ in the limit of a large number of colors $N_c\to \infty$. Particular attention is paid to the question to what extent the inclusion of an isospin asymmetry affects chiral condensates to have a spatial inhomogeneity in the form of the so-called chiral density waves (CDW) (chiral spirals). It is shown that at zero temperature and comparatively small values of $\mu$, i.e. at $\mu <{\mu }_c\approx 0.68M_0$ ($M_0$ is the dynamical quark mass in the vacuum) only the homogeneous charged pion condensation phase is realized for arbitrary nonzero values of ${\mu }_I$. Contrary to this, for large values of $\mu >{\mu }_c$, two CDW phases appear in the $({\mu }_I,\mu )$-phase diagram of the model. In the first phase, CDWs are clockwise twisted chiral spirals and in the second phase they are counterclockwise. The influence of nonzero temperature on the formation of the CDW phases is also investigated.

14 pages, 9 figures; typos corrected; one reference added

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Cited by in corpus (13)

• Inhomogeneous chiral condensates
• Fluctuations in the quark-meson model for QCD with isospin chemical potential
• Scrutinizing the pion condensed phase
• Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL${}_2$ model
• Dualities and inhomogeneous phases in dense quark matter with chiral and isospin imbalances in framework of effective model
• Duality between chiral symmetry breaking and charged pion condensation at large $N_c$: Consideration of an NJL${}_2$ model with baryon-, isospin- and chiral isospin chemical potentials
• Rotation induced charged pion condensation in a strong magnetic field: A Nambu--Jona-Lasino model study
• Competition and duality correspondence between inhomogeneous fermion-antifermion and fermion-fermion condensations in the NJL${}_2$ model
• Interplay between superconductivity and chiral symmetry breaking in a (2+1)-dimensional model with compactified spatial coordinate
• Quark beta decay in the inhomogeneous chiral phase and cooling of compact stars
• Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions
• Emergence of charge density wave and superconducting phase transitions through Lorentz-invariant interactions in the Haldane-Hubbard model
• Phase Transitions in Models with Discrete Symmetry