Abstract
The phase diagram of the two-dimensional Nambu-Jona-Lasinio (or chiral Gross-Neveu) model is characterized by an order parameter in the form of a chiral spiral. Its radius vanishes at a critical temperature, its period depends only on the chemical potential. We generalize these findings to chirally imbalanced systems by including a chiral chemical potential $\mu_5$. The relationship between the present, static approach and a previous, time dependent one is traced back to a half-local symmetry which the NJL$_2$ model shares with massless Dirac fermions, but which has been neglected so far. The structure of chiral spiral matter is further elucidated by computing fermion and antifermion momentum distribution functions, using a Bogoliubov transformation.
Highlights
Much can be learned from exactly solvable quantum field theories such as the Gross-Neveu model [1]
We have presented the full phase diagram of the NJL2 model in (μ, μ5, T) space
Without chiral imbalance (μ5 1⁄4 0), it has been known for some time that the physics is strongly dominated by a chiral spiral type mean field
Summary
Much can be learned from exactly solvable quantum field theories such as the Gross-Neveu model [1]. The motivation stems primarily from the chiral magnetic effect and other potentially observable signals from the chiral anomaly in ultrarelativistic heavy ion collisions, compact stars, or quasirelativistic condensed matter systems (for a recent review, see [6]) This incites us to revisit the chiral spiral in the context of chiral imbalance, even if this is not directly relevant for real physical systems. The full phase diagram in (T, μ, μ5) space is determined in a variational calculation, using as ansatz potentials of chiral spiral type We shall compare this approach to the present one at the end of Sec. II. We clarify the physics content of the chiral spiral state of matter by evaluating new observables, namely momentum distributions of “quarks” and “antiquarks.” The relation between the present static approach and the time-dependent one of Ref.
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