Chiral spiral in the presence of chiral imbalance

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.

11 pages, 13 figures, v2: Extended comparison with previous works, 2 references added, typos corrected

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Cited by in corpus (8)

• Charged pion condensation and duality in dense and hot chirally and isospin asymmetric quark matter in the framework of NJL${}_2$ model
• Phase structure of the 1+1 dimensional Nambu--Jona-Lasinio model with isospin
• Inhomogeneous phases in the chirally imbalanced $2+1$-dimensional Gross-Neveu model and their absence in the continuum limit
• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
• Revisiting the spatially inhomogeneous condensates in the $(1+1)$-dimensional chiral Gross-Neveu model via the bosonic two-point function in the infinite-$N$ limit
• Functional renormalization of QCD in $1+1$ dimensions: four-fermion interactions from quark-gluon dynamics
• Existence of a supersymmetric extension of the gauged non-linear $\Sigma$-model and the transition from integrability to chaos