  We consider a version of the Gross-Neveu model in 1+1 dimensions with
discrete chiral and continuous flavor symmetry (isospin). In 2+1 dimensions,
this model is known as chiral Heisenberg Gross-Neveu model. Spontaneous
symmetry breaking and the emergence of two massless and one massive scalar
bosons are shown. A duality to the Nambu--Jona-Lasinio model with isospin is
exhibited, provided that the isovector pseudoscalar mean field is constrained
to a plane in isospin space. This enables us to find the phase diagram as a
function of temperature, chemical potential and isospin chemical potential as
well as twisted kinks. A bare mass term acts quite differently when added to
this model as compared to other chiral variants of the Gross-Neveu model.
