  In this paper we investigate in the large-$N_c$ limit ($N_c$ is the number of
colored quarks) the phase structure of a massless (1+1)-dimensional quark model
with four-quark interaction and in the presence of baryon ($\mu_B$), isospin
($\mu_I$) and chiral isospin ($\mu_{I5}$) chemical potentials as well as at
nonzero temperature. It is established that chiral isospin chemical potential
leads to the generation of charged pion condensation (PC) in dense (nonzero
baryon density) and chiral asymmetric quark matter for a wide range of isospin
densities. It is shown that there exists a duality correspondence between the
chiral symmetry breaking and the charged PC phenomena at any values of
temperature even for very hot quark gluon plasma. Moreover, it is shown that
charged PC phase with nonzero baryon density can be induced in the model at
comparatively high temperatures. This opens up new possible physical systems,
where it can be of importance, such as heavy ion collisions, just born neutron
stars (proto-neutron stars), supernovas as well as neutron star mergers.
