  As recently shown, the ground state of dense QCD matter in a strong magnetic
field is an inhomogeneous condensate of neutral pions which was named Chiral
Soliton Lattice (CSL) phase in analogy with a state present for chiral magnets.
We continue this work by showing that similar phase is present for a class of
QCD-like theories which are accessible to standard lattice Monte-Carlo
simulations unlike the QCD itself which suffers from the notorious sign problem
if non-zero baryon chemical potential is considered. On the occasion of the
Gravitation session of the Moriond conference we also briefly comment on the
possible relevance of the CSL phase for neutron stars and gravitational wave
observations.
