Abstract
The ground state of QCD in sufficiently strong magnetic fields and at nonzero baryon chemical potential is a topological crystal made of neutral pions: the Chiral Soliton Lattice (CSL). Due to its topological nature, it carries nonzero baryon number density that can reach values relevant for the cores of neutron stars. The spectrum of excitations above the CSL ground state contains a soft, nonrelativistic mode that gives an anomalous contribution to pressure, scaling with temperature and magnetic field as $T^{5/2}B^{3/2}$. In stronger but still achievable magnetic fields, the neutral pion CSL background may catalyze Bose-Einstein condensation of charged pions.
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