Phase Boundary of Nuclear Matter in Magnetic Field

Nuclear matter with a strong magnetic field is prevalent inside neutron stars and heavy-ion collisions. In a sufficiently large magnetic field the ground state is either a chiral soliton lattice (CSL), an array of solitons of the neutral pion field, or a domain-wall Skyrmion phase in which Skyrmions emerge inside the chiral solitons. In the region of large chemical potential and a magnetic field lower than its critical value for CSL, a Skyrmion crystal is expected to take up the ground state based on the chiral perturbation theory at the next leading order. We determine the phase boundary between such a Skyrmion crystal and the QCD vacuum. There was a conjecture that a magnetic field deforms the Skyrmion into a pancake shape whose boundary is a superconducting ring of charged pions. In contrast, through the exact Skyrmion solution, we find that the pancake conjecture holds approximately in a strong magnetic field, but fails for a weak one. We also validate that a Skyrmion would shrink to null without the Skyrme term, although Derrick's scaling law is modified by a background magnetic field, and the stability at the leading order is not ruled out in theory.