Competition of chiral soliton lattice and Abrikosov vortex lattice in QCD with isospin chemical potential

Abstract We investigate the thermodynamics of two-flavor quark matter in presence nonzero isospin chemical potential and external magnetic field. It is known that at sufficiently high potential, charged pions undergo Bose–Einstein condensation (BEC). The condensate behaves as a superconductor, exhibiting Meissner effect weak fields. Stronger fields stress superconducting state, turning it first into an Abrikosov lattice vortices, eventually destroying altogether. On other hand, for strong low-to-moderate ground state quantum chromodynamics (QCD) expected to be spatially modulated neutral pions, induced by chiral anomaly: soliton (CSL). map phase diagram QCD function field part parameter space accessible low-energy effective theory description QCD. Our main result explicit account competition between CSL vortex lattice. This accomplished adopting fast numerical algorithm finding solution equation motion corresponding Gibbs energy. find persists diagram, separating uniform pion BEC from phase. precise layout depends sensitively on choice vacuum mass.