Magnetic vortex lattices in finite isospin chiral perturbation theory

Abstract

We study finite isospin chiral perturbation theory (χPT) in a uniform external magnetic field and find the condensation energy of magnetic vortex lattices using the method of successive approximations (originally used by Abrikosov) near the upper critical point beyond which the system is in the normal vacuum phase. The difference between standard Ginzburg-Landau (GL) theory (or equivalently the Abelian Higgs model) and χPT arises due to the presence of additional momentum-dependent (derivative) interactions in χPT and the presence of electromagnetically neutral pions that interact with the charged pions via strong interactions but do not couple directly to the external magnetic field. We find that while the vortex lattice structure is hexagonal similar to vortices in GL theory, the condensation energy (relative to the normal vacuum state in a uniform, external magnetic field) is smaller (larger in magnitude) due to the presence of derivative interactions. Furthermore, we establish that neutral pions do not condense in the vortex lattice near the upper critical field.

Pion and kaon condensation at zero temperature in three-flavor χPT at nonzero isospin and strange chemical potentials at next-to-leading order

“…[5,[14][15][16][17][18][19] one can find various applications of χPT including some partial next-to-leading order results. Since then finite isospin systems have been studied extensively in other versions of QCD including two-color and adjoint QCD [20,21], in the NJL [22][23][24][25][26][27][28][29][30][31][32][33][34], in the quark-meson model [35][36][37][38], but also through lattice QCD, where it does not suffer from the fermion sign problem (except at finite magnetic fields [39,40] due to the charge asymmetry of the up and down quarks). The first lattice QCD calculations of finite isospin QCD were done in refs.…”

Quark and pion condensates at finite isospin density in chiral perturbation theory

“…for values of |μ I | ≤ μ c I ≡ m π it vanishes, while for larger values of μ I , it is nonzero and we enter the pion-condensed phase of QCD. It is further known that pion condensates due to their electromagnetic charge form currents in a superconducting phase when a weak external magnetic field is present [20,21]. For larger magnetic fields, the pion condensate attains a spatially inhomogeneous structure in the form of a single vortex or a triangular vortex lattice similar in nature to the vortex lattice in type-II superconductors [22,23] explained by BCS theory [4].…”

Two-flavor chiral perturbation theory at nonzero isospin: pion condensation at zero temperature

“…The complex action problem is tackled by studying finite isospin densities for small magnetic fields, where the sign problem is mild. The lattice observes a diamagnetic phase [44], while studies in chiral perturbation theory valid for magnetic fields eB (4π f π ) 2 suggests that pions behave as a type-II superconductor [45].…”