Magnetic Vortex Lattices in Finite Isospin Chiral Perturbation Theory

Abstract

We study finite isospin chiral perturbation theory ($\chi$PT) 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 $\chi$PT arises due to the presence of additional momentum-dependent (derivative) interactions in $\chi$PT 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.

9 pages, 4 figures

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• Physics of Strongly Magnetized Neutron Stars
• QCD phase diagram for nonzero isospin-asymmetry
• The chiral condensate in a constant electromagnetic field
• Gauge k-vortices
• Magnetic structure of isospin-asymmetric QCD matter in neutron stars
• Pion condensation and phase diagram in the Polyakov-loop quark-meson model
• The chiral condensate in a constant electromagnetic field at O(p^6)
• Finite Isospin Chiral Perturbation Theory in a Magnetic Field
• Finite Density Two Color Chiral Perturbation Theory Revisited
• Vortex solutions in the Abelian Higgs Model with a neutral scalar
• Magnetic Vortices in the Abelian Higgs Model with Derivative Interactions
• Spontaneous electromagnetic superconductivity of vacuum induced by a strong magnetic field: QCD and electroweak theory

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• Competition of chiral soliton lattice and Abrikosov vortex lattice in QCD with isospin chemical potential
• Quark and pion condensates at finite isospin density in chiral perturbation theory
• Quark, pion and axial condensates in three-flavor finite isospin chiral perturbation theory
• Do charged pions condense in a magnetic field with rotation?
• Heavy-quark spin polarization induced by the Kondo effect in a magnetic field
• Phonon modes of magnetic vortex lattices in finite isospin chiral perturbation theory
• Strongly interacting matter in extreme magnetic fields
• Multicomponent superfluidity in two-color QCD at finite density at next-to-leading order
• Chiral Symmetry Breaking and Pion Decay in a Magnetic Field