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

TL;DR

This paper explores the competition between chiral soliton lattices and Abrikosov vortex lattices in QCD with isospin chemical potential, mapping their phase diagram and analyzing how external magnetic fields influence these states.

Contribution

It provides a detailed phase diagram of QCD phases involving chiral soliton and vortex lattices, using a novel numerical approach to solve the equations of motion.

Findings

Abrikosov vortex lattice phase exists between BEC and CSL phases.

The phase diagram's structure depends on the vacuum pion mass.

The study maps the competition between different QCD condensates under magnetic fields.

Abstract

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