Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice

Abstract

QCD matter in strong magnetic field exhibits a rich phase structure. In the presence of an external magnetic field, the chiral Lagrangian for two flavors is accompanied by the Wess-Zumino-Witten (WZW) term containing an anomalous coupling of the neutral pion ${\pi }_0$ to the magnetic field via the chiral anomaly. Due to this term, the ground state is inhomogeneous in the form of either chiral soliton lattice (CSL), an array of solitons in the direction of magnetic field, or domain-wall Skyrmion (DWSk) phase in which Skyrmions supported by ${\pi }_3[\mathrm{SU}(2)]\simeq \mathbb{Z}$ appear inside the solitons as topological lumps supported by ${\pi }_2(S^2)\simeq \mathbb{Z}$ in the effective worldvolume theory of the soliton. In this paper, we determine the phase boundary between the CSL and DWSk phases beyond the single-soliton approximation, within the leading order of chiral perturbation theory. To this end, we explore a domain-wall Skyrmion chain in multiple soliton configurations. First, we construct the effective theory of the CSL by the moduli approximation, and obtain the $\mathbb{C}{P}^1$ model or O(3) model, gauged by a background electromagnetic gauge field, with two kinds of topological terms coming from the WZW term: one is the topological lump charge in 2+1 dimensional worldvolume and the other is a topological term counting the soliton number. Topological lumps in the 2+1 dimensional worldvolume theory are superconducting rings and their sizes are constrained by the flux quantization condition. The negative energy condition of the lumps yields the phase boundary between the CSL and DWSk phases. We find that a large region inside the CSL is occupied by the DWSk phase, and that the CSL remains metastable in the DWSk phase in the vicinity of the phase boundary.

21 pages, 2 figures, v2: references added, v3: typos corrected, published version

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Cited by in corpus (10)

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• Skyrmion crystal phase on a magnetic domain wall in chiral magnets
• Solitonic ground state in supersymmetric theory in background
• Domain Wall Networks as Skyrmion Crystals in Chiral Magnets
• Creation of domain-wall Skyrmions in chiral magnets
• Holographic QCD Matter: Chiral Soliton Lattices in Strong Magnetic Field
• Examination of the possibility of ${\pi }^0$ condensation and magnetization in freely interpenetrating nuclei
• Chiral non-Abelian domain walls in the Ginzburg-Landau theory
• Fermionic domain-wall Skyrmions of QCD in a magnetic field
• Creation of domain-wall skyrmions in chiral magnets with Landau-Lifshitz-Gilbert dynamics and demagnetization