Formation of Chiral Soliton Lattice

TL;DR

This paper investigates the formation of the Chiral Soliton Lattice (CSL) in quantum chromodynamics and axion-like particles, analyzing nucleation mechanisms, critical magnetic fields, and stability conditions using an effective theory approach.

Contribution

It provides a detailed analysis of the quantum tunneling nucleation process of CSL, including critical magnetic field determination and application to QCD and ALPs.

Findings

Nucleation rate becomes significant at a critical magnetic field.

CSL formation is energetically favored under certain conditions.

ALP CSL formation is enhanced with stronger magnetic fields and chemical potentials.

Abstract

The Chiral Soliton Lattice (CSL) is a lattice structure composed of domain walls aligned in parallel at equal intervals, which is energetically stable in the presence of a background magnetic field and a finite (baryon) chemical potential due to the topological term originated from the chiral anomaly. We study its formation from the vacuum state, with describing the CSL as a layer of domain-wall disks surrounded by the vortex or string loop, based on the Nambu-Goto-type effective theory. We show that the domain wall nucleates via quantum tunneling when the magnetic field is strong enough. We evaluate its nucleation rate and determine the critical magnetic field strength with which the nucleation rate is no longer exponentially suppressed. We apply this analysis to the neutral pion in the two-flavor QCD as well as the axion-like particles (ALPs) with a finite (baryon) chemical potential under an external magnetic field. In the former case, even though the CSL state is more energetically stable than the vacuum state and the nucleation rate becomes larger for sufficiently strong magnetic field, it cannot be large enough so that the nucleation of the domain walls is not exponentially suppressed and promoted, without suffering from the tachyonic instability of the charged pion fluctuations. In the latter case, we confirm that the effective interaction of the ALPs generically includes the topological term required for the CSL state to be energetically favored. We show that the ALP CSL formation is promoted if the magnetic field strength and the chemical potential of the system is slightly larger than the scale of the axion decay constant.