Quantum nucleation of topological solitons

Abstract

The chiral soliton lattice is an array of topological solitons realized as ground states of QCD at finite density under strong magnetic fields or rapid rotation, and chiral magnets with an easy-plane anisotropy. In such cases, topological solitons have negative energy due to topological terms originating from the chiral magnetic or vortical effect and the Dzyaloshinskii-Moriya interaction, respectively. We study quantum nucleation of topological solitons in the vacuum through quantum tunneling in $2+1$ and $3+1$ dimensions, by using a complex ${\varphi }^4$ (or the axion) model with a topological term proportional to an external field, which is a simplification of low-energy theories of the above systems. In $2+1$ dimensions, a pair of a vortex and an anti-vortex is connected by a linear soliton, while in $3+1$ dimensions, a vortex is string-like, a soliton is wall-like, and a disk of a soliton wall is bounded by a string loop. Since the tension of solitons can be effectively negative due to the topological term, such a composite configuration of a finite size is created by quantum tunneling and subsequently grows rapidly. We estimate the nucleation probability analytically in the thin-defect approximation and fully calculate it numerically using the relaxation (gradient flow) method. The nucleation probability is maximized when the direction of the soliton is perpendicular to the external field. We find a good agreement between the thin-defect approximation and direct numerical simulation in $2+1$ dimensions if we read the vortex tension from the numerics, while we find a difference between them at short distances interpreted as a remnant energy in $3+1$ dimensions.

arXiv comment26 pages, 8 figures

References in corpus (60)

• Skyrmion Lattice in a Chiral Magnet
• Spontaneous Skyrmion Ground States in Magnetic Metals
• Cosmic strings
• Spinor Bose-Einstein condensates
• Berezinskii-Kosterlitz-Thouless Crossover in a Trapped Atomic Gas
• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Hydrodynamics with Triangle Anomalies
• Cosmological Experiments in Condensed Matter Systems
• Beyond skyrmions: Review and perspectives of alternative magnetic quasiparticles
• Big bang simulation in superfluid 3He-B -- Vortex nucleation in neutron-irradiated superflow
• Spontaneous vortices in the formation of Bose-Einstein condensates
• Tachyon Dynamics in Open String Theory
• Semilocal and Electroweak Strings
• The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals
• Solitons in the Higgs phase -- the moduli matrix approach --
• Quantum Anomalies in Dense Matter
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Skyrmion fractionalization and merons in chiral magnets with easy-plane anisotropy
• Skyrmion Lattice in Two-Dimensional Chiral Magnet
• Axial anomaly and magnetism of nuclear and quark matter
• Stable Skyrmions in SU(2) Gauged Bose-Einstein Condensates
• Quantum Vortex Strings: A Review
• Decay of Metastable Topological Defects
• Vortices and Other Topological Solitons in Dense Quark Matter
• Chiral Soliton Lattice and Charged Pion Condensation in Strong Magnetic Fields
• Anomalous effects of dense matter under rotation
• Cosmic Strings
• Creating vortons and three-dimensional skyrmions from domain wall annihilation with stretched vortices in Bose-Einstein condensates
• The spontaneous breaking of a metastable string
• Ferromagnetic neutron stars: axial anomaly, dense neutron matter, and pionic wall
• Berezinskii-Kosterlitz-Thouless transition of two-component Bose mixtures with inter-component Josephson coupling
• Constraints on two Higgs doublet models from domain walls
• Anomalous electrodynamics of neutral pion matter in strong magnetic fields
• Non-Abelian strings and domain walls in two Higgs doublet models
• Non-Abelian Sine-Gordon Solitons
• Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and $\mathbb{C}{P}^{N-1}$ Lumps
• Tachyon Condensation Due to Domain-Wall Annihilation in Bose-Einstein Condensates
• Bubble collisions in Abelian gauge theories and the geodesic rule
• Topological term, QCD anomaly, and the eta' chiral soliton lattice in rotating baryonic matter
• Intermediate phase in the spiral antiferromagnet Ba_2CuGe_2O_7
• Phases of rotating baryonic matter: non-Abelian chiral soliton lattices, antiferro-isospin chains, and ferri/ferromagnetic magnetization
• Anomaly-Induced Inhomogeneous Phase in Quark Matter without the Sign Problem
• Spontaneous Magnetization through Non-Abelian Vortex Formation in Rotating Dense Quark Matter
• Chiral soliton lattice phase in warm QCD
• Skyrmion interactions and lattices in chiral magnets: analytical results
• Formation of Topological Defects with Explicit Symmetry Breaking
• Isolated Skyrmions in the $C{P}^2$ nonlinear $\sigma$-model with a Dzyaloshinskii-Moriya type interaction
• Theory of magnetoelastic resonance in a mono-axial chiral helimagnet
• Chiral soliton lattice in QCD-like theories
• Anomalous low-temperature thermodynamics of QCD in strong magnetic fields
• Domain Walls and Vortices in Chiral Symmetry Breaking
• Competition of chiral soliton lattice and Abrikosov vortex lattice in QCD with isospin chemical potential
• Exact Ground States and Domain Walls in One Dimensional Chiral Magnets
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Chiral non-Abelian vortices and their confinement in three flavor dense QCD
• Vortex confinement transitions in the modified Goldstone model
• Tachyon Condensation and Brane Annihilation in Bose-Einstein Condensates: Spontaneous Symmetry Breaking in Restricted Lower-dimensional Subspace
• Spontaneous and Induced Decay of Metastable Strings and Domain Walls
• Brane Realization of Nambu Monopoles and Electroweak Strings
• Spontaneous decay of a metastable domain wall

Cited by in corpus (12)

• Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice
• Formation of Chiral Soliton Lattice
• Chiral Magnets from String Theory
• Chiral soliton lattice at next-to-leading order
• Quasicrystals in QCD
• Spin Statistics and Surgeries of Topological Solitons in QCD Matter in Magnetic Field
• Solitonic ground state in supersymmetric theory in background
• Interfacial Line Energy of a Topological Phase
• Holographic QCD Matter: Chiral Soliton Lattices in Strong Magnetic Field
• Quantum Hall liquids in high-density QCD
• Baryons, Skyrmions and $\theta$-periodicity anomaly in chiral and vector-like gauge theories
• Fermionic domain-wall Skyrmions of QCD in a magnetic field