Self-Consistent Large-$N$ Analytical Solutions of Inhomogneous Condensates in Quantum $\mathbb{C}{P}^{N-1}$ Model

Abstract

We give, for the first time, self-consistent large-$N$ analytical solutions of inhomogeneous condensates in the quantum $\mathbb{C}{P}^{N-1}$ model in the large-$N$ limit. We find a map from a set of gap equations of the $\mathbb{C}{P}^{N-1}$ model to those of the Gross-Neveu (GN) model (or the gap equation and the Bogoliubov-de Gennes equation), which enables us to find the self-consistent solutions. We find that the Higgs field of the $\mathbb{C}{P}^{N-1}$ model is given as a zero mode of solutions of the GN model, and consequently only topologically nontrivial solutions of the GN model yield nontrivial solutions of the $\mathbb{C}{P}^{N-1}$ model. A stable single soliton is constructed from an anti-kink of the GN model and has a broken (Higgs) phase inside its core,in which $\mathbb{C}{P}^{N-1}$ modes are localized,with a symmetric (confining) phase outside. We further find a stable periodic soliton lattice constructed from a real kink crystal in the GN model,while the Ablowitz-Kaup-Newell-Segur hierarchy yields multiple solitons at arbitrary separations.

19 pages, 3 figures. Updates in v2: References added. v3: Published version

References in corpus (9)

• Theory of ultracold Fermi gases
• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Instanton constituents in the O(3) model at finite temperature
• Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems
• Fermionic solutions of chiral Gross-Neveu and Bogoliubov-de Gennes systems in nonlinear Schrödinger hierarchy

Cited by in corpus (7)

• Casimir effect for lattice fermions
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Nonlinear dynamical Casimir effect at weak nonstationarity
• Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems
• Physics-informed neural networks for solving functional renormalization group on a lattice
• One-loop effective action of the $\mathbb{C}{P}^{N-1}$ model at large $\mu \beta$
• Lessons from $O(N)$ models in one dimension