Fractional Skyrmion molecules in a ℂPN−1 model

Abstract

We study fractional Skyrmions in a ℂP2 baby Skyrme model with a generalization of the easy-plane potential. By numerical methods, we find stable, metastable, and unstable solutions taking the shapes of molecules. Various solutions possess discrete symmetries, and the origin of those symmetries are traced back to congruencies of the fields in homogeneous coordinates on ℂP2.

Stable Z-strings with topological polarization in two Higgs doublet model

“…In condensed matter physics, this is actually known in ferromagnets in which the potential is called an easy-plane potential. The same happens for baby-Skyrmions in a baby Skyrme model, the O(3) sigma model with four-derivative term, with an easy-plane potential term [98][99][100][101]. In these cases, lumps and baby-Skyrmions are both topological solitons supported by a topological charge defined by the second homotopy class π 2 (instead of π 1 for vortices).…”

“…Although we have concentrated on the stability of a single non-topological Z-string in the form of a molecule of (1, 0) and (0, −1) topologicsl Z strings, it will be also interesting to explore the stability of multiple molecules. In related models admitting similar molecules mentioned below (baby Skyrme model [98][99][100][101] and two-component Bose-Einstein condensates (BECs) [102][103][104][105][106][107][108][109][110][111]), multiple strings are connected to form a sheet or a polygon as (meta)stable states [99,100]. For sufficiently large number of molecules, the most stable configuration is a square lattice (the baby Skyrme model [98]) or both square and triangu-JHEP02(2022)099 lar lattices (the BEC [106]).…”

Stable $Z$-strings with topological polarization in two Higgs doublet model

“…In condensed matter physics, this is actually known in ferromagnets in which the potential is called an easy-plane potential. The same happens for baby-Skyrmions in a baby Skyrme model, the O(3) sigma model with four-derivative term, with an easy-plane potential term [90][91][92][93]. In these cases, lumps and baby-Skyrmions are both topological solitons supported by a topological charge defined by the second homotopy class π 2 (instead of π 1 for vortices).…”

“…Although we have concentrated on the stability of a single non-topological Z-string in the form of a molecule of (1, 0) and (0, −1) topologicsl Z strings, it will be also interesting to explore the stability of multiple molecules. In related models admitting similar molecules mentioned below (baby Skyrme model [90][91][92][93] and two-component Bose-Einstein condensates (BECs) [94][95][96][97][98][99][100][101][102][103]), multiple strings are connected to form a sheet or a polygon as (meta)stable states [91,92]. For sufficiently large number of molecules, the most stable configuration is a square lattice (the baby Skyrme model [90]) or both square and triangular lattices (the BEC [98]).…”

Relations among topological solitons

“…For a CP N −1 model with a generalization of the easy plane potential, a single baby Skyrmion is split into a set of N U (1) N −1 global-vortex Skyrmions with 1/N lump (π 2 ) topological charges [151].…”