Hidden order in dielectrics: string condensation, solitons, and the charge-vortex duality

TL;DR

The paper builds a solitonic framework for electrons in dielectrics by treating them as polarization-field solitons whose interactions are screened by a polarization cloud, yielding short-range forces with a characteristic scale $\mu^{-1}$. It uncovers a charge–vortex duality: solitons can be quantized as fermions or bosons in 3D (and anyons in 2D), while magnetic vortices emerge with a topological contribution to magnetic susceptibility arising from closed-path polarization tunneling. The approach relies on a lattice electrodynamics–like description with a compact gauge field and a $2\pi$-periodic potential, and it analyzes both static properties and quantum aspects, including a proposed observable signature in nanoscale or synthetic dielectric systems. Potential experimental routes include covalent dielectrics, small nanocrystals exhibiting Mie resonances, and Josephson-junction arrays where both soliton statistics and magnetic responses may be tunable. Overall, the work provides a principled mechanism for hidden order in insulators and motivates targeted experiments to detect topological and statistical features of dielectric solitons and their magnetic counterparts.

Abstract

Description of electrons in a dielectric as solitons of the polarization field requires that the interaction between the solitons (prior to their coupling to electromagnetism) is short-ranged. We present an analytical study of the mechanism by which this is achieved. The mechanism is unusual in that it enables screening of electrically neutral soliton cores by polarization charges. We also argue that the structure of the solitons allows them to be quantized as either fermions or bosons. At the quantum level, the theory has, in addition to the solitonic electric, elementary magnetic excitations, which give rise to a topological contribution to the magnetic susceptibility.

Figures (4)

• Figure 1: A unit cell of a simple cubic lattice, with each face hosting a single component of the polarization vector $\bm{p}$.
• Figure 2: Profiles of the soliton field $\bm{p}$ and the density $\rho = - \nabla \cdot \bm{p}$ at the $(x,y)$ plane passing through the elementary ($q=1$) soliton center in three dimensions, computed numerically on a $22^3$ grid for the potential (\ref{['cos']}) with $\mu^2 = 0.1$.
• Figure 3: Same as in Fig. \ref{['fig:sfields']} but for the density profile of the unstable solution with charge $q=4$. One can see four maxima of the density; there are two more off the plane, for the total of six.
• Figure 4: Absolute value of the interaction energy of a soliton-antisoliton pair in 2D as a function of the separation, computed on a $100\times 50$ grid for $\mu^2 = 0.1$. $K_0$ is the modified Bessel function appearing in the analytical result (\ref{['Eint2']}).