Dynamics of Quantum Chiral Solitons

TL;DR

The paper develops a nonperturbative lattice framework to quantize chiral solitons in a 1D spin chain with DM interaction, thereby extending the sine–Gordon–Thirring S-duality to the lattice. It constructs explicit quantum soliton operators, applies a Wannierization procedure to produce orthonormal soliton states, and derives a tight-binding description that captures soliton tunneling and band structure across the Brillouin zone; crucially, the dominant soliton hopping obeys $\operatorname{sgn}(t_{1+}) = (-1)^{2S+1}$, distinguishing integer from half-integer spins. The quantum soliton sector reveals a free-fermion fixed point at the critical field $H_c$, with a subsequent Tomonaga–Luttinger-liquid phase when soliton density grows, and predicts distinct signatures in dynamical spin structure factors and thermodynamics that are accessible to inelastic neutron scattering. Numerical DMRG/TEBD validation confirms the effective theory's predictions and clarifies soliton–magnon hybridization patterns, offering a concrete route to experimentally probe nonperturbative dual quantum field theory features in condensed matter systems.

Abstract

We introduce a non-perturbative framework for quantizing chiral solitons in interacting quantum spin chains. This approach provides a direct lattice extension of the well-established $S$-duality between the sine-Gordon and Thirring models, thereby bridging the gap between continuum dualities and their lattice counterparts. By constructing the quantum chiral-soliton operators explicitly, we show how their unconventional dynamics appear in the excitation spectrum and correlation functions across the full Brillouin zone. A key result is that the dominant soliton tunneling amplitude alternates in sign, $\operatorname{sgn}(t_{1+}) = (-1)^{2S+1}$, sharply distinguishing half-odd-integer from integer spin chains. We further identify characteristic signatures of these chiral excitations in the dynamical spin structure factor, demonstrating their visibility in inelastic neutron scattering. Our results open a route to experimentally probing non-perturbative features of dual quantum field theories in condensed-matter settings.

Figures (18)

• Figure 1: Profile of the classical chiral soliton. Arrow directions indicate spin orientation, while their color encodes the value of the angle $\varphi$.
• Figure 2: a) Field dependence of the magnetization. b) Spatial profile of the soliton solution $\varphi_{+}(x)$ in units of $2\pi$. c) Spatial profile of the topological charge density $\mathcal{Q}(x)$ associated with a single soliton at the critical field $H = H_c$.
• Figure 3: Dynamical spin structure factor and magnon dispersion (blue dashed line) obtained from Linear Spin Wave Theory (LSWT) calculations. The spectral intensities were computed using Sunny.jl library (v0.7) Sunny2025.
• Figure 4: a) Schematic representation of the fermionic soliton and antisoliton bands in the massive Thirring model, both featuring minima at $k=\pi$ and possessing identical effective masses. The sine–Gordon vacuum corresponds to the half-filled case, where the chemical potential lies within the band gap ($c|q_0| < 2\lambda$ in Eq. \ref{['eq:HmT1']} ) and energies of solitons and antisolitons are positive. (b) Same as in (a), but for the effective lattice model Eq. \ref{['eq:Heff']}, where the dispersion minima occur at different momenta ($k=\pi$ for the soliton band and $k=0$ for the antisoliton band) and the effective masses are not equal (the soliton mass is significantly larger than that of the antisoliton).
• Figure 5: Schematic representation of the action of the soliton operator (a) and the Wannerized soliton operator (b).