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arXiv:2512.08220 · Physical Review X

Dynamics of Quantum Chiral Solitons

Leandro M. Chinellato, Oleg A. Starykh, Cristian D. Batista

Published May 11, 2026• 0 citations
arXivHTMLPDF

Abstract

We introduce a nonperturbative 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, sgn ( t 1 + ) = ( − 1 ) 2 S + 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 nonperturbative features of dual quantum field theories in condensed-matter settings.

DOI
10.1103/zgqj-tyfd

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We introduce a nonperturbative 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, sgn ( t 1 + ) = ( − 1 ) 2 S + 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 nonperturbative features of dual quantum field theories in condensed-matter settings.
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An intriguing chiral soliton phase has recently been identified in the S=12S=\frac{1}{2}S=21​ Kitaev spin chain. Here we show that for SSS = 1, 2, 3, 4, 5 an analogous phase can be identified, but contrary to the S=12S=\frac{1}{2}S=21​ case the chiral soliton phases appear as islands within the sea of the polarized phase. In fact, a small field applied in a general direction will adiabatically connect the integer spin Kitaev chain to the polarized phase. Only at sizable intermediate fields along symmetry directions does the soliton phase appear centered around the special point hx★=hy★=S{h}_{x}^{★}={h}_{y}^{★}=Shx★​=hy★​=S where two exact product ground states can be identified. The large-SSS limit can be understood from a semiclassical analysis, and variational calculations provide a detailed picture of the S=1S=1S=1 soliton phase. Under open boundary conditions, the chain has a single soliton in the ground state, which can be excited, leading to a proliferation of in-gap states. In contrast, even length periodic chains exhibit a gap above a twice-degenerate ground state. The presence of solitons leaves a distinct imprint on the low-temperature specific heat.
Interactions between elementary excitations in quasi-one-dimensional antiferromagnets are of experimental relevance and their quantitative theoretical treatment has been a theoretical challenge for many years. Using matrix product states, one can explicitly determine the wave functions of the one- and two-particle excitations, and, consequently, the contributions to dynamical correlations. We apply this framework to the (nonintegrable) frustrated dimerized spin-1/2 chain, a model for generic spin-Peierls systems, where low-energy quasiparticle excitations are bound states of topological solitons. The spin structure factor involving two quasiparticle scattering states is obtained in the thermodynamic limit with full momentum and frequency resolution. This allows very subtle features in the two-particle spectral function to be revealed which, we argue, could be seen, e.g., in inelastic neutron scattering of spin-Peierls compounds under a change of the external pressure.
While spin parity effects, physics crucially depending on whether the spin quantum number SSS is half-odd integral or integral, have for decades been a source of new developments for the quantum physics of antiferromagnetic spin chains, the investigation into their possible ferromagnetic counterparts has remained largely unchartered, especially in the fully quantum (as opposed to the semiclassical) regime. Here we present such studies for monoaxial chiral ferromagnetic spin chains. We start by examining magnetization curves for finite-sized systems, where a magnetic field is applied perpendicular to the helical axis. For half-odd integer SSS, the curves feature discontinuous jumps identified as a series of level crossings, each accompanied by a shift of the crystal momentum kkk by an amount of $\ensuremath{\pi}$. The corresponding curves for integer valued SSS are continuous and exhibit crossover processes. For the latter case, k=0k=0k=0 throughout. These characteristics are observed numerically when the strength of the Dzyaloshinskii-Moriya interaction (DMI) DDD is comparable to or larger than that of the ferromagnetic exchange interaction JJJ. Solitons are known to be responsible for stepwise changes seen in magnetization curves in the classical limit. These findings therefore prompt us to revise the notion of a soliton, for arbitrary SSS, into a quantum mechanical entity. To unravel this phenomenon at the fully quantum level as is appropriate to spin chains with small SSS, we examine in detail special limiting Hamiltonians amenable to rigorous analysis, consisting of only the DMI and the Zeeman energy. Dubbed the DHDHDH model (for S=12S=\frac{1}{2}S=21​) and the projected DHDHDH (pDH\mathrm{p}DHpDH) model (for general SSS), they have a set of 2S2S2S conserved quantities, each of which is the number of solitons of a specific integer-valued height (as measured in the Sz{S}_{z}Sz​ basis), which ranges from 1 to 2S2S2S. We discuss how to determine the exact crystal momentum of the lowest-energy state belonging to a sector with a given set of the 2S2S2S soliton numbers. Combined with energetic considerations, this information enables us to reproduce the spin parity effect in the magnetization curves. Finally, we show that the ground states of the special models have substantial numerical overlap with those for generic systems with a finite exchange interaction, suggesting the same physics to be valid there as well.