Recently, there has been a renewed interest in properties of the higher-spin Kitaev models, especially their low-dimensional analogs with additional interactions. These quasi-one-dimensional systems exhibit rich phase diagrams with symmetry-protected topological phases, Luttinger liquids, hidden order, and higher-rank magnetism. However, the nature of the pure spin-
S Kitaev chains is not yet fully understood. Earlier works found a unique ground state with short-ranged correlations for
S=1 and an intriguing double-peak structure in the heat capacity associated with an entropy plateau. To understand the low-energy excitations and thermodynamics for general
S, we study the anisotropic spin-
S Kitaev chain. Starting from the dimerized limit, we derive an effective low-energy Hamiltonian at finite anisotropy. For half-integer spins we find a trivial effective model, reflecting a nonlocal symmetry protecting the degeneracy, while for integer
S we find interactions among the flux degrees of freedom that select a unique ground state. The effective model for integer spins is used to predict the low-energy excitations and thermodynamics, and we make a comparison with the semiclassical limit through linear spin wave theory. Finally, we speculate on the nature of the isotropic limit.
Motivated by intense research on two-dimensional spin-
21 Kitaev materials, Kitaev spin chains and ladders, though geometrically limited, have been studied for their numerical simplicity and insights into extended Kitaev models. The phase diagrams under the magnetic field were also explored for these quasi-one-dimensional models. For an isotropic Kitaev chain, it was found that a magnetic field polarizes the ground state except along the symmetric field angle, where the chain is found to remain gapless up to a critical field strength where it enters an intriguing soliton phase before reaching the polarized state at higher field strengths. Here we study an anisotropic Kitaev chain under a magnetic field using the density matrix renormalization group technique, where the ground state has a macroscopic degeneracy with a finite gap in the absence of the magnetic field. When the field is mainly aligned parallel to the strong bond, four-site and large unit-cell ordered phases arise. In a certain angle of the field, another ordered phase characterized by a uniform chirality with six-site periodicity emerges. We employ a perturbation theory to understand such field-induced ordered phases. The effective model uncovers the presence of transverse Ising and Dzyaloshinskii-Moriya interactions between unit cells, as well as further-neighbor Ising interaction induced by the magnetic field, which collectively explain the mechanisms behind these ordered states. Open questions and challenges are also discussed.
While spin parity effects, physics crucially depending on whether the spin quantum number
S 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
S, the curves feature discontinuous jumps identified as a series of level crossings, each accompanied by a shift of the crystal momentum
k by an amount of $\ensuremath{\pi}$. The corresponding curves for integer valued
S are continuous and exhibit crossover processes. For the latter case,
k=0 throughout. These characteristics are observed numerically when the strength of the Dzyaloshinskii-Moriya interaction (DMI)
D is comparable to or larger than that of the ferromagnetic exchange interaction
J. 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
S, into a quantum mechanical entity. To unravel this phenomenon at the fully quantum level as is appropriate to spin chains with small
S, we examine in detail special limiting Hamiltonians amenable to rigorous analysis, consisting of only the DMI and the Zeeman energy. Dubbed the
DH model (for
S=21) and the projected
DH (
pDH) model (for general
S), they have a set of
2S conserved quantities, each of which is the number of solitons of a specific integer-valued height (as measured in the
Sz basis), which ranges from 1 to
2S. We discuss how to determine the exact crystal momentum of the lowest-energy state belonging to a sector with a given set of the
2S 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.
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.
The ground-state phase diagram of the frustrated spin-S XXZ chain with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied numerically by using the density-matrix renormalization-group method for the cases of
S=1/2, 3/2, and
2. We are particularly interested in the possible gapless and gapped chiral phases, in which the chirality ${\ensuremath{\kappa}}_{l}{=S}_{l}^{x}{S}_{l+1}^{y}\ensuremath{-}{S}_{l}^{y}{S}_{l+1}^{x}$ exhibits a finite long-range order whereas the spin correlation decays either algebraically or exponentially. We show that the gapless chiral phase appears in a broad region of the phase diagram for general S. By contrast, the gapped chiral phase is found for integer S in a narrow region of the phase diagram, while it has not been identified for half-odd integer S within our numerical accuracy. By combining the results with our previous result for
S=1, we discuss the S dependence of the phase diagram. The prediction from a bosonization analysis on the decay exponent of the spin correlation is verified.