We investigate the nature of low-energy excitations in a spin chain with antiferrmomagnetic nearest-neighbor
J1, next-nearest-neighbor
J2, and three-site
J3 interactions using the time-dependent density matrix renormalization group and the single mode approximation techniques. In the absence of the
J2 interaction, we identify clear distinctions in the spectral functions in the fully dimerized phase across the exactly dimerized line for different magnitudes of the spins. In contrast to the spin-
1/2 chain, where the spinon continuum dominates the spectral functions, the magnon modes are prominent in the spectral functions of the spin-
1 and spin-
3/2 chains. Through single mode approximation and valence bond solid approaches, we disentangle magnon and spinon contributions to the spectral functions. After including the
J2 interactions, for the spin-
1 chain we trace the evolution of the dynamical structure factor along the phase transition line between the Haldane phase and the fully dimerized phase. We find that the excitation spectrum is a continuum along this line and the spectral gap closes as the order of the transition changes from first order to second order. Along the line of first-order transitions, the spinon-like domain walls are deconfined, and the model exhibits their confinement into discrete bound states away from the transition line. A similar phenomenon occurs in the spin-
3/2 chain across the phase transition between partially dimerized to fully dimerized phases, revealing a universal spinon confinement phenomenon across first-order phase transitions. This study presents the dynamical structure factor corresponding to the ground state phase diagram and establishes a unified quasiparticle framework for understanding the fundamental nature of excitations across distinct quantum phases in frustrated
J1-
J2-
J3 Heisenberg spin chains.
We present a spin-1 chain with a Hamiltonian which has three exactly solvable ground states. Two of these are fully dimerized, analogous to the Majumdar-Ghosh (MG) states of a spin-
21 chain, while the third is of the Affleck-Kennedy-Lieb-Tasaki (AKLT) type. We use variational and numerical methods to study the low-energy excitations which interpolate between these ground states in different ways. In particular, there is a spin-
21 excitation which interpolates between the MG and AKLT ground states; this is the lowest excitation of the system and it has a surprisingly small gap. We discuss generalizations of our model of spin fractionalization to higher spin chains and higher dimensions.
We study the dynamical structure factor of the frustrated spin-$3/2\phantom{\rule{4pt}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg chains, with particular focus on the partially dimerized phase that emerges between two Kosterlitz-Thouless transitions. Using a valence bond solid Ansatz corroborated by density-matrix renormalization-group simulations, we investigate the nature of magnon and spinon excitations through the single-mode approximation. We show that the magnon develops an incommensurate dispersion at ${J}_{2}\ensuremath{\approx}0.32{J}_{1}$, while the spinons, viewed as domain walls between degenerate valence bond solid states, become incommensurate at ${J}_{2}\ensuremath{\approx}0.4{J}_{1}$ beyond the Lifshitz point $({J}_{2}\ensuremath{\approx}0.388{J}_{1})$. The dynamical structure factor exhibits rich spectral features shaped by the interplay between these excitations, with magnons appearing as resonances embedded in the spinon continuum. The spinon gap shows a nonmonotonic behavior, reaching a peak near the center of the partially dimerized phase and closing at the boundaries, suggesting the appearance of a floating phase as a result of the condensation of incommensurate spinons. Comparative analysis with the spin-
5/2 case confirms the universality of these phenomena across half-integer higher-spin systems. Our results provide detailed insight into how fractionalization and incommensurate condensation govern the spectral properties of frustrated spin chains, offering a unified picture across different spin magnitudes.
Motivated by the rich phase diagrams recently unveiled in frustrated spin-1 chains with competing next-nearest-neighbor and four-spin interactions, we investigate the nature of the elementary excitations of spin-1 chains in the vicinity of phase transitions using the matrix-product state (MPS) representation of elementary excitations. First, we show that both spinons and magnons naturally arise in
SU(2) invariant spin chains when describing ground states and elementary excitations using MPSs. Then we investigate the nature of the elementary excitations across the first-order transition between the Haldane phase and the topologically trivial next-nearest-neighbor Haldane phase. We show explicitly that spinons deconfine at the transition, and we calculate the dispersion of these deconfined spinons with MPSs. We also show that, immediately away from the transition line, spinons confine, forming dispersive spinon/antispinon bound states on both sides of the transition. Finally, we show that deconfined spinons also appear at the transition between the Haldane phase and the spontaneously dimerized phase when this transition is first order.
We investigate the effective interaction between two localized spin impurities embedded in a frustrated spin-1/2
J1−J2 Heisenberg chain. Treating the impurity spins as classical moments coupled locally to the host, we combine second--order perturbation theory with large--scale density matrix renormalization group (DMRG) calculations to determine the impurity--impurity interaction as a function of separation, coupling strength, and magnetic frustration. In the weak--coupling regime, we show that the interaction is governed by the the static spin susceptibility of the host and exhibits oscillatory power--law decay in the gapless phase, modified by universal logarithmic corrections at the SU(2)--symmetric critical point. In the gapped dimerized phase, the interaction decays exponentially with distance. For intermediate and strong impurity--host coupling, we observe a crossover to a boundary--dominated regime characterized by pronounced parity effects associated with the length of the chain segment between impurities, signaling a breakdown of the simple RKKY--like description. Our results establish impurity--impurity interactions as a sensitive probe of frustrated quantum spin liquids and provide a controlled framework for distinguishing gapless and gapped phases through local perturbations.