We reconsider the excitation spectra of a dimerized and frustrated antiferromagnetic Heisenberg chain. This model is taken as the simpler example of competing spontaneous and explicit dimerization relevant for spin-Peierls compounds. The bosonized theory is a two-frequency sine-Gordon field theory. We analyze the excitation spectrum by semiclassical methods. The elementary triplet excitation corresponds to an extended magnon whose radius diverges for vanishing dimerization. The internal oscillations of the magnon give rise to a series of excited states until another magnon is emitted and a two-magnon continuum is reached. We discuss, for weak dimerization, the manner in which the magnon forms as a result of a spinon-spinon interaction potential.
We reconsider the excitation spectra of a dimerized and frustrated antiferromagnetic Heisenberg chain. This model is taken as the simpler example of competing spontaneous and explicit dimerization relevant for spin-Peierls compounds. The bosonized theory is a two-frequency sine-Gordon field theory. We analyze the excitation spectrum by semiclassical methods. The elementary triplet excitation corresponds to an extended magnon whose radius diverges for vanishing dimerization. The internal oscillations of the magnon give rise to a series of excited states until another magnon is emitted and a two-magnon continuum is reached. We discuss, for weak dimerization, the manner in which the magnon forms as a result of a spinon-spinon interaction potential.
We study a model of a spin-Peierls material consisting of a set of antiferromagnetic Heisenberg chains coupled with phonons and interacting among them via an interchain elastic coupling. The excitation spectrum is analyzed by bosonization techniques and the self-harmonic approximation. The elementary excitation is the creation of a localized domain structure where the dimerized order is the opposite to the one of the surroundings. It is a triplet excitation whose formation energy is smaller than the magnon gap. Magnetic internal excitations of the domain are possible and give the further excitations of the system. We discuss these results in the context of recent experimental measurements on the inorganic spin-Peierls compound CuGeO3.
Excitation spectra of S=1/2 and 1 frustrated Heisenberg antiferromagnetic chains with bond alternation (explicit dimerization) are studied using a combination of analytical and numerical methods. The system undergoes a dimerization transition at a critical bond alternation parameter $\ensuremath{\delta}={\ensuremath{\delta}}_{\mathrm{c}}$, where ${\ensuremath{\delta}}_{\mathrm{c}}=0$ for the S=1/2 chain. The SU(2)-symmetric sine-Gordon theory is known to be an effective field theory of the system except at the transition point. The sine-Gordon theory has a SU(2)-triplet and a SU(2)-singlet of elementary excitation, and the mass ratio r of the singlet to the triplet is 3. However, our numerical calculation with the infinite time-evolving block decimation method shows that r depends on the frustration (next-nearest-neighbor coupling) and is generally different from 3. This can be understood as an effect of marginal perturbation to the sine-Gordon theory. In fact, at the critical frustration separating the second-order and first-order dimerization transitions, the marginal operator vanishes and r=3 holds. We derive the mass ratio r analytically using form-factor perturbation theory combined with a renormalization-group analysis. Our formula agrees well with the numerical results, confirming the theoretical picture. The present theory also implies that, even in the presence of a marginally irrelevant operator, the mass ratio approaches 3 in the very vicinity of the second-order dimerization critical point $\ensuremath{\delta}\ensuremath{\sim}{\ensuremath{\delta}}_{c}$. However, such a region is extremely small and would be difficult to observe numerically.
We present a detailed numerical analysis of the low-energy excitation spectrum of a frustrated and dimerized spin S=1/2 Heisenberg chain. In particular, we show that in the commensurate spin-Peierls phase the ratio of the singlet and triplet excitation gap is a universal function which depends on the frustration parameter only. We identify the conditions for which a second elementary triplet branch in the excitation spectrum splits from the continuum. We compare our results with predictions from the continuum limit field theory. We discuss the relevance of our data in connection with recent experiments on CuGeO3,NaV2O5, and (VO)2P2O7.
We have studied the low-energy excitation spectrum of a dimerized and frustrated antiferromagnetic Heisenberg chain. We use an analytic approach, based on a description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Additional singlet (S=0) and triplet (S=1) modes are found as two-particle bound states of the elementary triplets. We have also calculated the contributions of the elementary and collective excitations into the spin structure factor. Our results are in excellent agreement with exact diagonalizations and dimer series expansions data as long as the dimerization parameter \ensuremath{\delta} is not too small $(\ensuremath{\delta}>0.1),$ i.e., while the elementary triplets can be treated as localized objects.
Motivated by recent measurements on CuGeO3, the spectrum of magnetic excitations of an antiferromagnetic S=21 chain with alternating coupling strength is investigated. Wave-vector-dependent magnons and a continuum with square-root behavior at the band edges are found. The spectral density of the continua is calculated. Spin-rotation symmetry fixes the gap of the continuum to be twice the elementary magnon gap. This is in excellent agreement with experimental results. The existence of (anti)bound states of two magnons is predicted: below the continuum a singlet and a triplet, above the continuum a quintuplet.
The dynamical spin structure factor and the Raman response are calculated for structurally dimerized and spin-Peierls chains in a magnetic field, using exact diagonalization techniques. In both cases there is a spin liquid phase composed of interacting singlet dimers at small fields h<hc1, an incommensurate regime (hc1<h<hc2) in which the modulation of the triplet excitation spectra adapts to the applied field, and a fully spin-polarized phase above an upper critical field hc2. For structurally dimerized chains, the spin gap closes in the incommensurate phase, whereas spin-Peierls chains remain gapped. In the spin liquid regimes, the dominant feature of the triplet spectra is a one-magnon bound state, separated from a continuum of states at higher energies. There are also indications of a singlet bound state above the one-magnon triplet.