From spinons to magnons in explicit and spontaneously dimerized antiferromagnetic chains

We reconsider the excitation spectra of a dimerized and frustrated antiferromagnetic Heisenberg chain. This model is taken as the simpler example of compiting spontaneous and explicit dimerization relevant for Spin-Peierls compounds. The bosonized theory is a two frequency Sine-Gordon field theory. We analize the excitation spectrum by semiclassical methods. The elementary triplet excitation corresponds to an extended magnon whose radius diverge for vanishing dimerization. The internal oscilations of the magnon give rise to a series of excited state until another magnon is emited and a two magnon continuum is reached. We discuss, for weak dimerization, in which way the magnon forms as a result of a spinon-spinon interaction potential.Comment: 5 pages, latex, 3 figures embedded in the tex

Spectral properties of the 2D Holstein t-J model

Employing the Lanczos algorithm in combination with a kernel polynomial moment expansion (KPM) and the maximum entropy method (MEM), we show a way of calculating charge and spin excitations in the Holstein t-J model, including the full quantum nature of phonons. To analyze polaron band formation we evaluate the hole spectral function for a wide range of electron-phonon coupling strengths. For the first time, we present results for the optical conductivity of the 2D Holstein t-J model.Comment: 2 pages, Latex. Submitted to Physica C, Proc. Int. Conf. on M2HTSC

Domain excitations in spin-Peierls systems

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 inter-chain 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 CuGeO$_3$Comment: 5 pages, 2 figures, corrected version to appear in Phys. Rev.

Mixing of magnetic and phononic excitations in incommensurate Spin-Peierls systems

We analyze the excitation spectra of a spin-phonon coupled chain in the presence of a soliton. This is taken as a microscopic model of a Spin-Peierls material placed in a high magnetic field. We show, by using a semiclassical approximation in the bosonized representation of the spins that a trapped magnetic state obtained in the adiabatic approximation is destroyed by dynamical phonons. Low energy states are phonons trapped by the soliton. When the magnetic gap is smaller than the phonon frequencies the only low energy state is a mixed magneto-phonon state with the energy of the gap. We emphasize that our results are relevant for the Raman spectra of the inorganic Spin-Peierls material CuGeO$_3$.Comment: 5 pages, latex, 2 figures embedded in the tex

Polaron Formation in the Three-Band Peierls-Hubbard Model for Cuprate Superconductors

Exact diagonalization calculations show a continuous transition from delocalized to small polaron behavior as a function of intersite electron-lattice coupling. A transition, found previously at Hartree-Fock level [Yonemitsu et al., Phys. Rev. Lett. {\bf 69}, 965 (1992)], between a magnetic and a non magnetic state does not subsist when fluctuations are included. Local phonon modes become softer close to the polaron and by comparison with optical measurements of doped cuprates we conclude that they are close to the transition region between polaronic and non-polaronic behavior. The barrier to adiabatically move a hole vanishes in that region suggesting large mobilities.Comment: 7 pages + 3 poscript figures, Revtex 3.0, MSC-199

Microscopic theory for the incommensurate transition in TiOCl

We propose a microscopic mechanism for the incommensurate phase in TiOX compounds. The model includes the antiferromagnetic chains of Ti ions immersed in the phonon bath of the bilayer structure. Making use of the Cross-Fisher theory, we show that the geometrically frustrated character of the lattice is responsible for the structural instability which leads the chains to an incommensurate phase without an applied magnetic field. In the case of TiOCl, we show that our model is consistent with the measured phonon frequencies at $T=300K$ and the value of the incommensuration vector at the transition temperature. Moreover, we find that the dynamical structure factor shows a progressive softening of an incommensurate phonon near the zone boundary as the temperature decreases. This softening is accompanied by a broadening of the peak which gets asymmetrical as well when going towards the transition temperature. These features are in agreement with the experimental inelastic X-ray measurements.Comment: 6 pages, 5 figures. Published versio

Antiferromagnetism in doped anisotropic two-dimensional spin-Peierls systems

We study the formation of antiferromagnetic correlations induced by impurity doping in anisotropic two-dimensional spin-Peierls systems. Using a mean-field approximation to deal with the inter-chain magnetic coupling, the intra-chain correlations are treated exactly by numerical techniques. The magnetic coupling between impurities is computed for both adiabatic and dynamical lattices and is shown to have an alternating sign as a function of the impurity-impurity distance, hence suppressing magnetic frustration. An effective model based on our numerical results supports the coexistence of antiferromagnetism and dimerization in this system.Comment: 5 pages, 4 figures; final version to appear in Phys. Rev.

Density Matrix Renormalization Group Study of One-Dimensional Acoustic Phonons

We study the application of the density matrix renormalization group (DMRG) to systems with one-dimensional acoustic phonons. We show how the use of a local oscillator basis circumvents the difficulties with the long-range interactions generated in real space using the normal phonon basis. When applied to a harmonic atomic chain, we find excellent agreement with the exact solution even when using a modest number of oscillator and block states (a few times ten). We discuss the use of this algorithm in more complex cases and point out its value when other techniques are deficient.Comment: 12 pages. To be published in PRB rapid co

On the soliton width in the incommensurate phase of spin-Peierls systems

We study using bosonization techniques the effects of frustration due to competing interactions and of the interchain elastic couplings on the soliton width and soliton structure in spin-Peierls systems. We compare the predictions of this study with numerical results obtained by exact diagonalization of finite chains. We conclude that frustration produces in general a reduction of the soliton width while the interchain elastic coupling increases it. We discuss these results in connection with recent measurements of the soliton width in the incommensurate phase of CuGeO_3.Comment: 4 pages, latex, 2 figures embedded in the tex