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Physical review. B, Condensed matter

Dynamical properties of phonons in the XY spin chain coupled with lattices

Fei Ye, Guo-Hui Ding, Bo-Wei Xu

Published Aug 14, 2001• 2 citations
Publisher

Abstract

We study the dynamical properties of the phonons in the $\mathrm{XY}$ spin chain coupled with lattices subjected to the applied magnetic field with the path-integral approach. Dynamical structure factor is calculated in the presence of the magnetic field. A critical value of the bare \ensuremath{\pi}-mode phonon frequency ${\ensuremath{\Omega}}_{\ensuremath{\pi},c}$ is given such that for ${\ensuremath{\Omega}}_{\ensuremath{\pi}}<{\ensuremath{\Omega}}_{\ensuremath{\pi},c}$ the spin-Peierls transition is in the soft-mode regime and for ${\ensuremath{\Omega}}_{\ensuremath{\pi}}>{\ensuremath{\Omega}}_{\ensuremath{\pi},c}$ it is in the central-peak regime. We find that ${\ensuremath{\Omega}}_{\ensuremath{\pi},c}$ depends on the magnitude of the applied magnetic field.

DOI
10.1103/physrevb.64.094431

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We study the dynamical properties of the phonons in the XY\mathrm{XY}XY spin chain coupled with lattices subjected to the applied magnetic field with the path-integral approach. Dynamical structure factor is calculated in the presence of the magnetic field. A critical value of the bare \ensuremath{\pi}-mode phonon frequency \ensuremathΩ\ensuremathπ,c{\ensuremath{\Omega}}_{\ensuremath{\pi},c}\ensuremathΩ\ensuremathπ,c​ is given such that for \ensuremathΩ\ensuremathπ<\ensuremathΩ\ensuremathπ,c{\ensuremath{\Omega}}_{\ensuremath{\pi}}<{\ensuremath{\Omega}}_{\ensuremath{\pi},c}\ensuremathΩ\ensuremathπ​<\ensuremathΩ\ensuremathπ,c​ the spin-Peierls transition is in the soft-mode regime and for \ensuremathΩ\ensuremathπ>\ensuremathΩ\ensuremathπ,c{\ensuremath{\Omega}}_{\ensuremath{\pi}}>{\ensuremath{\Omega}}_{\ensuremath{\pi},c}\ensuremathΩ\ensuremathπ​>\ensuremathΩ\ensuremathπ,c​ it is in the central-peak regime. We find that \ensuremathΩ\ensuremathπ,c{\ensuremath{\Omega}}_{\ensuremath{\pi},c}\ensuremathΩ\ensuremathπ,c​ depends on the magnitude of the applied magnetic field.
Summary: The interplay of charge, spin and lattice degrees of freedom is studied for quasi-one-dimensional electron and spin systems coupled to quantum phonons. Special emphasis is put on the influence of the lattice dynamics on the Peierls transition. Using exact diagonalization techniques the ground-state and spectral properties of the Holstein model of spinless fermions and of a frustrated Heisenberg model with magneto-elastic coupling are analyzed on finite chains. In the non-adiabatic regime a (T = 0) quantum phase transition from a gapless Luttinger-liquid/spin-fluid state to a gapped dimerized phase occurs at a nonzero critical value of the electron/spin-phonon interaction. To study the nature of the spin-Peierls transition at finite temperatures for the infinite system, an alternative Green’s function approach is applied to the magnetostrictive XY model. With increasing phonon frequency the structure factor shows a remarkable crossover from soft-mode to central-peak behaviour. The results are discussed in relation to recent experiments on CuGeO3. 1
The spin-Peierls instability in a spin- XY chain coupled to dispersionless phonons of frequency has been studied in the non-adiabatic limit. We have chosen the Lang-Firsov variational wavefunction for the phonon subsystem to obtain an effective spin Hamiltonian. The effective spin Hamiltonian is then solved in the framework of the mean-field approximation and bond operator technique. We observed two types of phase transitions, one is from the spin liquid phase to the dimerized phase and the other is from the dimerized phase to the antiferromagnetic phase as we vary the spin-phonon coupling from a very low value. The variation of lattice distortion, dimerized order parameter and energy gap with spin-phonon coupling parameter have also been investigated here.
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,h<{h}_{c1},h<hc1​, an incommensurate regime (hc1<h<hc2){(h}_{c1}<h<{h}_{c2})(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.{h}_{c2}.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.
The phonon dynamics in a one dimensional Heisenberg spin chain coupled to finite-frequency bond phonons is studied. We present the first detailed phonon spectra for these systems using Quantum Monte Carlo. The quantum phase transition is dominated by a central peak, yet the renormalisation of the main phonon branch depends strongly on the bare phonon frequency omega_0. The main branch remains largely unaffected at omega_0 \gsim J, but it softens completely when omega_0 is low enough. This is an unusual scenario for a structural phase transition and was observable only on sufficiently large systems. Approaching the dimerized phase from finite temperature, the lattice dynamics mirrors the behavior of a three dimensional system. For the efficient measurement of Greens functions, we introduce a mapping from the stochastic series expansion to continuous imaginary time.
We use the density matrix renormalization group (DMRG) to map out the ground state of an XY spin chain coupled to dispersionless phonons of frequency $\ensuremath{\omega}$. We confirm the existence of a critical spin-phonon coupling ${\ensuremath{\alpha}}_{c}\ensuremath{\propto}{\ensuremath{\omega}}^{0.7}$ for the onset of the spin gap bearing the signature of a Kosterlitz-Thouless transition. We also observe a classical-quantum crossover when the spin-Peierls gap $\ensuremath{\Delta}$ is of order $\ensuremath{\omega}$. In the classical regime $\ensuremath{\Delta}>\ensuremath{\omega}$, the mean-field parameters are strongly renormalized by nonadiabatic corrections. This is the first application of the DMRG to phonons.
We revisit the problem of the spin-Peierls instability in a one-dimensional spin-12\frac{1}{2}21​ chain coupled to phonons. The phonons are treated within the mean-field approximation. We use bosonization techniques to describe the gapped spin chain and then use the thermodynamic Bethe ansatz to obtain quantitative results for the thermodynamics of the spin-Peierls system in a whole range of temperature. This allows us to predict the behavior of the specific heat and the magnetic susceptibility in the entire dimerized phase. We study the effect of small magnetic fields on the transition. Moreover, we obtain the parameters of the Landau-Ginzburg theory describing this continuous phase transition near the critical point.