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 one-dimensional spin-1/2 Heisenberg model with nearest-neighbour interaction coupled to Einstein phonons is of interest for the understanding of materials which show the spin-Peierls phase transition. I examined this model by performing a finite-temperature quantum Monte Carlo simulation by using the very efficient loop algorithm. I studied in detail the magnetic susceptibility, the specific heat, the phonon occupation, the dimerization, and the spin-spin correlation function of this model for various spin-phonon couplings and phonon frequencies. In particular I gave evidence for a global effective spin-spin coupling and for the transition from a gapless to the massive phase by studying the finite-size behavior of the magnetic susceptibility.
The zero and finite temperature spin-Peierls transitions in a quasi-one-dimensional spin-
21 Heisenberg model coupled to adiabatic bond phonons is investigated using the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method. The quantum phase transition from a gapless N\'eel state to a spin-gapped Peierls state is studied in the parameter space spanned by spatial anisotropy, interchain coupling strength, and spin-lattice coupling strength. It is found that for any finite interchain coupling, the transition to a dimerized Peierls ground state only occurs when the spin-lattice coupling exceeds a finite, nonzero critical value. This is in contrast to the pure 1D model (zero interchain coupling), where adiabatic/classical phonons lead to a dimerized ground state for any nonzero spin-phonon interaction. The phase diagram in the parameter space shows that for a strong interchain coupling, the relation between the interchain coupling and the critical value of the spin-phonon interaction is linear whereas for weak interchain coupling, this behavior is found to have a natural logarithmlike relation. No region was found to have a long range magnetic order and dimerization occurring simultaneously. Instead, the N\'eel state order vanishes simultaneously with the setting in of the spin-Peierls state. For the thermal phase transition, a continuous heat capacity with a peak at the critical temperature
Tc shows a second order phase transition. The variation of the equilibrium bond length distortion ${\ensuremath{\delta}}_{eq}$ with temperature showed a power law relation which decayed to zero as the temperature was increased to
Tc, indicating a continuous transition from the dimerized phase to a paramagnetic phase with uniform bond length and zero antiferromagnetic susceptibility.
Because the three-leg ladder behaves like a renormalized single Heisenberg chain, we argue that a spin-Peierls instability must occur in this system when it is coupled to three-dimensional phonons. Using the bond-mean-field theory, we show that this is indeed the case. The dimerized state below the spin-Peierls transition temperature forms into the columnar dimerized phase instead of the staggered one. This contrasts with the argument based on antiferromagnetism. A physical argument based rather on spin bonding into singlets could explain why the columnar configuration is favored. No quantum criticality (gaplessness) can occur in the columnar arrangement of the dimerized chains.
We study the one-dimensional Holstein model with spin-
21 electrons at half filling. Ground-state properties are calculated for long chains with great accuracy using the density-matrix renormalization-group method and extrapolated to the thermodynamic limit. We show that for small electron-phonon coupling or large phonon frequency, the insulating Peierls ground state predicted by mean-field theory is destroyed by quantum lattice fluctuations and that the system remains in a metallic phase with a nondegenerate ground state and power-law electronic and phononic correlations. When the electron-phonon coupling becomes large or the phonon frequency small, the system undergoes a transition to an insulating Peierls phase with a twofold degenerate ground state, long-range charge-density-wave order, a dimerized lattice structure, and a gap in the electronic excitation spectrum.
The spin-Peierls transition at
TSP of spin-
21 chains with isotropic exchange interactions has previously been modeled as correlated for
T>TSP and mean field for
T<TSP. We use correlated states throughout in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model with antiferromagnetic exchange
J1 and ${J}_{2}=\ensuremath{\alpha}{J}_{1}$ between first and second neighbors, respectively, and variable frustration $0\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}0.50$. The thermodynamic limit is reached at high
T by exact diagonalization of short chains and at low
T by density matrix renormalization group calculations of progressively longer chains. In contrast to mean field results, correlated states of 1D models with linear spin-phonon coupling and a harmonic adiabatic lattice provide an internally consistent description in which the parameter
TSP yields both the stiffness and the lattice dimerization $\ensuremath{\delta}(T)$. The relation between
TSP and $\mathrm{\ensuremath{\Delta}}(\ensuremath{\delta},\ensuremath{\alpha})$, the
T=0 gap induced by dimerization, depends strongly on $\ensuremath{\alpha}$ and deviates from the BCS gap relation that holds in uncorrelated spin chains. Correlated states account quantitatively for the magnetic susceptibility of TTF-
CuS4C4(CF3)4 crystals (
J1=79K, $\ensuremath{\alpha}=0$,
TSP=12K) and
CuGeO3 crystals (
J1=160K, $\ensuremath{\alpha}=0.35$,
TSP=14K). The same parameters describe the specific heat anomaly of
CuGeO3 and inelastic neutron scattering. Modeling the spin-Peierls transition with correlated states exploits the fact that $\ensuremath{\delta}(0)$ limits the range of spin correlations at
T=0 while
T>0 limits the range at $\ensuremath{\delta}=0$.