Effects of spin-Peierls fluctuation are examined in models of one-dimensional conductors. One-dimensional strongly correlated systems coupled to dynamical lattice distortion or polarization are examined by quantum Monte Carlo studies. Excitations are given by spinless charge solitons and neutral spin solitons when the system is doped away from a Mott insulator. A pairing mechanism due to a dynamical spin-Peierls fluctuation is discussed. Numerical results on the spin gap formation and the enhancement of pairing correlations in a dimerized t-J model and doped spin-1 Heisenberg model in one dimension are summarized.
A Wigner-Jordan (WJ) transformation is used to study the one-dimensional (1D) and two-dimensional (2D) quantum antiferromagnetic Heisenberg model. The advantage of using the Wigner-Jordan transformation is that it preserves all spin-commutation relations as well as the spin on-site exclusion principle. In the 1D case a nearest-neighbor covalent-bonding state of the WJ fermions is found to have a ground-state energy (-0.4351J per site) comparable with that from the Bethe-ansatz solution (-0.4431J per site), and a linear energy spectrum at low energies with velocity 1.6366J, in close agreement with the velocity obtained by Haldane for the quantum antiferromagnetic Heisenberg model with 1/
d2 interaction (1.5708J). The method used for studying the 1D model is then applied to the 2D Heisenberg model in a square lattice. The resulting state at finite temperature is the in-phase flux state, i.e., a flux state of the Wigner-Jordan spinless fermions with an in-phase fermion orbital current circulating around each elementary plaquette.The single-particle excitation spectrum, i.e., the energy dispersion of reversing orientation of a spin in the system, of the in-phase flux state is overall similar to that of spin waves, with significant difference near the edge point k=(\ensuremath{\pi},0), at which the excitation energy of the WJ fermion is zero, whereas that of the spin-wave excitation is 2J. The specific heat of the in-phase flux state predicts a correct temperature dependence over the entire temperature range, namely a
T2 dependence at low temperature, a peak near T/J=0.6, and a 1/
T2 decreasing at high temperature. It also gives excellent agreement with the specific heat calculated from numerical methods. In contrast, the spin-wave theory only correctly predicts a
T2 dependence at low temperature. The Raman spectrum of the in-phase flux state is calculated and shows significant improvement over that from spin-wave theories compared with the experimental spectrum of
La2CuO4. The exchange parameter, J, obtained from the comparison is 1060 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, in agreement with that obtained from analyzing the neutron-scattering data.
Using exact diagonalizations, we consider self-consistently the lattice distortions in odd Peierls-Hubbard and spin-Peierls periodic rings in the adiabatic harmonic approximation. From the tails of the inherent spin soliton the dimerization ${d}_{\ensuremath{\infty}}$ of regular even rings is found by extrapolations to infinite ring lengths. Considering a wide region of electron-electron on-site interaction values
U>0 compared with the band width
4t0 at intermediately strong electron-phonon interaction
g, known relationships obtained by other methods are reproduced and/or refined within one unified approach: an example is the maximum of ${d}_{\ensuremath{\infty}}$ at $U\ensuremath{\simeq}{3t}_{0}$ for $g\ensuremath{\simeq}0.5$ and its shift to zero for $g\ensuremath{\rightarrow}{g}_{c}\ensuremath{\approx}0.7.$ The hyperbolic tangent shape of the spin soliton is retained for any
U and $g\ensuremath{\lesssim}0.6.$ In the spin-Peierls limit the ${d}_{\ensuremath{\infty}}$ are found to be in agreement with results of density-matrix-renormalization-group computations.
One-dimensional spin- anisotropic Heisenberg antiferromagnet in a longitudinal external magnetic field is studied using bosonization method and Gaussian wave functional techniques which take account of the spatial structure. The magnetization and the energy of the ground state which depend on the external magnetic field are calculated. For the case of anisotropic parameter , increasing of the external magnetic field above the threshold value leads to the appearance of the soliton lattice state in the ground state, until to an another critical field where the ground state changes to the canted state phase. Therefore, with increasing external magnetic field, the ground state experiences four different phases successively, namely, antiferromagnetic Ising, soliton lattice state canted state, and magnetization saturated phases. When , the soliton lattice state phase does not appear, with increasing external field, the paramagnetic phase smoothly evolves into the canted state phase, finally reaches magnetization saturated phase.
One-dimensional spin-1-2 anisotropic Heisenberg antiferromagnet in a longitudinal external magnetic field is studied using bosonization method and Gaussian wave functional techniques which take account of the spatial structure.The magnetization and the energy of the ground state which depend on the external magnetic field are calculated.For the case of anisotropic parameter △＞△0,increasing of the external magnetic field above the threshold value leads to the appearance of the soliton lattice state in the ground state,until to an another critical field where the ground state changes to the canted state phase.Therefore,with increasing external magnetic field,the ground state experiences four different phases successively,namely,antiferromagnetic Ising,soliton lattice state canted state,and magnetization saturated phases.When △＜△0,the soliton lattice state phase does not appear,with increasing external field,the paramagnetic phase smoothly evolves into the canted state phase,finally reaches magnetization saturated phase.
The Jordan–Wigner transformation is applied to the spatially anisotropic spin-1/2 Heisenberg model on a square lattice with the nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions. The transformed Hamiltonian describes the interacting spinless fermions that hop between neighbor sites in a gauge field. Using the mean-field-type approximation to both the direct interaction between fermions and the phase factors, which represent the gauge field, the problem is reduced to that concerning a free Fermi gas. Two types of antiferromagnetic ordering (the N´eel and collinear ones) are considered. By calculating the ground-state energies, the phase transitions induced by the interaction frustration were analyzed.