Dynamical Properties of One-Dimensional Antiferromagnets
Abstract
This dissertation describes a new method for obtaining the dynamical properties of one-dimensional antiferromagnets. The new method combines the well-known world-line quantum Monte Carlo and maximum entropy methods. World-line quantum Monte Carlo stochastically evaluates the imaginary-time correlation functions S_{zz}(q, tau). Maximum entropy converts S _{zz}(q,tau) into an approximate result for the dynamical spin structure factor S_{zz}(q, omega). S_{zz}(q, omega) is the important quantity which directly describes neutron scattering experiments and the lowest energy excitations of a magnetic system. Results produced with this dynamical method are compared to exact results for the Ising and xy models. It is found that this dynamical method broadens the exact result with a broadening width that increases with the frequency omega. We then examine the antiferromagnetic Heisenberg model for S = 1/2, 1, 3/2 and 2 where S _{zz}(q,omega) is not known. The difference between half-integer and integer spin values predicted by Haldane is clearly displayed. We obtain an excitation gap of 0.40J for S = 1 which agrees with the result found with other methods. Using 32, 64 and 128 lattice sites, we find an excitation gap of 0.08J for S = 2. For S = 1/2 S_{zz} (q,omega) shows a broad continuum of excitations. This continuum shrinks when S increases to S = 3/2, indicating the approach to the classical limit (S toinfty) where S _{zz}(q,omega) is dominated by one frequency. When on-site anisotropy is included for the S = 1 Heisenberg model, we find a splitting of the excitation gap that gives a good description of the gap splitting found for NENP. Results for the t - J model at electron filling of 0.75/site are also described. S_{zz}(q, omega) shows the cross-over from Hubbard -like behavior for J/t <= 2 to Heisenberg -like behavior for J/t > 3.25 when phase separation of electrons and holes occurs. In the cross -over region, 2t < J < 3.25t, S_{zz}(q,omega ) is dominated by high-energy excitations which suggests the formation of strongly bound singlet pairs. However, we find no gap in the spin excitation spectrum implying the singlet pairs are weakly coupled to each other. We also obtain the charge structure factor, S_ {nn}(q,omega). S_{nn}(q,omega ) is dominated by high-energy particle-hole-like excitations. However, new low-energy features are found when J/t increases from zero.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- February 1991
- Bibcode:
- 1991PhDT........63D
- Keywords:
-
- MONTE CARLO;
- HEISENBERG MODEL;
- Physics: Condensed Matter