V. S. Viswanath

Recursion method in quantum spin dynamics: The art of terminating a continued fraction

The results obtained from applications of the recursion method to quantum many‐body dynamics can be greatly improved if an appropriate termination function is employed in the continued‐fraction representation of the corresponding relaxation function. We present a general recipe for the construction and use of such termination functions along with two applications in spin dynamics. The method can be adapted to any other problem in quantum many‐body dynamics.

The Recursion Method Applied to the T=0 Dynamics of the 1D s=1/2 Heisenberg and XY Models

The frequency‐dependent spin autocorrelation functions for the 1D s=1/2 Heisenberg and XY models at zero temperature are determined by the recursion method. These applications further demonstrate the efficacy of a new calculational scheme developed for the termination of continued fractions. A special feature of the recursion method highlighted here is its capability to predict the exponent of the infrared singularities in spectral densities.

Dynamics of semi-infinite quantum spin chains at T=∞

Time-dependent spin autocorrelation functions and their spectral densities for the semi-infinite one-dimensionals=1/2 XY and XXZ models atT=∞ are determined in part by rigorous calculations in the fermion representation and in part by the recursion method in the spin representation. Boundary effects yield valuable new insight into the different dynamical processes which govern the transport of spin fluctuations in the two models. The results obtained for theXXX model bear the unmistakable signature of spin diffusion in the form of a squareroot infrared divergence in the spectral density.

Dynamical Properties of Quantum Spin Systems in Magnetically Ordered Product Ground States

The one‐dimensional spin‐s XYZ model in a magnetic field of particular strength has a ferro‐ or antiferromagnetically ordered product ground state. The recursion method is employed to determine T=0 dynamic structure factors for systems with s=1/2, 1, 3/2. The line shapes and peak positions differ significantly from the corresponding spin‐wave results, but their development for increasing values of s suggests a smooth extrapolation to the spin‐wave picture.

Deterministic and stochastic spin diffusion in classical Heisenberg magnets

This computer simulation study provides further evidence that spin diffusion in the one‐dimensional classical Heisenberg model at T=∞ is anomalous: 〈Sj(t)⋅Sj〉 ∼t−α1 withα1 ≳1/2. However, the exponential instability of the numerically integrated phase‐space trajectories transforms the deterministic transport of spin fluctuations into a computationally generated stochastic process in which the global conservation laws are still satisfied to high precision. This may cause a crossover in 〈Sj(t)⋅Sj〉 from anomalous spin diffusion (α1 ≳ 1/2) to normal spin diffusion (α1 = 1/2) at some characteristic time lag that depends on the precision of the numerical integration.

Spin diffusion in classical Heisenberg magnets with uniform, alternating, and random exchange

We have carried out an extensive simulation study for the spin autocorrelation function at T=∞ of the one‐dimensional classical Heisenberg model with four different types of isotropic bilinear nearest‐neighbor coupling: uniform exchange, alternating exchange, and two kinds of random exchange. For the long‐time tails of all but one case, the simulation data seem incompatible with the simple ∼t−1/2 leading term predicted by spin diffusion phenomenology.

Dynamics of the one‐dimensional spin‐1 Heisenberg antiferromagnet with exchange and single‐site anisotropy

The T=0 dynamical properties of the one‐dimensional s=1 XXZ model with an additional single‐site term are investigated by means of the recursion method. The dynamic structure factors Sμμ(q=π,ω), μ=x,z bear the characteristic signatures of several different phase transitions. In the s=1 Heisenberg antiferromagnet, the intrinsic linewidth (at fixed q) of Sμμ(q,ω) is larger for small q than for q near π, in contrast to well‐established results for the corresponding s=1/2 model.