a Quantum Theory for Ferromagnetic and Antiferromagnetic Heisenberg Spin Chains at Low Temperatures.

Minoru Takahashi

Xin Wan, Kun Yang, R. N. Bhatt

We study the thermodynamics of a one-dimensional quantum spin-1/2 Heisenberg ferromagnetic system with random antiferromagnetic impurity bonds. In the dilute impurity limit, we generalize the modified spin-wave theory for random spin chains, where local chemical potentials for spin waves in ferromagnetic spin segments are introduced to ensure zero magnetization at finite temperature. This approach successfully describes the crossover from the behavior of a pure one-dimensional ferromagnet at high temperatures to a distinct Curie behavior due to randomness at low temperatures. We discuss the effects of impurity bond strength and concentration on the crossover and low-temperature behavior.

Kazuo Hida

The low temperature magnetization process of the ferromagnetic-antiferromagnetic Heisenberg chain is studied using the interacting boson approximation. In the low field regime and near the saturation field, the spin wave excitations are approximated by the $δ$ function boson gas for which the Bethe ansatz solution is available. The finite temperature properties are calculated by solving the integral equation numerically. The comparison is made with Monte Carlo calculation and the limit of the applicability of the present approximation is discussed.

Pedro D Sacramento

Yinxiang Li, Bin Chen

Ozan S. Sarıyer, A. Nihat Berker, Michael Hinczewski

The anisotropic $XXZ$ spin-$\frac{1}{2}$ Heisenberg chain is studied using renormalization-group theory. The specific heats and nearest-neighbor spin-spin correlations are calculated throughout the entire temperature and anisotropy ranges in both ferromagnetic and antiferromagnetic regions, obtaining a global description and quantitative results. We obtain, for all anisotropies, the antiferromagnetic spin-liquid spin-wave velocity and the Ising-like ferromagnetic excitation spectrum gap, exhibiting the spin-wave to spinon crossover. A number of characteristics of purely quantum nature are found: The in-plane interaction ${s}_{i}^{x}{s}_{j}^{x}+{s}_{i}^{y}{s}_{j}^{y}$ induces an antiferromagnetic correlation in the out-of-plane ${s}_{i}^{z}$ component, at higher temperatures in the antiferromagnetic $XXZ$ chain, dominantly at low temperatures in the ferromagnetic $XXZ$ chain, and, in-between, at all temperatures in the $XY$ chain. We find that the converse effect also occurs in the antiferromagnetic $XXZ$ chain: an antiferromagnetic ${s}_{i}^{z}{s}_{j}^{z}$ interaction induces a correlation in the ${s}_{i}^{xy}$ component. As another purely quantum effect, (i) in the antiferromagnet, the value of the specific heat peak is insensitive to anisotropy and the temperature of the specific heat peak decreases from the isotropic (Heisenberg) with introduction of either type (Ising or $XY$) of anisotropy; and (ii) in complete contrast, in the ferromagnet, the value and temperature of the specific heat peak increase with either type of anisotropy.