Spin-wave damping in the quantum Ising-Heisenberg chain

Eugène Gutkin

Ueli Glaus, Stephen William Lovesey, E. Stoll

Numerical calculations of the transverse response function for short-length quantum-spin chains are used to study spin-wave damping at temperatures small compared with the Heisenberg exchange coupling. Results are presented for ferromagnetically coupled systems at several temperatures, for both spin \textonehalf{} and 1. At low temperatures, the numerical results are shown to be in good quantitative agreement with the predictions of nonlinear spin-wave theory.

Horaƫiu Năstase

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.

T. Schneider, E. Stoll

Xin Li, Zhong-Fang Li, Zhi-Long Shi +1 more

Based on the solvable spin-1/2 Heisenberg chain we demonstrate how two many-body systems are entangled due to their partial entanglement. The entanglement wave in the two spin chains displays a damped oscillation if the spin number is N > 3, and only propagates with a certain velocity depending on the coupling constant J. Moreover, the entanglement wave will be reflected on the other ends of the two spin chains. A simple scheme for transferring some special two-qubit states to other two distant qubits is also proposed.