Spin- Quantum Heisenberg Magnet

We will use our first example, the spin- quantum Heisenberg magnet, to further illustrate the world-line quantum Monte Carlo method. The model we present is the quantum XXZ model  

All other matrix elements are zero. The only nonvanishing matrix elements are those between states with the same total spin in the two Trotter slices, reflecting the spin conservation of the Hamiltonian. Note that the off-diagonal 

---

In present-day quantum chemistry the Heisenberg Spin Hamiltonian is widely applied for the description of magnetic coupling in transition-metal clusters and may read in the case of a many-electron system,... 

Low-dimensional Solids. - 2.10.1 Introduction. The magnetic properties of one and two-dimensional arrays of localized spins coupled by Heisenberg exchange interactions have been studied as a rather specialized branch of theoretical physics since the earliest days of quantum mechanics. However, recent advances in theory, and the preparation of real materials that are a good approximation to the theoretical models, have made low-dimensional systems much more central to condensed-matter science. There is enormous scope for synthetic chemistry in this area and, as will be seen later in this section, many new materials have been discovered recently. 

---