Quantum phase transitions in spin-lattice systems:: An ab initio treatment via the coupled cluster method

The coupled cluster method (CCM) has become one of the most pervasive of all ab initio formulations of quantum many-body theory. It has yielded numerical results which are among the most accurate available for a wide range of both finite and extended physical systems defined on a spatial continuum. This widespread success has spurred many recent applications to quantum systems defined on a lattice. We discuss here a typical example of a two-dimensional spin-half Heisenberg magnet with two kinds of nearest-neighbour bonds. We show how the CCM can successfully describe the influence of strong quantum fluctuations on the zero-temperature phases and their quantum phase transitions. The model shows how the CCM can successfully describe the effects of competition between magnetic bonds with and without the presence of frustration. The frustrated case is particularly important since many other methods, including quantum Monte Carlo simulations, typical fail in this regime.