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Abstract
Theoretical investigations of quantum spin systems have been given renewed impetus by the discoveries and successful syntheses of new magnetic materials which display rich quantum phenomena that demand explanations. In this work quantum spin- lattice systems are studied using the coupled cluster method (CCM). One of our goals is to devise new approximation schemes that can capture the most important configurations at low orders and which thus lead to a more rapid convergence of the calculated quantites in the respective truncation indices. We have devised two new approximation schemes, namely the DSUBm and LPSUBm schemes. They have been applied to the XXZ and the XY spin-1/2 Heisenberg antiferromagnetic models on the square lattice in two dimensions. The ground-state energy, the staggered magnetization, and the quantum critical point are calculated, and are found to be in good agreement with those from the quantum Monte Carlo and series expansion methods and with those from the CCM using the earlier LSUBn scheme. The CCM has also been applied to a strongly frustrated J1-J1`-J2 model on the 2D square lattice for both the cases of spin-1/2 and spin-1. We choose to study this model as it can well describe many interesting low-dimensional magnetic materials, such as the undoped precursors to the high-temperature copper-oxide superconductors. The influence of the interchain coupling J1` on the ground-state properties is investigated. For the spin-1/2 case an intermediate phase emerges for J1` > 0.6±0.03 with a corresponding triple point (TP). A second-order phase transition is observed between the Neel and stripe-ordered phases (these are the only phases present in the classical model) below the TP. By contrast, no intermediate phase is observed for the case of spin-1, but it is interesting to observe now the emergence of a tricritical point at J1` > 0.66 ± 0.03, where a line of second-order phase transitions between the quasi-classical Neel and stripe-ordered phases (for J1` <? 0.66) meets a line of first-order phase transitions between the same two states (for J1` > 0.66).