Investigation of One- and Two-Dimensional Quantum Spin Systems by Monte Carlo Simulations

A method for simulating quantum spin systems with nearest neighbour interaction is reviewed. In the framework of a path-integral approach based on the Trotter formula, the quantum spin system is mapped into the limit of a sequence of classical spin systems with one extra dimension. Numerical questions connected to this limit are discussed. The role of particle and winding numbers is clarified. An overview of the problems investigated by our group is given. In particular, two new results are presented. A simulation of the one-dimensional spin S isotropic Heisenberg antiferromagnet, S=1/2, 1, 3/2, 2, supports Haldane's conjecture that the mass gap is zero for half­ integer S and nonzero for integer S. For the two-dimensional spin 1/2 xy model we discuss evidence for a Kosterlitz-Thouless transition. In particular, we show that the helicity modulus can be computed directly from our simulaton.