Field Theoretic Studies of Quantum Spin Systems in One Dimension

We describe some field theoretic methods for studying quantum spin systems in one dimension. These include the nonlinear σ-model approach which is particularly useful for large values of the spin, the idea of Luttinger liquids and bosonization which are more useful for small values of spin such as spin-1/2, and the technique of low-energy effective Hamiltonians which can be useful if the system under consideration is perturbatively close to an exactly solvable model. We apply these techniques to similar spin models, such as spin chains with dimerization and frustration, and spin ladders in the presence of a magnetic field. This comparative study illustrates the relative strengths of the different methods.