Computational Studies of Quantum Spin Systems

TL;DR

This paper provides an overview of computational methods for quantum spin systems, including Monte Carlo and exact diagonalization, with applications to key models in quantum magnetism and phase transitions.

Contribution

It introduces and compares various computational techniques for quantum spin systems, emphasizing their application to fundamental models and phase transition studies.

Findings

Monte Carlo methods effectively analyze classical and quantum spin systems.

Exact diagonalization provides detailed insights into ground states.

Quantum Monte Carlo captures finite-temperature properties.

Abstract

These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of Monte Carlo studies of classical spin systems, to illustrate finite-size scaling at continuous and first-order phase transitions. Exact diagonalization and quantum Monte Carlo (stochastic series expansion) algorithms and their computer implementations are then discussed in detail. Applications of the methods are illustrated by results for some of the most essential models in quantum magnetism, such as the S=1/2 Heisenberg antiferromagnet in one and two dimensions, as well as extended models useful for studying quantum phase transitions between antiferromagnetic and magnetically disordered states.