Computational Studies of Quantum Spin Systems

Details Computational Studies of Quantum Spin Systems Computational Studies of Quantum Spin Systems

2011-01-17

arxiv.org/abs/1101.3281v1

AIP Conf.Proc.1297:135,2010

Physics

Condensed Matter

Strongly Correlated Electrons

207 pages, 91 figures. Lecture notes for course given at the 14th Training Course in Physics of Strongly Correlated Systems, S

Scientific paper

10.1063/1.3518900

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.

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