Computational Studies of Quantum Spin Systems
Abstract
These lecture notes introduce quantum spin systems and several computational methods for studying their groundstate and finitetemperature properties. Symmetrybreaking and critical phenomena are first discussed in the simpler setting of Monte Carlo studies of classical spin systems, to illustrate finitesize scaling at continuous and firstorder 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.
 Publication:

Lectures on the Physics of Strongly Correlated Systems Xiv: Fourteenth Training Course in the Physics of Strongly Correlated Systems
 Pub Date:
 November 2010
 DOI:
 10.1063/1.3518900
 arXiv:
 arXiv:1101.3281
 Bibcode:
 2010AIPC.1297..135S
 Keywords:

 quantum theory;
 Monte Carlo methods;
 antiferromagnetic materials;
 phase transitions;
 excited states;
 75.10.Jm;
 61.43.Bn;
 75.50.Ee;
 75.30.Kz;
 71.15.Qe;
 Quantized spin models;
 Structural modeling: serialaddition models computer simulation;
 Antiferromagnetics;
 Magnetic phase boundaries;
 Excited states: methodology;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Lattice
 EPrint:
 207 pages, 91 figures. Lecture notes for course given at the 14th Training Course in Physics of Strongly Correlated Systems, Salerno (Vietri sul Mare), Italy, in October 2009