This course introduces quantum spin systems and several computational methods for studying their groundstate
and finitetemperature properties. Exact diagonalization and quantum Monte Carlo algorithms and their computer
implementations are discussed in detail (including the use of lattice symmetries in complete and Lanczos
diagonalization studies, and quantum Monte Carlo methods based on the stochastic series expansion as well as
groundstate projection in the valencebond basis). 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 in two dimensions.
PART 1: Introduction to classical and quantum spin systems and quantum magnetism
[April 05] Classical and quantum spin systems and their significance; origin of quantum antiferromagnetism
[April 06] Spinwave theory of the Neel state and its quantum fluctuations
[April 07] Nonmagnetic states, frustrated interactions, examples of quantum phase transitions
[April 08] Quantum and classical phase transitions, criticality and finitesize scaling behavior
[April 09] Classical Monte Carlo simulations, symmetrybreaking, autocorrelation functions
Ising Program used in tutorials April 1213: [Ising.f90]

PART 2: Exact diagonalization methods
[April 12] Bit representation of spins, constructing the hamiltonian matrix, fixedmagnetization blocks
[April 13] Translational symmetry and momentum states, reflection symmetry (parity)
[April 14] Semimomentum states, spininversion symmetry, thermodynamics, the Lanczos method
[April 15] Computer implementation of the Lanczos method, convergence properties
[April 16] Properties of spin chains, standard Heisenberg model, frustrated chain, longrange interactions
[April 19] Momentum states in 2D, quantum rotor states of the Heisenberg model
Programs used in tutorial and homework April 15,19,20: [program list and instructions]

PART 3: Quantum Monte Carlo methods
[April 19] Pathintegral formulation of quantum statistical mechanics
[April 20] Stochastic series expansion (SSE), implementation for the S=1/2 Heisenberg model
[April 21] More on SSE implementation, tests of correctness, properties of long Heisenberg chains
[April 22] Properties of Heisenberg ladders, 2D systems, spin stiffness, quantum criticality
[April 23] Calculations with the valencebond basis, NeelVBS transition in "JQ" models
Programs used in tutorial and homework April 23: [SSE code and instructions]

