Richard Scalettar
Quantum Monte Carlo for Lattice Bosons

1. Lecture 1:
   1. This lecture will develop the mapping of quantum mechanical problems onto equivalent classical problems via the path integral method. In particular, the "world-line" QMC algorithm, in which operators are eliminated through the discretization of the inverse temperature beta and the introduction of complete sets of states will be introduced within the context of the simplest possible example: the quantum harmonic oscillator. Questions of discretization errors, subtleties in the evaluation of the kinetic energy, correlation times, and Fourier acceleration will be addressed in a context where considerable analytic development is also possible.
2. Lecture
   1. This lecture will build on the first by describing the world-line algorithm in a physically non-trivial problem- the one-dimensional Ising model in a transverse magnetic field. It will be shown that the resulting classical model is the two-dimensional, anisotropic, Ising model. The idea of the dynamic critical exponent will be introduced. Finally, some introductory material on quantum bosons, for example the relation to quantum spin-1/2 systems in the hard core limit, will be presented in preparation for the third lecture.
3. Lecture 3:
   1. The world-line algorithm for quantum bosons will be developed. Algorithmic issues like winding number constraints, grand-canonical vs. canonical simulations, and the evaluation of non-local off diagonal observables will be addressed.

Last modified: Thu Jun 11 17:20:05 EDT 1998