Solving sign problems with meron cluster algorithms : simulating field theories at non-zero chemical potential

Abstract

Numerical simulation of quantum systems develop sign problems upon the introduction of a chemical potential. The sign problem thus makes many interesting physical systems very difficult to study numerically. In this thesis, two related systems which develop sign problems in this way are considered: a D-Theory representation of a 1+1 dimensional 0(3) quantum field theory with a chemical potential, and antiferromagnetic Heisenberg quantum spin ladders in a magnetic field. In both cases, meron cluster algorithms are used to completely solve the sign problem. Using these algorithms, numerical results were generated in the two models for, respectively, the particle number as a function of the chemical potential and magnetization as a function of the external field. These results are in agreement with corresponding analytic predictions.