The Worm Algorithm for the CP(N-1) Model

The problem of critical slowing down is reviewed and a comprehensive description of how to measure the efficiency of Monte Carlo algorithms in practice is given. Special regard is paid to the O(N) and CP(N-1) models. The dynamic critical exponents of Wolff's single-cluster algorithm are determined on the two-dimensional O(3) and CP(3) models to confirm its efficiency on the former and inefficiency on the latter. The idea of worm algorithms is explained on the exemplary Ising model and the analogous formalism based on the high-temperature expansion by Chandrasekharan is derived for the CP(N-1) model with general N. An efficient computer implementation is provided in detail, and the algorithm is verified. Consistency with existing numerical results is reported for CP(1) in two dimensions to very high precision, together with a dynamic critical exponent of z = 0.32(3) for winding numbers and z = 0 for energy and magnetic susceptibility. The algorithm is found to lack ergodicity for N > 2, and the problem is quantified numerically. An effort to include the disconnected piece of the CP(N-1) Green's function into the sampling scheme results in a sign problem