Spin chain simulations with a meron cluster algorithm

We apply a meron cluster algorithm to the XY spin chain, which describes a quantum rotor. This is a multi-cluster simulation supplemented by an improved estimator, which deals with objects of half-integer topological charge. This method is powerful enough to provide precise results for the model with a theta-term - it is therefore one of the rare examples, where a system with a complex action can be solved numerically. In particular we measure the correlation length, as well as the topological and magnetic susceptibility. We discuss the algorithmic efficiency in view of the critical slowing down. Due to the excellent performance that we observe, it is strongly motivated to work on new applications of meron cluster algorithms in higher dimensions.Comment: 18 pages, 9 figures, published versio

Spectral properties of the Wilson Dirac operator in the ϵ\epsilon-regime

We investigate the spectral properties of the Wilson Dirac operator in quenched QCD in the microscopic regime. We distinguish the topological sectors using the index as determined by the Wilson flow method. Consequently, the distributions of the low-lying eigenvalues of the Wilson Dirac operator can be compared in each of the topological sectors to predictions from random matrix theory applied to the $\epsilon$-regime of chiral perturbation theory. We find rather good agreement for volumes as small as $(1.5 \, \text{fm})^4$ and lattice spacings as coarse as $0.1\, \text{fm}$, and demonstrate that it is indeed possible to extract low-energy constants for Wilson fermions from the spectral properties of the Wilson Dirac operator.Comment: Changed normalizations for some of the results, cosmetic updates to several plots. Conclusions not affected. Version accepted for publication by JHEP. 22 pages, 12 figure