Two-step Multi-boson Research Articles

Updating algorithms with multi-step stochastic correction

Nested multi-step stochastic correction offers a possibility to improve updating algorithms for numerical simulations of lattice gauge theories with fermions. The corresponding generalisations of the two-step multi-boson (TSMB) algorithm as well as some applications with hybrid Monte Carlo (HMC) algorithms are considered.

Two Algorithms and Lattice U(1) Model

Two algorithms in the dynamical fermions approach, the hybrid Monte Carlo method and the two-step multiboson algorithm, are tested in case of the Wilson U(1) model on a four-dimensional lattice. Relations for the parameters and for the performance values of the algorithms are proposed. A comparison of the algorithms by the correlation functions evaluated and by the efficiency is carried out, and a conclusion about the suitability of the algorithms for studies of the lattice U(1) model is given.

Unquenched domain wall quarks with TSMB

The numerical simulation of domain wall quarks with the two-step multi-boson (TSMB) algorithm is investigated. Tests are performed on a 8 3 · 4 lattice with N f = 2 quark flavours.

Lattice QCD with light dynamical quarks

We report on the simulation of QCD with light dynamical quarks using the two-step multi-boson (TSMB) algorithm. In an exploratory study with two flavours of quarks at lattice spacing about 0.27 fm and with quark mass down to one sixth of the strange quark mass eigenvalue spectra and autocorrelations have been studied. Here we present results on the volume dependence as well as tests of possible algorithmic improvements.

Numerical simulation tests with light dynamical quarks

Two degenerate flavors of quarks are simulated with small masses down to about one fifth of the strange quark mass by using the two-step multi-boson (TSMB) algorithm. The lattice size is $8^3 \times 16$ with lattice spacing about $a \simeq 0.27 {\mathrm {fm}}$ which is not far from the N t =4 thermodynamical cross-over line. Autocorrelations of different physical quantities are estimated as a function of the quark mass. The eigenvalue spectra of the Wilson-Dirac operator are investigated.

Unquenched domain wall quarks with multi-bosons

The numerical simulation of domain wall quarks with the two-step multi-boson (TSMB) algorithm is considered. The inclusion of single quark flavours, as required for strange quarks, is discussed. The usage of computer memory can be kept relatively low, independently of the order of polynomial approximations. Tests are performed with two flavours ( N f =2) of degenerate quarks near the N t =4 thermodynamical cross over.

Performance studies of the two-step multiboson algorithm in compact lattice QED

The performance of the two-step multiboson (TSMB) algorithm is investigated in comparison with the hybrid Monte Carlo (HMC) method for compact lattice QED with standard Wilson fermions both in the Coulomb and confinement phases. The restriction to QED allows for extensive measurements of autocorrelation times. Preliminary results show that the TSMB algorithm is at least competitive with standard HMC.

Numerical study of dense adjoint matter in two color QCD

We identify the global symmetries of SU(2) lattice gauge theory with N flavors of staggered fermion in the presence of a quark chemical potential mu, for fermions in both fundamental and adjoint representations, and anticipate likely patterns of symmetry breaking at both low and high densities. Results from numerical simulations of the model with N=1 adjoint flavor on a 4^3x8 lattice are presented, using both hybrid Monte Carlo and Two-Step Multi-Boson algorithms. It is shown that the sign of the fermion determinant starts to fluctuate once the model enters a phase with non-zero baryon charge density. HMC simulations are not ergodic in this regime, but TSMB simulations retain ergodicity even in the dense phase, and in addition appear to show superior decorrelation. The HMC results for the equation of state and the pion mass show good quantitative agreement with the predictions of chiral perturbation theory, which should hold only for N>=2. The TSMB results incorporating the sign of the determinant support a delayed onset transition, consistent with the pattern of symmetry breaking expected for N=1.