An exact Polynomial Hybrid Monte Carlo algorithm for dynamical Kogut-Susskind fermions

We present an exact local bosonic algorithm for the simulation of dynamical fermions in lattice QCD. It is based on a non-hermitian polynomial approximation of the inverse of the quark matrix and a global Metropolis accept/reject correction of the systematic errors. We show that this algorithm is a real alternative to the Hybrid Monte Carlo algorithm.

Numerical simulations based on electronic structure calculations are finding ever growing applications in many areas of physics. A major limiting factor is however the cubic scaling of the algorithms used. Building on previous work [F. R. Krajewski and M. Parrinello, Phys.Rev. B71, 233105 (2005)] we introduce a novel statistical method for evaluating the inter-atomic forces which scales linearly with system size and is applicable also to metals. The method is based on exact d...

We present a set of related Hybrid Monte Carlo methods to simulate an arbitrary number of dynamical overlap fermions. Each fermion is represented by a chiral pseudo-fermion field. The new algorithm reduces critical slowing down in the chiral limit and for sectors of nontrivial topology.

A summary of recent developments in the field of simulation algorithms for dynamical fermions is given.

A new Monte Carlo method is proposed for fermion systems interacting with classical degrees of freedom. To obtain a weight for each Monte Carlo sample with a fixed configuration of classical variables, the moment expansion of the density of states by Chebyshev polynomials is applied instead of the direct diagonalization of the fermion Hamiltonian. This reduces a cpu time to scale as $O(N_{\rm dim}^{2} \log N_{\rm dim})$ compared to $O(N_{\rm dim}^{3})$ for the diagonalization...

We present the benchmark of the polynomial expansion Monte Carlo method to a Kondo lattice model with classical localized spins on a geometrically frustrated lattice. The method enables to reduce the calculation amount by using the Chebyshev polynomial expansion of the density of states compared to a conventional Monte Carlo technique based on the exact diagonalization of the fermion Hamiltonian matrix. Further reduction is brought by a real-space truncation of the vector-mat...

Efficient and stable algorithms for the calculation of spectral quantities and correlation functions are some of the key tools in computational condensed matter physics. In this article we review basic properties and recent developments of Chebyshev expansion based algorithms and the Kernel Polynomial Method. Characterized by a resource consumption that scales linearly with the problem dimension these methods enjoyed growing popularity over the last decade and found broad app...

This article contains lecture notes on the constrained path Monte Carlo method and its applications to study the Hubbard model. The lectures were given at the NATO Advanced Summer Institute held in Ithaca NY (1998). The article is published as a chapter in the book `Quantum Monte Carlo Methods in Physics and Chemistry,' Ed. M.P. Nightingale and C.J. Umrigar (Kluwer Academic Publishers, 1999).

We show that in practical simulations of lattice QCD with two dynamical light fermion species the PHMC algorithm samples configuration space differently from the commonly used HMC algorithm.

An approximate treatment of exchange in finite-temperature path integral Monte Carlo simulations for fermions has been proposed. In this method, some of the fine details of density matrix due to permutations have been smoothed over or averaged out by using the coarse-grained approximation. The practical usefulness of the method is tested for interacting fermions in a three dimensional harmonic well. The results show that, the present method not only reduces the sign fluctuati...