Monte Carlo procedure for 2-dimensional fermion systems

Shenglong Xu, Congjun Wu

Michael A. Lee, Kazi A. Motakabbir, Kevin E. Schmidt

J. E. Hirsch, Douglas J. Scalapino, Robert L. Sugar +1 more

A new Monte Carlo approach applicable to systems with fermion and boson degrees of freedom is proposed. The main advantage of the method is its speed: For systems in one space and one time dimension (1 + 1) the calculation reduces to doing Monte Carlo computations on a two-dimensional classical system with local interactions. Here the potential of the method is illustrated by application to various (1 + 1)-dimensional systems.

Yasuhiro Hatsugai, Masatoshi Imada

Michael J. Creutz

I discuss algorithms for simulating many-fermion systems via global updatings of auxiliary fields followed by an accept-reject stage which eliminates finite-step-size errors. When the system size is larger than the correlation length, these procedures should require computer time growing only slightly faster than linearly with the system volume V. A corrected Langevin scheme should asymptotically display a ${V}^{4/3}$ behavior, while the hybrid Monte Carlo scheme can behave as ${V}^{5/4}$. I present some tests of the latter algorithm on a simple model of interacting electrons on a two-dimensional lattice.

I. Morgenstern