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arXiv · 0812.0677

Simulating the All-Order Hopping Expansion II: Wilson Fermions

Ulli Wolff
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Abstract

We investigate the extension of the Prokof'ev-Svistunov worm algorithm to Wilson lattice fermions in an external scalar field. We effectively simulate by Monte Carlo the graphs contributing to the hopping expansion of the two-point function on a finite lattice to arbitrary order. Tests are conducted for a constant background field i. e. free fermions at some mass. For the method introduced here this is expected to be a representative case. Its advantage is that we know the exact answers and can thus make stringent tests on the numerics. The approach is formulated in both two and three space-time dimensions. In D=2 Wilson fermions enjoy special positivity properties and the simulation is similarly efficient as in the Ising model. In D=3 the method also works at sufficiently large mass, but there is a hard sign problem in the present formulation hindering us to take the continuum limit.

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Ulli Wolff. 2008-12-03. Simulating the All-Order Hopping Expansion II: Wilson Fermions. https://doi.org/10.1016/j.nuclphysb.2009.01.018

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