On the Fermionic Shadow Wave Function and novel attempts to solve its sign problem

Francesco Calcavecchia, Francesco Pederiva, and Thomas D. Kuehne

Institute of Physical Chemistry, Johannes Gutenberg-University Mainz, Staudinger Weg 9, D-55128 Mainz, Germany

Dipartimento di Fisica, University of Trento, via Sommerive 14, I-38050 Povo, Trento, Italy

Lawrence Livermore National Laboratory Livermore, California 94550, USA

Center for Computational Sciences, Johannes Gutenberg-University Mainz, Staudinger Weg 9, D-55128 Mainz, Germany

Journal of Unsolved Questions, 1, 2, Articles 13-18, 2011 (Received June 11th, accepted June 30th, published online July 9th 2011)

We present the Fermionic Shadow Wave Function in the context of variational quantum Monte Carlo for disordered systems. Using the example of liquid 3He it is demonstrated that this allows for very accurate calculations, but due to its sign problem only for small systems. For this reason two novel methods are proposed that in principle solve the associated sign problem, but do not allow for realistic simulations yet.

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Keywords: Fermionic Shadow Wave Function, Variational Monte Carlo