Comment on ‘What is the sign of ℏ ?’

D. Galanakis, Shuxiang Yang, Fakher F. Assaad +3 more

This a comment on arXiv:0907.3243v2. We demonstrate that the method proposed by Efetov {\it et. al.} is just a reformulation of the Blankenbeckler, Scalapino, and Sugar approach and thus it contains exactly the same sign problem, including the dependence of the sign on the smoothness of the paths.

Brian P. Anderson

Brian P. Anderson

K. S. D. Beach, Matthieu Mambrini, Fabien Alet

Quantum Monte Carlo methods are sophisticated numerical techniques for simulating interacting quantum systems. In some cases, however, they suffer from the notorious ``sign problem'' and become too inefficient to be useful. A recent publication [J. Wojtkiewicz, Phys. Rev. B 75, 174421 (2007)] claims to have solved the sign problem for a certain class of frustrated quantum spin systems through the use of a bipartite valence bond basis. We show in this Comment that the apparent positivity of the path integral is due to a misconception about the resolution of the identity operator in this basis and that consequently the sign problem remains a severe obstacle for the simulation of frustrated quantum magnets.

Max Born

Guangri Jin, Dong Zhou

This paper has been withdrawn by the author(s), due a crucial sign error in conclusion .