An efficient method to compute the residual phase on a Lefschetz thimble

M. Cristoforetti (1, 2) , F. Di Renzo (3) , G. Eruzzi (3) , A. Mukherjee (1, 2) , C. Schmidt (4) , L. Scorzato (5) , C. Torrero (6, 7)

1 ECT* - European Center for Theoretical Studies in Nuclear Physics and Related Areas
2 UR LISC - Laboratoire d'ingénierie pour les systèmes complexes
3 Dipartimento di Fisica [Parma]
4 Fakultät für Physik
5 INFN-TIFPA
6 CPT - E3 Cosmologie
7 CPT - Centre de Physique Théorique - UMR 7332

We propose an efficient method to compute the so-called residual phase that appears when performing Monte Carlo calculations on a Lefschetz thimble. The method is stochastic and its cost scales linearly with the physical volume, linearly with the number of stochastic estimators and quadratically with the length of the extra dimension along the gradient flow. This is a drastic improvement over previous estimates of the cost of computing the residual phase. We also report on basic tests of correctness and scaling of the code.

Domaines: Physique des Hautes Energies - Réseau [hep-lat]

M. Cristoforetti, F. Di Renzo, G. Eruzzi, A. Mukherjee, C. Schmidt, et al.. An efficient method to compute the residual phase on a Lefschetz thimble. Physical Review D, 2014, 89 (11), pp.114505. ⟨10.1103/PhysRevD.89.114505⟩. ⟨hal-01252917⟩