Schwinger-Keldysh formalism on the lattice: A faster algorithm and its application to field theory
G. Başar, A. Alexandru, P.F. Bedaque, G.W. Ridgway · Carolina Digital Repository (University of North Carolina at Chapel Hill) · 2022
A new algorithm is developed allowing the Monte Carlo study of a 1+1-dimensional theory in real time. The main algorithmic development is to avoid the explicit calculation of the Jacobian matrix and its determinant in the update process. This improvement has a wide applicability and reduces the cost of the update in thimble-inspired calculations from O(N3) to less than O(N2). As an additional feature, the algorithm leads to improved Monte Carlo proposals. We exemplify the use of the algorithm to the real-time dynamics of a scalar φ4 theory with weak and strong couplings.