Novel real-time lattice techniques for strongly correlated quantum systems

The central scientific goal of this proposal is to generalize the Euclidean simulation method described in the previous proposal into a genuine real-time simulation method. The strategy for reaching this goal relies on incorporating the findings of the original reference (Phys.Lett. B778 (2018) 221), as well as further research carried out during the last year, into the complex Langevin approach. This real-time method has been deployed with limited success so far, as its naive implementation suffers from instabilities. The use of a deformed and possibly decoupled Schwinger-Keldysh contour, as discussed in the above reference, however promises a way to overcome these difficulties. This conceptual research will benefit greatly from exchange with leading researchers, working on complementary approaches to the complex Langevin method, as well as those that work on related but conceptually different approaches, such as Lefshetz thimbles. I intend to spend 6 months on this conceptual work, before using its results to implement and carry out first proof of principles simulations in genuine 1+1 dimensional field theory models over a time frame of 2-3 months. Bringing these developments together in a coherent new proposal document, will take up another 2-3 months at the beginning of the summer semester of 2019.