Southwest Quantum Information and Technology

Lefschetz thimble quantum Monte Carlo for spin systems

Presenting Author: Connor Mooney, George Mason University
Contributing Author(s): Jacob Bringewatt, Lucas Brady

Monte Carlo simulations are often useful tools for modeling quantum systems, but in some cases they run into the sign problem, where the translation from quantum to classical systems results in an oscillating phase attached to the probabilities. This sign problem generally leads to an exponential slow down in the time taken by a Monte Carlo algorithm to reach any given level of accuracy, and it has been shown that completely solving the sign problem for any given quantum system is an NP-hard task. Several techniques exist for mitigating the slow down associated with the sign problem for specific cases, however, and one effective method in high energy field theories has been to deform the Monte Carlo simulation's plane of integration onto Lefschetz thimbles, that is, complex hypersurfaces of stationary phase. We extend this methodology to discrete spin systems by utilizing spin coherent state path integrals to re-express the discrete spin system's partition function in a continuous variable setting. This translation introduces additional challenges into the Lefschetz thimble method which we address. We show that these techniques do indeed work to lessen the sign problem in spin systems and demonstrate them on simple systems with sign problems.

(Session 5 : Thursday from 12:00pm-2:00 pm)