Towards (spin) coherent resolutions of the sign problem: Lefschetz thimble quantum Monte Carlo for spin systems
QuICS, University of Maryland at College Park
Monday, April 3, 2023, from 12:30–1:30 pm
3301 Exploratory Hall
Fairfax Campus, George Mason University
JMonte Carlo simulations are useful tools for modeling quantum systems, but in some cases, they suffer from a sign problem, where cancellations between negative and positive weights when evaluating quantities lead to an exponential slowdown in their convergence. While solving the sign problem is generically NP-hard, many techniques exist for mitigating the sign problem in specific cases. In this talk, I will describe one such method: the so-called Lefschetz thimble approach, where one deforms the Monte Carlo simulation’s plane of integration, seeking a complex hypersurface of stationary phase. This approach has seen significant success in the context of quantum field theory and I will describe how to port this methodology to spin systems by utilizing spin coherent state path integrals to re-express the spin system’s partition function in terms of continuous variables. While we are able to demonstrate the success of these methods for mitigating the sign problem in toy spin systems, a number of issues arise related to the uncontrolled approximations made in the standard spin coherent path integral. I will comment on our current work aimed at addressing these problems and raise a number of related open questions that I think are of interdisciplinary interest and worthy of further investigation. Based on: Phys. Rev. B 106, 214416 (2022).