# The 39th International Symposium on Lattice Field Theory (Lattice 2022)

Aug 8 – 13, 2022
Hörsaalzentrum Poppelsdorf
Europe/Berlin timezone

## Reducing the Sign Problem using Line Integrals

Aug 8, 2022, 5:10 PM
20m
CP1-HSZ/1st-1.004 - HS7 (CP1-HSZ)

### CP1-HSZ/1st-1.004 - HS7

#### CP1-HSZ

70
Oral Presentation Algorithms (including Machine Learning, Quantum Computing, Tensor Networks)

### Speaker

Rasmus Larsen (University of Stavanger)

### Description

We present a novel strategy to strongly reduce the severity of the sign problem, using line integrals along paths of changing imaginary action. Highly oscillating regions along these paths cancel out, decreasing their contributions. As a result, sampling with standard Monte-Carlo techniques becomes possible in cases which otherwise requires methods taking advantage of complex analysis, such as Lefschetz-thimbles or Complex Langevin. We lay out how to write down an ordinary differential equation for the line integrals. As an example of its usage, we apply the results to a 1d quantum mechanical anharmonic oscillator with a $x^4$ potential in real time, finite temperature.

### Primary author

Rasmus Larsen (University of Stavanger)