The Sign Problem in Many Body Physics

Undergraduate: Mitchell Young

Faculty Advisor: Joaquin Drut
Department: Physics & Astronomy

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We investigate two numerical techniques applicability towards quantum many-body problems. Specifically we explore there usefulness for those problems which suffer from the numerical sign problem. Initially a Numerical Recursive Integration Technique was tested following the 2016 paper by Ammon, Genz, and Hartung. The method was tested against the 1-D topological oscillator for which it performed well, however the method gets considerably more complex and cumbersome for higher dimensional problems lacking in symmetry. As such, it was determined to be ill-suited for tackling the sign problem in many body physics. Next the much more promising Complex Langevin Method was investigated. Many other studies have shown the method is quite effective at tackling the sign problem inherent in many body problems. To see for ourselves it was tested on a repulsive 2-D Hubbard Model. As of now the code/tests are still running. As the research moves forward we hope to be able to use this method to model high Tc superconductivity in the 2-D Hubbard model as well.