Controlling the numerical sign problem via complex path integration in a simple bosonic model of quantum frustration.

Geometric frustration is a paradigmatic instance of the numerical sign problem in condensed matter systems, where the presence of non-positive or, more generally, complex quantum amplitudes renders quantum Monte Carlo techniques uncontrolled. This work employs the recently introduced complex path integration (CPI) method to overcome this obstruction in a simple geometrically frustrated bosonic model defined on a triangular chain with negative hopping amplitudes at a finite chemical potential. Within the CPI method, the path integral is deformed into a complex plane manifold, which is set by the holomorphic flow. Remarkably, we find a dramatic reduction in the severity of the numerical sign problem. This progress allows us to accurately determine the many-body ground state properties away from commensurate fillings. Specifically, we tune an order-disorder quantum phase transition by varying the chemical potential and present the evolution of various observables along the transition, including the vanishing many-body gap, boson particle number, and condensate fraction. Extensions of our work and refinements of the CPI method will be discussed.