Complex path simulations of geometrically frustrated ladders

TL;DR

This paper introduces a complex path integration method to simulate geometrically frustrated quantum ladders with interacting bosons, overcoming the sign problem and enabling analysis of phase transitions and ground state properties.

Contribution

The authors develop a novel complex path integration approach that allows quantum Monte Carlo simulations of frustrated systems, previously hindered by the sign problem.

Findings

Identification of quantum phase transition driven by chemical potential

Observation of quasi-long-range order emergence

Detection of critical softening of the single particle gap

Abstract

Quantum systems with geometrical frustration remain an outstanding challenge for numerical simulations due to the infamous numerical sign problem. Here, we overcome this obstruction via complex path integration in a geometrically frustrated ladder of interacting bosons at finite density. This enables studies of the many-body ground state properties, otherwise inaccessible with standard quantum Monte Carlo methods. Specifically, we study a chemical potential tuned quantum phase transition, along which we track the emergence of quasi-long-range order and critical softening of the single particle gap. We chart future methodological improvements and applications in generalized geometrically frustrated lattice models.