Multi-Worm Algorithm for Path Integral Quantum Monte Carlo in Ultracold Dipolar Gases

Clark University, Worcester MA

Investigators

Abstract

The goal of this project is to investigate quantum phases of strongly correlated systems with an emphasis on cold polar molecule setups. Strong correlations are at the core of many fascinating biological, chemical, and physical systems. The understanding of these systems is one of the major challenges facing physicists and a key issue in the community. Indeed, strongly correlated systems hold great potential in revolutionizing technological applications in medicine, communications, and computations. Within the framework of this project, novel extensions of a path-integral quantum Monte Carlo algorithm will be developed. The use of these Monte Carlo techniques will produce reliable and accurate results with controlled uncertainty. Unbiased theoretical predictions are timely and crucial to guide experimentalists in helping interpret experimental results and/or suggest observables. Moreover, the numerical results that will be obtained in this project can provide a platform for testing and validating analytical techniques. Indeed, these numerical techniques will also greatly contribute to the deeper understanding of certain classes of quantum many-body models which are, or will soon be, realizable in Atomic Molecular and Optical (AMO) experiments. In this project, the investigator and her students will develop extensions of quantum Monte Carlo techniques needed to study strongly-correlated many-body systems with an emphasis on cold polar molecules in optical lattice setups. When free of the sign problem, quantum Monte Carlo is a powerful theoretical tool to study equilibrium properties of strongly interacting systems, especially in dimensions higher than one. In this project the investigator will use the Worm algorithm to study properties of many-body strongly correlated systems of bosonic polar molecules trapped in optical lattice geometries. Emphasis will be given on geometries for which the anisotropic nature of the dipolar interaction will play a major role in determining the phase diagram of the system. The geometries that will be studied include stacks of one- and two-dimensional layers, and two-dimensional gases where molecules have tilted dipole moments. Considering the recent successful experimental advances in cold polar molecule experiments, these phases are very likely to be within reach in the near future. Therefore, accurate and reliable theoretical predictions are timely and valuable to the experimental community. The single-worm algorithm is not suitable to study the quantum phases of these multimers. In this project, the investigator plans to develop three different non-trivial extensions of the single-worm algorithm: (i) N-distinguishable-worms, (ii) N-indistinguishable-worms, and (iii) a hybrid algorithm with both distinguishable and indistinguishable worms. These multi-worm algorithms for quantum systems will allow for the study of multimer formation in a rich variety of optical lattice dipolar systems.