Path Integral and Stochastic Series Expansion Quantum Monte Carlo methods for Confined Planar Rotors

In this work, we propose the analysis of the quantum critical behaviour of a system of N confined planar rotors with dipole-dipole interactions using the Path Integral Ground State (PIGS) and the Stochastic Series Expansion (SSE) quantum Monte Carlo methods. The angular momentum basis representation is chosen to structure the theory. Its discrete essence makes the advantageous rejection-free Gibbs sampling a natural choice. In addition to that, we show that cluster loop moves are necessary to overcome ergodicity issues and to achieve efficiency on the sampling process when employing the PIGS formulation. Furthermore, in this basis representation the system Hamiltonian becomes stoquastic. This feature is fundamental to avoid the sign problem, and also provides a suitable setting for the application of the SSE method. As a result, SSE with the Directed Loop Algorithm (DLA) is applied and constructed. This adaptation of the usual DLA for a more complex Hamiltonian yields new theoretical and computational tools of great importance for the field of many-body physics and for the study of quantum materials. Lastly, ground state energies, orientational correlation functions, dipole polarizations, and Rényi entanglement entropies are computed and compared with Density Matrix Renormalization Group (DMRG) calculations used as a benchmark.