Path Integral Monte Carlo for Entanglement in Bosonic Lattices at T = 0

Path-Integral Monte Carlo Worm Algorithm is one of many Quantum Monte Carlo (QMC) methods that serve as powerful tools for the simulation of quantum many-body systems. Developed in the late 90’s, this algorithm has been used with great success to study a wide array of physical models where exact calculation of observables is not possible due to the exponential size of the Hilbert space. One type of systems that have eluded PIMC-WA implementation are lattice models at zero temperature, which are of relevance in experimental settings, such as in optical lattices of ultra-cold atoms. In this thesis, we develop a PIMC Worm Algorithm for the simulation of interacting bosonic lattices at zero temperature. The algorithm is benchmarked with exact diagonalization by computing conventional estimators, such as kinetic and potential energies, and also quantum entanglement estimators. We implement our algorithm to numerically confirm new finite-size scaling forms that we derive for various entanglement measures, such as the operationally accessible, and symmetry- resolved Rényi entropies in the Bose-Hubbard model. We finalize by introducing a method for the direct sampling of two dimensional truncated exponential distribution for the reduction of autocorrelation times, an example of the algorithmic development that will be needed moving forward to expand the applicability of our algorithm to even more complex systems.