Emanuel Casiano-Diaz, Chris M. Herdman, Adrian Del Maestro
A ground state path integral quantum Monte Carlo algorithm is introduced that allows for the simulation of lattice bosons at zero temperature. The method is successfully benchmarked against the one dimensional Bose-Hubbard model through comparison with the potential and kinetic energy computed via exact diagonalization. After successful validation, an estimator is introduced to measure the Rényi entanglement entropy between spatial subregions which is explored across the phase diagram of the one dimensional Bose-Hubbard model for systems consisting of up to 256 sites at unit-filling, far beyond the reach of exact diagonalization. The favorable scaling of the algorithm is demonstrated through a further measurement of the Rényi entanglement entropy at the two dimensional superfluid-insulator critical point for large system sizes, confirming the existence of the expected entanglement boundary law in the ground state. The Rényi entanglement estimator is extended to measure the symmetry resolved entanglement that is operationally accessible as a resource.
This repository includes links, code, scripts, and data to generate the plots in the above paper.
The data in this project was generated via a new path integral Monte Carlo algorithm for the ground state of bosonic lattice models: pigsfli.
The data contained in the ProcessedData directory of this repository was obtained by processing raw data 
.py scripts found in the src directory. Figures were generated using the .ipynb notebook files contained there.
The creation of these materials was supported in part by the National Science Foundation under Award Nos. DMR-1553991 and DMR-2041995.
Figures are relesed under CC BY-SA 4.0 and can be freely copied, redistributed and remixed.