A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons

Abstract

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 L = 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 superfluidinsulator critical point for large system sizes, confirming the existence of the expected entanglement boundary law in the ground state. The Rényi estimator is extended to measure the symmetry resolved entanglement that is operationally accessible as a resource.

Reduction of Autocorrelation Times in Lattice Path Integral Quantum Monte Carlo via Direct Sampling of the Truncated Exponential Distribution

“…Thus, truly independent measurements can only be performed for samples separated by T O MCMC steps, and any algorithmic improvement leading to a reduction in T O will improve the overall efficiency of a simulation. In a recent work [5], a subset of the authors of this paper introduced a path integral Monte Carlo algorithm for The paths propagate in the direction of imaginary time (vertical) and space (horizontal). Three kinks are shown at imaginary times τ 1 , τ 2 , τ 3 and occur due to a particle hopping between adjacent sites.…”

“…We direct the reader to Ref. [5] for complete details of the algorithm which can be used to evaluate ground state expectation values:…”

“…( 1). For updates that shift worm ends in the imaginary time direction, sampling from this distribution actually leads to perfect direct sampling [12,5] (R = 1).…”

“…In a recently developed Path Integral Monte Carlo (PIMC) algorithm [5], the acceptance ratio of certain updates depends on drawing random variates from a one or two dimensional truncated exponential distributionan exponential distribution restricted to a finite domain. In this paper, we describe how to directly sample two random variates from a two dimensional truncated exponential distribution, and apply this sampling strategy in PIMC.…”

“…The direct sampling of variates from both one and two dimensional truncated exponential distributions is then applied to the QMC algorithm of Ref. [5] for the simulation of bosonic lattices at zero temperature and it is shown that direct sampling results in decreased autocorrelation times for the kinetic and potential ground state energies at no performance cost.…”