Efficient and scalable path integral Monte Carlo simulations with worm-type updates for Bose-Hubbard and XXZ models

Abstract

We present a novel and open-source implementation of the worm algorithm, which is an algorithm to simulate Bose-Hubbard and sign-positive spin models using a path-integral representation of the partition function. The code can deal with arbitrary lattice structures and assumes spin-exchange terms, or bosonic hopping amplitudes, between nearest-neighbor sites, and local or nearest-neighbor interactions of the density-density type. We explicitly demonstrate the near-linear scaling of the algorithm with respect to the system volume and the inverse temperature and analyze the autocorrelation times in the vicinity of a U(1)U(1) second order phase transition. The code is written in such a way that extensions to other lattice models as well as closely-related sign-positive models can be done straightforwardly on top of the provided framework.

A path integral ground state Monte Carlo algorithm for entanglement of lattice bosons

“…Path Integral Ground State (PIGS) quantum Monte Carlo utilizes the projection of a trial wave function in imaginary time to obtain stochastically exact results for the ground state of a quantum many-body system. It has been previously formulated in first quantization for non-relativistic Hamiltonians in the spatial continuum [16,24] and in second quantization on a lattice at finite temperature [15,17,22,23]. Here we present the T = 0 projector formalism for lattice systems, focusing on the imaginary time wordlines of a local bosonic Hamiltonian.…”

“…Of particular importance is the Worm Algorithm [14,[17][18][19][20], which expands the configuration space of D + 1 dimensional worldlines to include discontinuous paths representing finite particle trajectories in imaginary time. The imaginary-time dynamics of these worms improve ergodicity and allow for the direct sampling of the bosonic Hilbert space at finite temperature [17,21], and open source packages implementing the algorithm are available [22,23]. At zero temperature, PIMC has a projector variant known as path integral ground state Monte Carlo (PIGS) that has been previously implemented for non-relativistic bosons in the spatial continuum [24,25], with other Monte Carlo methods inspired by the PIGS formalism applied to spin models and fermionic lattices [26].…”