# Stochastic Green function algorithm.

@article{Rousseau2008StochasticGF,
title={Stochastic Green function algorithm.},
author={V. G. Rousseau},
journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
year={2008},
volume={77 5 Pt 2},
pages={
056705
}
}
• V. Rousseau
• Published 24 November 2007
• Mathematics, Physics, Medicine
• Physical review. E, Statistical, nonlinear, and soft matter physics
We present a stochastic Green function algorithm designed for bosons on lattices. This quantum Monte Carlo algorithm is independent of the dimension of the system, works in continuous imaginary time, and is exact (no error beyond statistical errors). Hamiltonians with several species of bosons (and one-dimensional Bose-Fermi Hamiltonians) can be easily simulated. Some important features of the algorithm are that it works in the canonical ensemble and gives access to n -body Green functions.

#### Figures and Topics from this paper

Directed update for the stochastic Green function algorithm.
• V. Rousseau
• Mathematics, Physics
• Physical review. E, Statistical, nonlinear, and soft matter physics
• 2008
This work proposes here a modified version of the update scheme that keeps the simplicity and generality of the original SGF algorithm, and significantly enhances its efficiency. Expand
Quantum Monte Carlo study of the hardcore bosons with finite-range interactions in one-dimensional optical lattices
• Physics
• 2021
Abstract Using Quantum Monte Carlo algorithm, we study the quantum behaviors of the hardcore bosons with finite-range interactions in one-dimensional optical lattices, such finite-range interactionsExpand
Quantum annealing – foundations and frontiers
• Physics
• 2015
We briefly review various computational methods for the solution of optimization problems. First, several classical methods such as Metropolis algorithm and simulated annealing are discussed. WeExpand
Efficient iterative diagonalization of the Bose–Hubbard model for ultracold bosons in a periodic optical trap
• Chemistry
• 2012
Abstract Composite electronic systems are sometimes modeled by the Bose–Hubbard Hamiltonian. Iterative solution of this model, yielding a handful of the lowest-lying states is presented. The effectExpand
Fermion-induced decoherence of bosons in optical lattices
• Physics
• 2013
Bose-Fermi mixtures with attractive Bose-Fermi interactions in one-dimensional optical lattices are studied by using Quantum Monte Carlo simulations of an extended Bose-Fermi Hubbard model. We firstExpand
Quantum Monte Carlo study of the Rabi-Hubbard model
• Physics
• 2016
Abstract We study, using quantum Monte Carlo (QMC) simulations, the ground state properties of a one dimensional Rabi-Hubbard model. The model consists of a lattice of Rabi systems coupled by aExpand
Mott Transition of Bose-Fermi Mixtures in Optical Lattices Induced by Attractive Interactions
• Physics
• 2013
We numerically studied Bose–Fermi mixtures in one-dimensional optical lattices using a modified Bose–Fermi–Hubbard model. We derived the modified Bose–Fermi–Hubbard model in a tight-bindingExpand
Variational Monte-Carlo study of the extended Bose-Hubbard model with short- and infinite-range interactions
• Physics
• The European Physical Journal B
• 2019
In this paper, we study the two-dimensional Bose-Hubbard model with short- and long-range interactions in the canonical ensemble. Using a Variational Monte-Carlo method, we obtain the phase diagramsExpand
Cluster Bose Metals
• Physics
• 2016
Quantum phases of matter are usually characterised by broken symmetries. Identifying physical mechanisms and microscopic Hamiltonians that elude this paradigm is one of the key present challenges inExpand
Finite temperature phase diagram of spin-1/2 bosons in two-dimensional optical lattice
• Physics
• 2012
AbstractWe study a two-species bosonic Hubbard model on a two-dimensional square lattice by means of quantum Monte Carlo simulations and focus on finite temperature effects. We show in two differentExpand

#### References

SHOWING 1-10 OF 60 REFERENCES
Quantum Monte Carlo simulation in the canonical ensemble at finite temperature.
• Physics, Medicine
• Physical review. E, Statistical, nonlinear, and soft matter physics
• 2006
A quantum Monte Carlo method with a nonlocal update scheme based on a path-integral decomposition and a worm operator which is local in imaginary time that generates states with a fixed number of particles and respects other exact symmetries. Expand
Loop updates for quantum Monte Carlo simulations in the canonical ensemble.
• Physics, Medicine
• Physical review letters
• 2006
We present a new nonlocal updating scheme for quantum Monte Carlo simulations, which conserves particle number and other symmetries. It allows exact symmetry projection and direct evaluation of theExpand
World-line quantum Monte Carlo algorithm for a one-dimensional Bose model.
• Physics, Medicine
• Physical review. B, Condensed matter
• 1992
A quantum Monte Carlo algorithm is described that incorporates in an efficient manner the required bosonic wave-function symmetry and provides an unambiguous characterization of the recently observed Bose and Anderson glass phases. Expand
Quantum critical phenomena in one-dimensional Bose systems.
• Physics, Medicine
• Physical review letters
• 1990
From the critical behavior of the superfluid density and the compressibility, the exponents \ensuremath{\nu} and z, which agree with predictions based on a scaling analysis, are measured. Expand
Quantum Monte Carlo study of confined fermions in one-dimensional optical lattices
• Physics
• 2004
Using quantum Monte Carlo (QMC) simulations we study the ground-state properties of the one-dimensional fermionic Hubbard model in traps with an underlying lattice. Since due to the confiningExpand
Local quantum criticality in confined fermions on optical lattices.
• Physics, Medicine
• Physical review letters
• 2003
Using quantum Monte Carlo simulations, we show that the one-dimensional fermionic Hubbard model in a harmonic potential displays quantum critical behavior at the boundaries of a Mott-insulatingExpand
A generalization of Handscomb's quantum Monte Carlo scheme-application to the 1D Hubbard model
A recently introduced generalization of Handscomb's quantum Monte Carlo scheme (1962) is further developed. Expressions for expectation values of various observables are studied in detail. A moreExpand
Exact, complete, and universal continuous-time worldline Monte Carlo approach to the statistics of discrete quantum systems
• Physics, Mathematics
• 1998
The principles found for the update in continuous time generalize to any continuous variables in the space of discrete virtual transitions, and in principle make it possible to simulate continuous systems exactly. Expand
Quantum degenerate Bose-Fermi mixtures on one-dimensional optical lattices
• Physics
• 2006
We study numerically and analytically the phases of a mixture of ultracold bosons and spin-polarized fermions in a one-dimensional lattice. In particular, along a symmetry plane in the parameterExpand
Phase diagram of Bose-Fermi mixtures in one-dimensional optical lattices.
• Physics, Medicine
• Physical review letters
• 2006
The ground state phase diagram of the one-dimensional Bose-Fermi Hubbard model is studied in the canonical ensemble using a quantum Monte Carlo method and in case of equal hopping is distinguished among phase separation, a Luttinger liquid phase, and a phase characterized by strong singlet pairing between the species. Expand