scholarly journals The ALF (Algorithms for Lattice Fermions) project release 1.0. Documentation for the auxiliary field quantum Monte Carlo code

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Martin Bercx ◽  
Florian Goth ◽  
Johannes Stephan Hofmann ◽  
Fakher Assaad
Keyword(s):  
Monte Carlo ◽  
Hubbard Model ◽  
Quantum Monte Carlo ◽  
Kondo Lattice ◽  
Monte Carlo Algorithm ◽  
Auxiliary Field ◽  
Honeycomb Lattice ◽  
Monte Carlo Code ◽  
Single Body ◽  
Lattice Fermions

The Algorithms for Lattice Fermions package provides a general code for the finite temperature auxiliary field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to an Ising field with given dynamics. We provide predefined types that allow the user to specify the model, the Bravais lattice as well as equal time and time displaced observables. The code supports an MPI implementation. Examples such as the Hubbard model on the honeycomb lattice and the Hubbard model on the square lattice coupled to a transverse Ising field are provided and discussed in the documentation. We furthermore discuss how to use the package to implement the Kondo lattice model and the SU(N)SU(N)-Hubbard-Heisenberg model. One can download the code from our Git instance at and sign in to file issues.

A SINGLE HOLE IN THE TWO-DIMENSIONAL INFINITE-U HUBBARD MODEL IN AN ORBITAL MAGNETIC FIELD

1994 ◽  
Vol 08 (06) ◽  
pp. 707-725
Author(s):  
S. V. MESHKOV ◽  
J. C. ANGLÈS D'AURIAC
Keyword(s):  
Magnetic Field ◽  
Monte Carlo ◽  
Hubbard Model ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Applied Field ◽  
Monte Carlo Algorithm ◽  
Two Dimensional ◽  
Thermodynamical Properties ◽  
Single Hole

Using an original Quantum Monte Carlo algorithm, we study the thermodynamical properties of a single hole in the two-dimensional infinite-U Hubbard model at finite temperature. We investigate the energy and the spin correlators as a function of an external orbital magnetic field. This field is found to destroy the Nagaoka ferromagnetism and to induce chirality in the spin background. The applied field is partially screened by a fictitious magnetic field coming from the chirality. Our algorithm allows us to reach a temperature low enough to discuss the ground state properties of the model.

QUANTUM MONTE CARLO ALGORITHM FOR CONSTRAINED FERMIONS

1991 ◽  
Vol 05 (19) ◽  
pp. 1255-1265 ◽  
Author(s):  
X. Y. ZHANG
Keyword(s):  
Monte Carlo ◽  
Hubbard Model ◽  
Path Integral ◽  
Quantum Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Double Occupancy ◽  
Path Integral Quantization ◽  
Lattice Fermion

Using path integral quantization in the subspace that forbids double occupancy, we introduce a quantum Monte Carlo algorithm for simulation of fermion models with constraint. The algorithm can be applied to a class of lattice fermion models, including the infinite-U Hubbard model and the t - J model.

NEGATIVE WEIGHTS IN QUANTUM MONTE CARLO SIMULATIONS AT FINITE-TEMPERATURES USING THE AUXILIARY FIELD METHOD

1994 ◽  
Vol 05 (03) ◽  
pp. 599-613 ◽  
Author(s):  
J.E. GUBERNATIS ◽  
X.Y. ZHANG
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Topological Defects ◽  
Field Method ◽  
Monte Carlo Algorithm ◽  
Auxiliary Field ◽  
Sign Problem ◽  
Time Patterns ◽  
Ill Conditioned Matrices ◽  
Quantum Monte Carlo Simulations

We study the conditions under which negative weights (the sign problem) can exist in the finite-temperature, auxiliary field, quantum Monte Carlo algorithm of Blankenbecler, Scalapino, and Sugar. We specifically consider whether the sign problem arises from round-off error resulting from operations involving very ill-conditioned matrices or from topological defects in the auxiliary fields mirroring the space-time patterns of the physical fields. While we demonstrate these situations can generate negative weights, the results of our numerical tests suggest that these factors are most likely not the dominant sources of the problem. We also argue that the negative weights should not be considered as just a fermion problem. If it exists for the fermion problem, it will also exist for an analogous boson problem.

Sign in / Sign up

Export Citation Format

Share Document