scholarly journals Computation of dynamical correlation functions for many-fermion systems with auxiliary-field quantum Monte Carlo

2016 ◽  
Vol 94 (8) ◽  
Author(s):  
Ettore Vitali ◽  
Hao Shi ◽  
Mingpu Qin ◽  
Shiwei Zhang
Keyword(s):  
Monte Carlo ◽  
Correlation Functions ◽  
Quantum Monte Carlo ◽  
Auxiliary Field ◽  
Dynamical Correlation ◽  
Fermion Systems

scholarly journals AUXILIARY FIELDS AND THE SIGN PROBLEM

1995 ◽  
Vol 06 (03) ◽  
pp. 427-465 ◽  
Author(s):  
J.H. SAMSON
Keyword(s):  
Monte Carlo ◽  
Correlation Functions ◽  
Quantum Monte Carlo ◽  
Heisenberg Model ◽  
Functional Integral ◽  
Auxiliary Field ◽  
Operator Product ◽  
Phase Problem ◽  
Stochastic Field ◽  
Sign Problem

The auxiliary-field quantum Monte Carlo method is reviewed. The Hubbard-Stratonovich transformation converts an interacting Hamiltonian into a non-interacting Hamiltonian in a time-dependent stochastic field, allowing calculation of the resulting functional integral by Monte Carlo methods. The method is presented in a sufficiently general form to be applicable to any Hamiltonian with one- and two-body terms, with special reference to the Heisenberg model and one- and many-band Hubbard models. Many physical correlation functions can be related to correlation functions of the auxiliary field; general results are given here. Issues relating to the choice of auxiliary fields are addressed; operator product identities change the relative dimensionalities of the attractive and repulsive parts of the interaction. Frequently the integrand is not positive-definite, rendering numerical evaluation unstable. If the auxiliary field violates time-reversal invariance, the integrand is complex and this sign problem becomes a phase problem. The origin of this sign or phase is examined from a number of geometrical and other viewpoints and illustrated by simple examples: the phase problem by the spin (1/2) Heisenberg model, and the sign problem by the attractive SU(N) Hubbard model on a triangular molecule with negative hopping integrals. In the latter case, widely studied in the Jahn-Teller literature, the sign is due neither to fermions nor spin, but to frustration. This system is used to illustrate a number of suggested interpretations of the sign problem.

scholarly journals Auxiliary-field quantum Monte Carlo calculations of the molybdenum dimer

2016 ◽  
Vol 144 (24) ◽  
pp. 244306 ◽  
Author(s):  
Wirawan Purwanto ◽  
Shiwei Zhang ◽  
Henry Krakauer
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Auxiliary Field ◽  
Monte Carlo Calculations
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