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function e = measure(H_k, phi, Phi_T, invO_matrix_up, invO_matrix_dn, N_up, N_par, U)
% function e = measure(H_k, phi, Phi_T, invO_matrix_up, invO_matrix_dn, N_up, N_par, U)
% Calculate the mixed estimator for the ground state energy of a walker
% Inputs:
% H_k: the one-body kinetic Hamiltonian
% phi: the matrix of a single walker
% Phi_T: the matrix of the trial wave function
% invO_matrix_up: the inverse of the spin up sector of the walker's overlap matrix
% invO_matrix_dn: the inverse of the spin down sector of the walker's overlap matrix
% N_up: the number of spin up electrons
% N_par: the total number of electrons of both spins
% U: the on-site repulsion strength in the Hubbard model
% Outputs:
% e: the mixed estimator for the ground state energy of the input walker
%
% Huy Nguyen, Hao Shi, Jie Xu and Shiwei Zhang
% ©2014 v1.0
% Package homepage: http://cpmc-lab.wm.edu
% Distributed under the <a href="matlab: web('http://cpc.cs.qub.ac.uk/licence/licence.html')">Computer Physics Communications Non-Profit Use License</a>
% Any publications resulting from either applying or building on the present package
% should cite the following journal article (in addition to the relevant literature on the method):
% "CPMC-Lab: A Matlab Package for Constrained Path Monte Carlo Calculations" Comput. Phys. Commun. (2014)
%% calculate the single-particle Green's function matrix for each spin:
temp_up=phi(:,1:N_up)*invO_matrix_up;
temp_dn=phi(:,N_up+1:N_par)*invO_matrix_dn;
G_up=temp_up*Phi_T(:,1:N_up)';
G_dn=temp_dn*Phi_T(:,N_up+1:N_par)';
%% calculate the potential energy:
n_int=(diag(G_up)).'*diag(G_dn);
potentialEnergy=n_int*U;
%% calculate the kinetic energy:
kineticEnergy=sum(sum(H_k.'.*(G_up+G_dn))); % note the element-wise multiplication
%% calculate the total energy:
e=potentialEnergy+kineticEnergy;
end