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hartree.py
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hartree.py
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#!/usr/bin/env python
from numpy import *;
from share_fun import *;
import functions;
import average_green;
import system_dependence as system;
import os;
def getDensity(gmat, p):
X = p['X'];
W = p['W'];
BETA = p['BETA'];
n_f = zeros((gmat.shape[1],), dtype = 'f8');
for i in range(0, gmat.shape[1]):
n_f[i] = 0.5 + 2./BETA*real(sum(W/X * gmat[:, i]));
return n_f;
def generateGaussPoints(Nm):
Jn = zeros((Nm,Nm));
n = arange(1,Nm, dtype='f8');
# for Matsubara summation
a0 = 1. / 12.;
an = 1. / (32.*n**2 + 16.*n - 6.);
bn = 1. / (4096.*n**4 - 4096.*n**3 + 512.*n**2 + 256.*n - 48);
Jn[0,0] = a0;
for i in n:
Jn[i, i] = an[i-1];
Jn[i-1,i] = Jn[i,i-1] = sqrt(bn[i-1]);
d, v = linalg.eig(Jn);
xi = asarray(d);
wi = abs(v[0,:])**2/8;
ind = argsort(xi);
xi = xi[ind];
wi = wi[ind];
return asarray(xi), asarray(wi)
def averageGreen(delta0, mu0, w, SelfEnergy, parms, Nd, Ntot, tuneup, extra):
BETA = float(parms["BETA"]);
N_LAYERS = int(parms['N_LAYERS']); FLAVORS = int(parms['FLAVORS']); SPINS = int(parms['SPINS']);
rot_mat = extra['rot_mat'];
# calculate intersite Coulomb energy here
Vc = zeros(N_LAYERS, dtype = 'f8');
# convert self energy to the C++ form
SelfEnergy_rot = array([functions.irotate(SelfEnergy[s], extra['rot_mat']) for s in range(SPINS)]);
SE = [array([s.flatten() for s in SelfEnergy_rot[n]]) for n in range(SPINS)];
v_delta = empty(0, 'f8');
v_nd = empty(0, 'f8');
ddelta = 0.; delta_step = 1.;
dmu = 0.; mu_step = 5;
tol = 0.005;
# Delta loop
while True:
delta = delta0 + ddelta;
v_mu = empty(0, 'f8');
v_n = empty(0, 'f8');
# mu loop
while True:
mu = mu0 + dmu;
Gavg = average_green.integrate(w, delta, mu, SE, parms, extra);
Gavg_diag = array([Gavg[0, :, i, i] for i in range(int(parms['NORB']))]).T;
nf = getDensity(Gavg_diag, parms);
my_ntot = 2*sum(nf); # factor of 2 due to spin
if tuneup: print " adjust mu: " + str(mu) + " " + str(dmu) + " " + str(my_ntot);
if Ntot < 0 or abs(Ntot - my_ntot) < tol or not tuneup: break;
v_mu = r_[v_mu, dmu];
v_n = r_[v_n, my_ntot];
if v_n.min() < Ntot and v_n.max() > Ntot: dmu = interp_root(v_mu, v_n, Ntot);
else: dmu += (1. if my_ntot < Ntot else -1.)*mu_step;
my_nd = 2*sum(nf[:N_LAYERS*FLAVORS]);
if tuneup: print "adjust double counting: " + str(delta) + " " + str(ddelta) + " " + str(my_nd) + " " + str(my_nd/N_LAYERS);
if Nd < 0 or abs(Nd - my_nd) < tol or not tuneup: break;
v_delta = r_[v_delta, ddelta];
v_nd = r_[v_nd, my_nd];
if v_nd.min() < Nd and v_nd.max() > Nd: ddelta = interp_root(v_delta, v_nd, Nd);
else: ddelta += (1. if my_nd < Nd else -1.)*delta_step;
Gavg = array([functions.rotate_all(Gavg[s], rot_mat) for s in range(SPINS)]);
return Gavg, delta, mu, Vc;
def HartreeRun(parms, extra):
print "Initialization using Hartree approximation\n"
N_LAYERS = int(parms['N_LAYERS']);
FLAVORS = int(parms['FLAVORS']);
SPINS = 1;
p = dict({
'MU' : float(val_def(parms, 'MU', 0)),
'N_LAYERS': N_LAYERS,
'NORB' : int(parms['NORB']),
'U' : float(parms['U']),
'J' : float(parms['J']),
'DELTA': float(val_def(parms, 'DELTA', 0)),
'ND' : N_LAYERS*float(val_def(parms, 'ND', -1)),
'DENSITY' : N_LAYERS*float(parms['DENSITY']),
'FLAVORS' : FLAVORS,
'SPINS' : 1,
'OUTPUT' : '.' + parms['DATA_FILE'] + '_HartreeInit',
'NN' : None,
'N_MAX_FREQ' : 30,
'BETA' : float(parms['BETA']),
'NUMK' : int(val_def(parms, 'INIT_NUMK', 8)),
'TUNEUP' : int(val_def(parms, 'NO_TUNEUP', 0)) == 0,
'MAX_ITER' : 15,
'ALPHA' : 0.5, # pay attention at this parm sometimes
'DTYPE' : parms['DTYPE'],
'INTEGRATE_MOD' : val_def(parms, 'INTEGRATE_MOD', 'integrate'),
'np' : parms['np']
});
for k, v in p.iteritems(): print k + ': ', v;
bp, wf = grule(p['NUMK']);
X, W = generateGaussPoints(p['N_MAX_FREQ']);
wn = 1/sqrt(X)/p['BETA'];
p.update({
'X' : X,
'W' : W,
'w' : wn
});
if p['NN'] is None and os.path.isfile(p['OUTPUT']+'.nn'): p['NN'] = p['OUTPUT'];
# running
TOL = 1e-2;
if p['NN'] is None:
nn = ones(N_LAYERS*FLAVORS, dtype = 'f8') * p['DENSITY']/p['NORB']/2; # 2 for spin
mu = p['MU'];
delta = p['DELTA'];
else:
print 'Continue from '+p['NN'];
nn = genfromtxt(p['NN']+'.nn')[2:];
mu = genfromtxt(p['NN']+'.nn')[1];
delta = genfromtxt(p['NN']+'.nn')[0];
Gavg = zeros((p['N_MAX_FREQ'], p['NORB']), dtype = 'c16');
se = zeros((SPINS, p['N_MAX_FREQ'], N_LAYERS*FLAVORS), dtype = 'c16');
stop = False;
count = 0;
ALPHA = p['ALPHA'];
corr1 = system.getDMFTCorrIndex(parms, all = False);
corr2 = array([i for i in range(FLAVORS) if i not in corr1]); # index for eg bands
old_GaussianData = extra['GaussianData'];
extra['GaussianData'] = [bp, wf];
while not stop:
count += 1;
nn_old = nn.copy();
p['MU'] = mu;
p['DELTA'] = delta;
Gavg_old = Gavg.copy();
for L in range(N_LAYERS):
se_coef = functions.get_asymp_selfenergy(p, array([nn[L:N_LAYERS*FLAVORS:N_LAYERS]]))[0, 0, :];
for s in range(SPINS):
for f in range(len(se_coef)): se[s, :, f*N_LAYERS+L] = se_coef[f];
Gavg, delta, mu, Vc = averageGreen(delta, mu, 1j*wn, se, p, p['ND'], p['DENSITY'], p['TUNEUP'], extra);
Gavg = mean(Gavg, 0);
nn = getDensity(Gavg, p);
# no spin/orbital polarization, no charge order
for L in range(N_LAYERS):
nf1 = nn[0:N_LAYERS*FLAVORS:N_LAYERS];
for id in range(FLAVORS):
if id in corr1: nf1[id] = mean(nf1[corr1]);
else: nf1[id] = mean(nf1[corr2]);
nn[L:N_LAYERS*FLAVORS:N_LAYERS] = nf1;
err = linalg.norm(r_[delta, mu, nn] - r_[p['DELTA'], p['MU'], nn_old]);
savetxt(p['OUTPUT']+'.nn', r_[delta, mu, nn]);
print 'Step %d: %.5f'%(count, err);
if (err < TOL): stop = True; print 'converged';
if count > p['MAX_ITER']: break;
mu = ALPHA*mu + (1-ALPHA)*p['MU'];
delta = ALPHA*delta + (1-ALPHA)*p['DELTA'];
nn = ALPHA*nn + (1-ALPHA)*nn_old;
# DOS
NFREQ = 500;
BROADENING = 0.03;
extra['GaussianData'] = old_GaussianData;
parms_tmp = parms.copy(); parms_tmp['DELTA'] = delta;
Eav = system.getAvgDispersion(parms_tmp, 3, extra)[0,0,:];
Ed = mean(Eav[:N_LAYERS*FLAVORS][corr1]);
Ep = mean(Eav[N_LAYERS*FLAVORS:]) if N_LAYERS*FLAVORS < p['NORB'] else Ed;
emax = min(4, p['U']);
emin = -(Ed - Ep + max(se_coef) + min(4, p['U']));
print "Energy range for HF DOS: ", emin, emax
w = linspace(emin, emax, NFREQ) + 1j*BROADENING;
se = zeros((SPINS, NFREQ, N_LAYERS*FLAVORS), dtype = 'c16');
for L in range(N_LAYERS):
se_coef = functions.get_asymp_selfenergy(p, array([nn[L:N_LAYERS*FLAVORS:N_LAYERS]]))[0, 0, :];
for s in range(SPINS):
for f in range(len(se_coef)): se[s, :, f*N_LAYERS+L] = se_coef[f];
Gr = average_green.averageGreen(delta, mu, w, se, p,p['ND'], p['DENSITY'], 0, extra)[1][0];
savetxt(parms['ID']+'.dos', c_[w.real, -1/pi*Gr.imag], fmt = '%.6f');
print ('End Hartree approx.:%d Ntot=%.2f Nd=%.2f Delta=%.4f '
'Delta_eff=%.4f')%(count, 2*sum(nn)/N_LAYERS,
2*sum(nn[:N_LAYERS*FLAVORS]/N_LAYERS),
delta, delta-mean(se_coef[corr1])), ': \n', \
nn[:N_LAYERS*FLAVORS].reshape(-1, N_LAYERS),\
'\n\n'
# os.system('rm ' + p['OUTPUT']+'.nn');
return delta, mu, array([nn for s in range(int(parms['SPINS']))]), Vc;