DMFT-05 OSMT
Tutorial 05: Orbitally Selective Mott Transition
An interesting phenomenon in multi-orbital models is the orbitally selective Mott transition, first examined by Anisimov et al. A variant of this, a momentum-selective Mott transition, has recently been discussed in cluster calculations as a cluster representation of pseudogap physics.
In an orbitally selective Mott transition some of the orbitals involved become Mott insulating as a function of doping or interactions, while others stay metallic.
As a minimal model we consider two bands: a wide band and a narrow band. In addition to the intra-orbital Coulomb repulsion $U$ we consider interactions $U’$, and $J$, with $U’ = U-2J$. We limit ourselves to Ising-like interactions - a simplification that is often problematic for real compounds.
We choose here a case with two bandwidth $t1=0.5$ and $t2=1$ and density-density like interactions of $U’=U/2$, $J=U/4$, and $U$ between $1.8$ and $2.8$, where the first case shows a Fermi liquid-like behavior in both orbitals, the $U=2.2$ is orbitally selective, and $U=2.8$ is insulating in both orbitals.
The python command lines for running the simulations are found in tutorial5a.py
:
import pyalps
import numpy as np
import matplotlib.pyplot as plt
import pyalps.plot
#prepare the input parameters
parms=[]
for cp in [[1.8,0.45],[2.2,0.55],[2.8,0.7]]:
parms.append(
{
'CONVERGED' : 0.001,
'FLAVORS' : 4,
'H' : 0,
'H_INIT' : 0.,
'MAX_IT' : 15,
'MAX_TIME' : 600,
'MU' : 0,
'N' : 500,
'NMATSUBARA' : 500,
'N_MEAS' : 2000,
'N_ORDER' : 50,
'SEED' : 0,
'SOLVER' : 'hybridization',
'SC_WRITE_DELTA' : 1,
'SYMMETRIZATION' : 1,
'SWEEPS' : 10000,
'BETA' : 30,
'THERMALIZATION' : 500,
'U' : cp[0],
'J' : cp[1],
't0' : 0.5,
't1' : 1,
'CHECKPOINT' : 'dump'
}
)
#write the input file and run the simulation
for p in parms:
input_file = pyalps.writeParameterFile('parm_u_'+str(p['U'])+'_j_'+str(p['J']),p)
res = pyalps.runDMFT(input_file)
A paper using the same sample parameters can be found here.
As discussed in the previous tutorial ALPS 2 Tutorials:DMFT-04 Mott, the (non-)metallicity of the Green’s function is best observed by plotting the data on a logarithmic scale.
listobs = ['0', '2'] # flavor 0 is SYMMETRIZED with 1, flavor 2 is SYMMETRIZED with 3
data = pyalps.loadMeasurements(pyalps.getResultFiles(pattern='parm_u_*h5'), respath='/simulation/results/G_tau', what=listobs, verbose=True)
for d in pyalps.flatten(data):
d.x = d.x*d.props["BETA"]/float(d.props["N"])
d.y = -d.y
d.props['label'] = r'$U=$'+str(d.props['U'])+'; flavor='+str(d.props['observable'][len(d.props['observable'])-1])
plt.figure()
plt.yscale('log')
plt.xlabel(r'$\tau$')
plt.ylabel(r'$G_{flavor}(\tau)$')
plt.title('DMFT-05: Orbitally Selective Mott Transition on the Bethe lattice')
pyalps.plot.plot(data)
plt.legend()
plt.show()
Convergency may be checked by tutorial5b.py
, showing all iterations of $G_f^{it}(\tau)$ on logarithmic scale.
Tutorial by Emanuel - Please don’t hesitate to ask!
Contributors
- Emanuel Gull