mirror of
https://github.com/triqs/dft_tools
synced 2024-11-01 19:53:45 +01:00
880f30b086
This is to avoid keeping code snippets that do not work in the doc. At least there will be an error message.
72 lines
2.8 KiB
ReStructuredText
72 lines
2.8 KiB
ReStructuredText
|
|
Dynamical mean-field theory on a Bethe lattice
|
|
----------------------------------------------
|
|
|
|
.. note::
|
|
|
|
Requires TRIQS and the :doc:`application cthyb_matrix <../../applications>`
|
|
|
|
|
|
In the case of Bethe lattice the dynamical mean-field theory (DMFT) self-consistency condition takes a particularly simple form
|
|
|
|
.. math::
|
|
|
|
G^{-1}_{0,\sigma} (i \omega_n) = i \omega_n + \mu - t^2 G_{\sigma} (i \omega_n).
|
|
|
|
|
|
Hence, from a strictly technical point of view, in this case the DMFT cycle can be implemented by modifying
|
|
the previous single-impurity example to the case of a bath with semi-circular density of states and adding a python loop to update :math:`G_0` as function of :math:`G`.
|
|
|
|
Here is a complete program doing this plain-vanilla DMFT on a half-filled one-band Bethe lattice:
|
|
|
|
|
|
.. runblock:: python
|
|
|
|
from pytriqs.gf.local import *
|
|
from pytriqs.operators import *
|
|
from pytriqs.archive import *
|
|
import pytriqs.utility.mpi as mpi
|
|
|
|
# Set up a few parameters
|
|
U = 2.5
|
|
half_bandwidth = 1.0
|
|
chemical_potential = U/2.0
|
|
beta = 100
|
|
n_loops = 5
|
|
|
|
# Construct the CTQMC solver
|
|
from pytriqs.applications.impurity_solvers.cthyb_matrix import Solver
|
|
S = Solver(beta = beta, gf_struct = [ ('up',[1]), ('down',[1]) ])
|
|
|
|
# Initalize the Green's function to a semi circular
|
|
S.G <<= SemiCircular(half_bandwidth)
|
|
|
|
# Now do the DMFT loop
|
|
for IterationNumber in range(n_loops):
|
|
|
|
# Compute S.G0 with the self-consistency condition while imposing paramagnetism
|
|
g = 0.5 * ( S.G['up'] + S.G['down'] )
|
|
for name, g0block in S.G0:
|
|
g0block <<= inverse( iOmega_n + chemical_potential - (half_bandwidth/2.0)**2 * g )
|
|
|
|
# Run the solver
|
|
S.solve(H_local = U * N('up',1) * N('down',1), # Local Hamiltonian
|
|
quantum_numbers = { 'Nup' : N('up',1), 'Ndown' : N('down',1) }, # Quantum Numbers (operators commuting with H_Local)
|
|
n_cycles = 5000, # Number of QMC cycles
|
|
length_cycle = 200, # Length of a cycle
|
|
n_warmup_cycles = 1000, # How many warmup cycles
|
|
n_legendre = 30, # Use 30 Legendre coefficients to represent G(tau)
|
|
random_name = "mt19937", # Use the Mersenne Twister 19937 random generator
|
|
use_segment_picture = True) # Here we can use the segment picture
|
|
|
|
# Some intermediate saves
|
|
if mpi.is_master_node():
|
|
R = HDFArchive("single_site_bethe.h5")
|
|
R["G-%s"%IterationNumber] = S.G
|
|
del R
|
|
|
|
# Here we would usually write some convergence test
|
|
# if Converged : break
|
|
|
|
|