Dynamical Mean Field Theory and Impurity Solvers

List of Parameters

Physical parameters

Parameters for the self-consistency loop

General parameters

Parameters for the initial/final Weiss field

Parameters setting the precision of representation of the Green’s function and the Weiss field

Hybridization1 expansion impurity solver parameters

Interaction expansion1 impurity solver parameters

Additional parameters

Usage notes

• Remark on bipartite lattices: the ANTIFERROMAGNET option does assume a Neel-like ordering and requires thus a bipartite lattice. Note that on a bipartite lattice the density of states is symmetric (unless you apply a global potential shift).
• Since revision 6217, if you provide the DOSFILE or if you use TWODBS and if none of the parameters EPS_i, EPSSQ_i, EPSSQAV is set, then the EPS_i will be set to the first moment of the normalized DOS (in case of TWODBS: 0) and the EPSSQ_i and EPSSQAV will be set to the second moment of the normalized DOS using the provided density of states (in case of TWODBS: using the hard-coded values).
• Since revision 6217 you may use TWODBS=“hexagonal” to simulate the 2-dimensional hexagonal lattice (nearest-neighbor hoppings only). If you use TWODBS with other value, square lattice is assumed.

Input/output files

The files with prefix BASENAME: (where BASENAME is the name of the parameter input file)

• BASENAME: it is the input file to be loaded by the application dmft
• BASENAME.h5: contains the iteration resolved impurity Green’s function $G(\tau)$ and the Weiss field $G^0(\tau)$ in the imaginary time representation; if the selfconsistency loop has been performed in Matsubara representation (= if OMEGA_LOOP has been on) then there will be stored the $G(i\omega_n)$ and $G^0(i\omega_n)$ as well. The selfenergy is there not stored directly, but may be obtained via Dyson equation easily (look into DMFT-01 An introduction to DMFT)

The output/input files in Matsubara representation: (text file which consists of NMATSUBARA rows, each for one Matsubara frequency)

• G_omega_i (G0_omega_i): contains the imaginary part of the Green’s function (Weiss field) given in Matsubara frequencies after the i-th iteration; rows contain the $\omega_n$ followed by the imaginary part of the Green’s function (Weiss field) for each flavor; thus there are 1+FLAVORS columns in the file
• G_omegareal_i (G0_omegareal_i): the same as above for the real part
• selfenergy_i: contains the selfenergy after the i-th iteration; each row consists of $\omega_n$ followed by the real and imaginary part of the selfenergy for each flavor; thus there are 1+2FLAVORS columns in the file
• G0omega_output (unless not specified differently by the variable G0OMEGA_output): contains the n (corresponding to $\omega_n=\frac{(2n+1)\pi}{\beta})$ followed by the complex Weiss field for each flavor; thus there is one integer column followed by FLAVORS columns of complex numbers defined by the real and imaginary part in brackets
• G0OMEGA_INPUT: variable specifying the input file with the initial Weiss field in Matsubara representation; does expect the same format as the above output file; thus you may copy it and start a simulation from it

The output/input files in imaginary time representation: (text file which consists of $N+1$ rows, each for one imaginary time $\in\langle 0,\beta\rangle$)

• G_tau_i (G0_tau_i): contains the (real) Green’s function (Weiss field) after the i-th iteration; rows contain the $\tau_n$ followed by the Green’s function (Weiss field) for each flavor; thus there are 1+FLAVORS columns in the file
• G0tau_output (unless not specified differently by the variable G0TAU_output): contains the n (corresponding to $\tau_n=\frac{n}{N}\beta$) followed by the complex Weiss field for each flavor; thus there is one integer column followed by FLAVORS columns of complex numbers defined by the real and imaginary part in brackets; in total $N+1$ rows
• G0OMEGA_INPUT: variable specifying the input file with the initial Weiss field in imaginary time representation; does expect the same format as the above output file; thus you may copy it and start a simulation from it

The output files with prefix given by the optional variable CHECKPOINT:

• CHECKPOINT.h5: contains the measurements for each iteration
• CHECKPOINT.xml: contains the input parameters and run information
• CHECKPOINT.run*: contains information to rerun the simulation (these are the true checkpoints); for each process

The output files for the hybridization expansion impurity solver: (text files)

• overlap: i-th row contains the $\langle n_\downarrow n_\uparrow\rangle$ in the i-th iteration
• matrix_size:

Literature

• A review on DMFT: A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys. 68, 13 (1996).
• On the hybridization expansion impurity solver: P. Werner and A. J. Millis, Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models, Phys. Rev. B 74, 155107 (2006).