# Documentation

## Miscelaneous

### Python reference manual

class nrgljubljana_interface.Flat(half_bandwidth)[source]

The Hilbert transform of a flat density of states, with cut-off

$g(z) = \int \frac{A(\omega)}{z-\omega} d\omega$

where $$A(\omega) = \theta( D^2 - \omega^2)/(2D)$$.

(Only works in combination with frequency Green’s functions.)

Methods

 __call__(G) Call self as a function.
class nrgljubljana_interface.SemiCircular(half_bandwidth, chem_potential=0.0)[source]

Hilbert transform of a semicircular density of states, i.e.

$g(z) = \int \frac{A(\omega)}{z-\omega} d\omega$

where $$A(\omega) = \theta( D - |\omega|) 2 \sqrt{ D^2 - \omega^2}/(\pi D^2)$$.

(Only works in combination with frequency Green’s functions.)

Methods

 __call__(G) Call self as a function.
class nrgljubljana_interface.Solver(**params_kw)[source]
Attributes:
A_w

The spectral function

B_w

The spectral function of the auxiliary correlator F_w

Delta_w

The hybridization function in real frequencies

F_w

The auxiliary Green function F_w = Sigma_w * G_w

G_w

The retarded Greens function

Sigma_w

The retarded Self energy

be_quiet
chi_NN_w

Charge susceptibility

chi_SS_w

Spin susceptibility

chi_struct

The susceptibility structure object

constr_params
expv

Expectation values of local impurity operators

gf_struct

The Green function structure object

last_solve_params
log_mesh

Logarithmic mesh

nrg_params

Low-level NRG parameters

tdfdm

Thermodynamic variables (FDM algorithm)

verbose
write_gamma

Methods

check_model_params

Signature : (nrgljubljana_interface::solve_params_t sp) -> None

create_tempdir

Signature : (str tempdir_) -> str

generate_param_file

Signature : (float z) -> None

hdf5_format

Signature : () -> str

instantiate

Signature : (float z, str taskdir) -> None

readA

Signature : (str name, std::optional<g_w_t> A_w, triqs::hilbert_space::gf_struct_t _gf_struct) -> None Read a block spectral function name-block-ij.dat; here we assume that the spectral function is purely real.

readGF

Signature : (str name, std::optional<g_w_t> G_w, triqs::hilbert_space::gf_struct_t _gf_struct) -> None Read a block Green's function (im/re)name-block-ij.dat

read_structure

Signature : (str filename, bool mandatory) -> triqs::hilbert_space::gf_struct_t

readexpv

Signature : (int Nz) -> None Read expectation values

set_nrg_params

set_verbosity

Signature : (bool v) -> None

solve(**params_kw)

Solve the impurity problem.

solve_one

Signature : (str taskdir) -> None

solve(**params_kw)[source]

Solve the impurity problem.

Parameters:
params_kwdict {‘param’:value} that is passed to the core solver.
class nrgljubljana_interface.SolverCore

The Solver class

Attributes:
A_w

The spectral function

B_w

The spectral function of the auxiliary correlator F_w

Delta_w

The hybridization function in real frequencies

F_w

The auxiliary Green function F_w = Sigma_w * G_w

G_w

The retarded Greens function

Sigma_w

The retarded Self energy

be_quiet
chi_NN_w

Charge susceptibility

chi_SS_w

Spin susceptibility

chi_struct

The susceptibility structure object

constr_params
expv

Expectation values of local impurity operators

gf_struct

The Green function structure object

last_solve_params
log_mesh

Logarithmic mesh

nrg_params

Low-level NRG parameters

tdfdm

Thermodynamic variables (FDM algorithm)

verbose
write_gamma

Methods

check_model_params

Signature : (nrgljubljana_interface::solve_params_t sp) -> None

create_tempdir

Signature : (str tempdir_) -> str

generate_param_file

Signature : (float z) -> None

hdf5_format

Signature : () -> str

instantiate

Signature : (float z, str taskdir) -> None

readA

Signature : (str name, std::optional<g_w_t> A_w, triqs::hilbert_space::gf_struct_t _gf_struct) -> None Read a block spectral function name-block-ij.dat; here we assume that the spectral function is purely real.

readGF

Signature : (str name, std::optional<g_w_t> G_w, triqs::hilbert_space::gf_struct_t _gf_struct) -> None Read a block Green's function (im/re)name-block-ij.dat

read_structure

Signature : (str filename, bool mandatory) -> triqs::hilbert_space::gf_struct_t

readexpv

Signature : (int Nz) -> None Read expectation values

set_nrg_params

set_verbosity

Signature : (bool v) -> None

solve

Solve method that performs NRGLJUBLJANA_INTERFACE calculation

solve_one

Signature : (str taskdir) -> None

A_w

The spectral function

B_w

The spectral function of the auxiliary correlator F_w

Delta_w

The hybridization function in real frequencies

F_w

The auxiliary Green function F_w = Sigma_w * G_w

G_w

The retarded Greens function

Sigma_w

The retarded Self energy

check_model_params()

Signature : (nrgljubljana_interface::solve_params_t sp) -> None

chi_NN_w

Charge susceptibility

chi_SS_w

Spin susceptibility

chi_struct

The susceptibility structure object

create_tempdir()

Signature : (str tempdir_) -> str

expv

Expectation values of local impurity operators

generate_param_file()

Signature : (float z) -> None

gf_struct

The Green function structure object

static hdf5_format()

Signature : () -> str

instantiate()

Signature : (float z, str taskdir) -> None

log_mesh

Logarithmic mesh

nrg_params

Low-level NRG parameters

Signature : (str name, std::optional<g_w_t> A_w, triqs::hilbert_space::gf_struct_t _gf_struct) -> None Read a block spectral function name-block-ij.dat; here we assume that the

spectral function is purely real.

Signature : (str name, std::optional<g_w_t> G_w, triqs::hilbert_space::gf_struct_t _gf_struct) -> None Read a block Green’s function (im/re)name-block-ij.dat

Signature : (str filename, bool mandatory) -> triqs::hilbert_space::gf_struct_t

Signature : (int Nz) -> None Read expectation values

set_nrg_params()

Parameter Name

Type

Default

Documentation

dmnrg

bool

false

Perform DMNRG (density-matrix NRG) calculation

cfs

bool

false

Perform CFS (complete Fock space) calculation

fdm

bool

true

Perform FDM (full-density-matrix) calculation

fdmexpv

bool

true

Calculate expectation values using FDM algorithm

dmnrgmats

bool

false

DMNRG calculation on Matsubara axis

fdmmats

bool

false

FDM calculation on Matsubara axis

mats

size_t

100

Number of Matsubara points to collect

specgt

std::string

“”

Conductance curves to compute

speci1t

std::string

“”

I_1 curves to compute

speci2t

std::string

“”

I_2 curves to compute

v3mm

bool

false

Compute 3-leg vertex on matsubara/matsubara axis?

mMAX

int

-1

Number of sites in the star representation

Nmax

int

-1

Number of sites in the Wilson chain

xmax

double

-1.0

Largest x in the discretization ODE solver

discretization

std::string

“Z”

Discretization scheme

z

double

1.0

Parameter z in the logarithmic discretization

tri

std::string

“old”

Tridiagonalisation approach

preccpp

size_t

2000

Precision for tridiagonalisation

diag

std::string

“default”

Eigensolver routine (dsyev|dsyevr|zheev|zheevr|default)

diagratio

double

1.0

Ratio of eigenstates computed in partial diagonalisation

dsyevrlimit

size_t

100

Minimal matrix size for dsyevr

zheevrlimit

size_t

100

Minimal matrix size for zheevr

restart

bool

true

Restart calculation to achieve truncation goal?

restartfactor

double

2.0

Rescale factor for restart=true

safeguard

double

1e-5

Additional states to keep in case of a near degeneracy

safeguardmax

size_t

200

fixeps

double

1e-15

Threshold value for eigenvalue splitting corrections

betabar

double

1.0

Parameter bar{beta} for thermodynamics

gtp

double

0.7

Parameter p for G(T) calculations

chitp

double

1.0

Parameter p for chi(T) calculations

finite

bool

false

Perform Costi-Hewson-Zlatic finite-T calculation

cfsgt

bool

false

CFS greater correlation function

cfsls

bool

false

CFS lesser correlation function

fdmgt

bool

false

FDM greater correlation function?

fdmls

bool

false

FDM lesser correlation function?

fdmexpvn

size_t

0

Iteration where we evaluate the expectation values

finitemats

bool

false

T>0 calculation on Matsubara axis

dm

bool

false

Compute density matrixes?

double

3.0

omega0

double

-1.0

Smallest energy scale in the problem

omega0_ratio

double

1.0

omega0 = omega0_ratio x T

diagth

int

1

substeps

bool

false

Interleaved diagonalization scheme

strategy

std::string

“kept”

Recalculation strategy

Ninit

size_t

0

Initial Wilson chain ops

reim

bool

false

Output imaginary parts of correlators?

dumpannotated

size_t

0

Number of eigenvalues to dump

dumpabs

bool

false

Dump in terms of absolute energies

dumpscaled

bool

true

Dump using omega_N energy units

dumpprecision

size_t

8

Dump with # digits of precision

dumpgroups

bool

true

Dump by grouping degenerate states

grouptol

double

1e-6

Energy tolerance for considering two states as degenerate

dumpdiagonal

size_t

0

Dump diagonal matrix elements

savebins

bool

true

bool

false

emin

double

-1.0

Lower binning limit

emax

double

-1.0

Upper binning limit

bins

size_t

1000

accumulation

double

0.0

Shift of the accumulation points for binning

linstep

double

0

Bin width for linear mesh

double

1e-16

Peak clipping at the end of the run

double

1e-16

Peak clipping on the fly

goodE

double

2.0

Energy window parameter for patching

NN1

bool

false

Do N/N+1 patching?

NN2even

bool

true

Use even iterations in N/N+2 patching

NN2avg

bool

false

Average over even and odd N/N+2 spectra

NNtanh

double

0.0

a in tanh[a(x-0.5)] window function

width_td

size_t

16

Width of columns in ‘td’ output file

width_custom

size_t

16

Width of columns in ‘custom’ output file

prec_td

size_t

10

Precision of columns in ‘td’ output file

prec_custom

size_t

10

Precision of columns in ‘custom’ output file

prec_xy

size_t

10

Precision of spectral function output

resume

bool

false

Attempt restart?

log

std::string

“”

List of tokens to define what to log

logall

bool

false

Log everything

done

bool

true

Create DONE file?

calc0

bool

true

Perform calculations at 0-th iteration?

lastall

bool

false

Keep all states in the last iteratio for DMNRG

lastalloverride

bool

false

Override automatic lastall setting

dumpsubspaces

bool

false

Save detailed subspace info

dump_f

bool

false

Dump <f> matrix elements

dumpenergies

bool

false

Dump (all) energies to file?

logenumber

size_t

10

# of eigenvalues to show for log=e

stopafter

std::string

“”

Stop calculation at some point?

forcestop

int

-1

Stop iteration?

removefiles

bool

true

Remove temporary data files?

noimag

bool

true

Do not output imaginary parts of expvs

checksumrules

bool

false

Check operator sumrules

checkdiag

bool

false

Test diag results

checkrho

bool

false

Test tr(rho)=1

set_verbosity()

Signature : (bool v) -> None

solve()

Solve method that performs NRGLJUBLJANA_INTERFACE calculation

Parameter Name

Type

Default

Documentation

Lambda

double

2.0

Logarithmic discretization parameter

Nz

int

1

Number of discretization meshes

Tmin

double

1e-4

Lowest scale on the Wilson chain

keep

size_t

100

Maximum number of states to keep at each step

keepenergy

double

-1.0

Cut-off energy for truncation

keepmin

size_t

0

Minimum number of states to keep at each step

T

double

0.001

Temperature, k_B T/D,

alpha

double

0.3

Width of logarithmic gaussian

gamma

double

0.2

Parameter for Gaussian convolution step

method

std::string

“fdm”

Method for calculating the dynamical quantities

bandrescale

double

-1.0

Band rescaling factor (half-width of the support of the hybridisation function)

model_parameters

std::map<std::string, double>

Model parameters

solve_one()

Signature : (str taskdir) -> None

tdfdm

Thermodynamic variables (FDM algorithm)