Parameter Reference

NRG Ljubljana reads a file named param from the current working directory. The same file is consumed in two stages:

1. nrginit reads model, discretization, and Wilson-chain settings and writes data.
2. nrg reads runtime, algorithm, and output settings and consumes data.

This page is the user-facing reference for the current release. Parameters are case-sensitive. Defaults in the tables are the values used when a key is absent, except where an effective default is described separately.

Portable File Syntax

Use this syntax for files that must be accepted by both nrginit and nrg:

[param]
# Whole-line comments begin with #.
symtype=QS
Lambda=2.0
keep=100

[extra]
# Model-specific settings go here.

• Put one key=value assignment on each line.
• Block names and keys are case-sensitive.
• Leading and trailing ASCII spaces around a key or value are ignored. Do not use tabs: the nrginit parser does not strip them.
• Blank lines and lines whose first character after stripping ASCII spaces is # are ignored. Tab-indented comments are not portable.
• Inline comments are not supported. For example, T=0.1 # kelvin is not a valid numeric assignment.
• Do not quote strings. Quotes become part of the value.
• Do not repeat a key. The C++ parser rejects duplicates, while the Mathematica parser can overwrite them.
• Boolean values are case-insensitive and accept yes, true, or 1 and no, false, or 0.
• List-valued parameters such as ops and specd use whitespace-separated tokens unless their entry below states otherwise.

An nrginit value beginning with ! is evaluated as a Mathematica expression. The perturb parameter and advanced hook files also execute Mathematica code without that prefix. Use these features only with trusted input. They are not part of the portable literal syntax recommended for reproducible runs.

Ownership And Diagnostics

Settings such as model, band, Nmax, Tmin, U, and Gamma are read by nrginit but are not runtime parameters. When these keys are in [param], nrg prints them under Unused settings; values in [extra] are instead printed under Extra params. The unused list is expected for documented initializer-only keys, but it is also where spelling mistakes appear, so review it on every run.

Several settings are read by both stages. Regenerate data after changing any of these generation-locked values:

symtype, Lambda, z, discretization, bandrescale, polarized, pol2x2, rungs, tri, Ninit, floquet, ops, and data_has_rescaled_energies.

Nmax is intentionally different: nrginit stores the resulting chain length in data, and nrg obtains it from that file. When Tmin_ratio is used, T and Tmin_ratio also determine that generated chain length.

Physical energies, temperatures, and frequencies are normally expressed in units of the half-bandwidth D, with k_B=1. keepenergy is a dimensionless shell cutoff. Other degeneracy and patching thresholds act in the current eigenspectrum convention: shell-rescaled units normally and unscaled physical units when absolute=true.

Initializer Parameters

These settings define the model and the data file generated by nrginit. Shared settings also appear in the runtime tables because nrg validates or uses them again.

Model And Initialization

Parameter	Type	Default	Meaning
symtype	string	required	Symmetry implementation. It must also be available in the selected build.
model	string	SIAM	Built-in model name, or a Mathematica file ending in .m.
variant	string	empty	Model-specific variant selector.
options	string list	empty	Advanced initializer options. See Initializer options.
perturb	Mathematica expression	empty	Expression added to the Hamiltonian after its normal check; this executes without a leading !.
ops	string list	empty	Operators to encode in data; names are sorted by nrginit.
U	number	0.1	Common model interaction. [extra] U takes precedence.
Gamma	number	0.1	Common hybridization strength. [extra] Gamma takes precedence.
delta	number	0	Common level-energy parameter. [extra] delta takes precedence.
t	number	0	Common hopping parameter. [extra] t takes precedence.
spinless	boolean	false	Use the spinless initializer basis where supported.
checkHc	boolean	true	Check the Hamiltonian before perturb is added; it does not validate the final perturbation.
mmadebug	integer	1	Mathematica-side diagnostic verbosity.
readdir	path	.	First directory searched for saved basis, Hamiltonian, and operator expressions; .. is a fallback.
writedir	path	empty	Prefix for saved Mathematica expressions; it does not relocate data or mmalog.

Recognized built-in symmetry names are:

QS QST QSTZ QSZTZ QJ ISO ISO2 QSZ ISOLR ISO2LR QSLR QSC3
QSZLR DBLQSZ DBLSU2 DBLISOSZ SU2 U1 SPSU2 SPU1 SPU1LR
SPSU2LR SPSU2C3 SPSU2T SL SL3 P PP NONE ISOSZ ISOSZLR

Builds made without the extended symmetry sets support only a subset. Complex data is required by the complex-only implementations.

Discretization And Wilson Chain

Parameter	Type	Default	Meaning
Lambda	number	2.0	Logarithmic discretization parameter; must be greater than 1.
z	number	1.0	Twist of the logarithmic mesh.
band	string	flat	Band construction method. See the values below.
bandrescale	number	1	Support and energy rescaling factor.
discretization	string	Z	Y, C, or Z; only the first uppercase character is used.
polarized	boolean	false	Generate spin-dependent coefficients; supported by QSZ, U1, SPU1, P, PP, and NONE.
pol2x2	boolean	false	Generate a full spin-space 2x2 Wilson chain; supported with U1.
rungs	boolean	false	Include channel-mixing terms for supported two-channel QS and QSZ calculations.
Ninit	non-negative integer	0	Highest Wilson orbital included in the initial Hamiltonian.
Nmax	positive integer	required unless derived	Requested chain length. It is mutually exclusive with an explicit Tmin.
Tmin	number	unset	Derive Nmax from the lowest retained energy scale.
Tmin_ratio	number	unset	If positive and T is also explicitly present and positive, set a provisional Tmin=T*Tmin_ratio; an explicit Tmin takes precedence.
tri	string	old	Tridiagonalization implementation.
wilsonchain	string	legacy	Coefficient-table interface. matrix is an experimental initializer output not consumed by a normal build.
prec	integer	method-dependent	Mathematica precision used for tridiagonalization.
preccpp	non-negative integer	2000	C++ tridiagonalization precision when tri=cpp.
nrxi	integer	-1	Number of discretization intervals; a negative value follows Nmax, and the resolved value must be in 0..998.
mMAX	integer	derived	Number of Lanczos input values; normally max(80, 2*nrxi) and constrained to 1..998.
dos	path	Delta.dat	Tabulated density of states for methods that require one.
xmax	number	30	Largest argument used by the asymode and adapt solver tables.
solpath	path	..	Directory containing FSOL* and GSOL* files.
floquet	boolean	false	Generate input for Floquet quasi-energies; runtime use also requires [extra] Omega and ops=m.
data_has_rescaled_energies	boolean	true	Compatibility switch for the seed-energy convention in data.

Recognized tri values are old, sc, sc2, orth, cpp, none, nambu, manual, manual_nambu, and manual_nambu_new. Manual methods need coefficient files in the working directory. none intentionally emits no coefficient table and is only useful for an external hand-off; its direct data output is not runnable by the normal runtime. nambu is currently a zero-filled placeholder rather than a production tridiagonalization method.

Built-in band branches include flat, cosine, dmft, nambu, manual, manual_V, asymode, adapt, and flat_with_bulk_field. A value ending in .m loads custom Mathematica code. Non-flat branches can require additional files and parameters such as hardgap, boundary, gap, shift0, bcsgap, bcsgap1, bcsgap2, bcsgap3, globalB, globalh, or bulkh; consult the documentation supplied with that band implementation before using it.

The nambu band branch is currently a placeholder. asymode, adapt, and flat_with_bulk_field require discretization=Z; the bulk-field branch also requires polarized=true and SPU1 or QSZ. band=dmft requires a [dmft] block containing either gamma=<value> or run=<path> and can additionally use [dmft] discchecksum=<value>. Normal DMFT chains require discretization=Y or C, and the superconducting DMFT path requires Y.

polarized=true and pol2x2=true are mutually exclusive.

Advanced Initializer Hooks

These settings expose implementation and Mathematica extension points rather than ordinary physical parameters:

Parameter	Type	Default	Meaning
disccheck	presence flag	absent	Print Wilson-coefficient checks when the key is present.
Hcsimpl	Mathematica file	empty	Load code while simplifying/checking the conduction Hamiltonian.
hook_basis	Mathematica file	empty	Load code during basis construction.
hook_pre_lanczosinit	Mathematica file	empty	Load code before Wilson-chain initialization.
hook_post_lanczosinit	Mathematica file	empty	Load code after Wilson-chain initialization.
hook_bcs	Mathematica file	empty	Load code while applying superconducting coefficient changes.

Hook files execute in the initializer process and must be treated as trusted code.

Initializer Options

options is a whitespace-separated advanced token list. Tokens used by the bundled initializer include:

PARAMPRE WRITE READBASIS READHAM READOPS EPSCLIP TEMPLATE
LRTRICK COMPLEX MPVCSLOW GENERATE_TEMPLATE GENERATE_TEMPLATE_ALL
GENERATE_TEMPLATE_F LRSPIN NOGSSHIFT CHOP NOSCHUR

Some models accept valued tokens such as Nph=value. Options affect generated Mathematica artifacts and are not a general replacement for named parameters.

The [extra] Block

[extra] contains model-specific values. Built-in models and custom .m models can introduce arbitrary keys, so there is no finite global table for this block. Every entry becomes available to Mathematica model code. The C++ runtime normally preserves these as strings; the built-in exception is floquet=true, which requires Omega in [extra] and an operator named m in generated input (ops=m).

For reproducibility, document the model name and all [extra] keys alongside published results. Do not assume that an unknown [extra] key is validated.

Runtime Parameters

The following tables contain all active param<T> settings read by nrg. An empty string default means that the feature or list is disabled.

Chain, Iteration, Truncation, And Temperature

Parameter	Type	Default	Meaning
symtype	string	empty, but required	Symmetry name; it must match the header in data.
Lambda	number	2.0	Logarithmic discretization; must be greater than 1.
discretization	string	Z	Y, C, or Z; legacy names beginning with that uppercase character are accepted.
z	number	1.0	Logarithmic-mesh twist.
bandrescale	number	1.0	Band and energy rescaling factor.
polarized	boolean	false	Use spin-dependent Wilson coefficients.
pol2x2	boolean	false	Use the full 2x2 spin structure.
rungs	boolean	false	Use channel-mixing Wilson-chain terms.
tri	string	old	Coefficient source; exact cpp selects C++ tridiagonalization.
preccpp	non-negative integer	2000	Precision used by C++ tridiagonalization.
diag	string	default	Eigensolver. See Eigensolvers and backends.
saveram	boolean	false	Request minimal documented LAPACK workspace sizes.
mult	string	blas	Matrix multiplication backend, blas or cuda; case-insensitive.
diagratio	number	1.0	Fraction of eigenpairs requested from partial eigensolvers; range (0,1].
restart	boolean	true	Retry partial diagonalization when too few states were found.
restartfactor	number	2.0	Multiplier applied to diagratio on retry; values must exceed 1 for a failed partial solve to make progress.
keep	non-negative integer	100	Maximum retained states; must be greater than 1.
keepenergy	number	-1.0	Positive values enable a shell-rescaled energy cutoff; retention extends through the first state above the cutoff, subject to keep.
keepmin	non-negative integer	0	Minimum retained states with energy-cutoff truncation; cannot exceed keep.
keepall	string	empty	even, odd, or comma-separated iteration numbers to retain completely.
safeguard	number	1e-5	Near-degeneracy tolerance in current eigenspectrum units; non-positive disables it.
safeguardmax	non-negative integer	200	Maximum extra states retained by safeguard.
fixeps	number	1e-15	Threshold in current eigenspectrum units for correcting floating-point eigenvalue splitting.
floquet	boolean	false	Interpret energies as Floquet quasi-energies; requires [extra] Omega and an operator named m in data.
T	number	0.001	Physical temperature; must be positive.
betabar	number	1.0	Effective inverse-temperature factor for shell thermodynamics.

Operators And Algorithms

Parameter	Type	Default	Meaning
ops	string list	empty	Operators requested during input generation; retained for configuration reporting at runtime.
specs	string list	empty	Singlet correlator pairs.
specd	string list	empty	Doublet spectral-function pairs.
spect	string list	empty	Triplet response pairs.
specq	string list	empty	Quadruplet spectral-function pairs.
specot	string list	empty	Orbital-triplet response pairs.
specgt	string list	empty	Operator pairs for temperature-dependent conductance.
speci1t	string list	empty	Operator pairs for first transport moments.
speci2t	string list	empty	Operator pairs for second transport moments.
gtp	number	0.7	Parameter p used for conductance and transport curves.
specchit	string list	empty	Operator pairs for k_B*T*chi(T), emitted with the chit prefix.
chitp	number	1.0	Parameter p used for susceptibility.
chitp_ratio	number	-999	If positive, overrides chitp with chitp_ratio/betabar.
finite	boolean	false	Enable the finite-temperature Costi-Hewson-Zlatic algorithm.
dmnrg	boolean	false	Enable DM-NRG real-frequency spectra.
cfs	boolean	false	Enable complete-Fock-space spectra.
cfsgt	boolean	false	Enable CFS greater correlators.
cfsls	boolean	false	Enable CFS lesser correlators.
fdm	boolean	false	Enable full-density-matrix NRG spectra and thermodynamics.
fdm_cutoff	number	1e-16	Non-negative shell-weight cutoff for FDM energy moments; only shells with w_n > fdm_cutoff contribute.
fdmgt	boolean	false	Enable FDM greater correlators.
fdmls	boolean	false	Enable FDM lesser correlators.
fdmexpv	boolean	false	Calculate FDM expectation values.
fdmexpvn	non-negative integer	0	Iteration at which FDM expectation values are emitted.
finitemats	boolean	false	Enable finite-temperature Matsubara output.
dmnrgmats	boolean	false	Enable DM-NRG Matsubara output.
fdmmats	boolean	false	Enable FDM Matsubara output.
mats	non-negative integer	100	Number of Matsubara frequencies.
dm	boolean	false	Internal second-phase/storage switch automatically enabled by algorithms that need density matrices; setting it alone does not prepare one.
checkrho	boolean	build-dependent	Check density-matrix trace normalization; default is true in debug and false in release builds.

Spectrum lists contain whitespace-separated operator pairs. The usual token is operator1-operator2; polarized variants can add -u or -d. Every named operator must have been included in the generated data file.

Broadening And Execution Control

Parameter	Type	Default	Meaning
broaden_max	number	10	Largest positive frequency on the broadening mesh.
broaden_min	number	-99	Smallest frequency; non-positive selects broaden_min_ratio times the final shell scale.
broaden_min_ratio	number	3.0	Multiplier for the automatic broaden_min.
broaden_ratio	number	1.05	Ratio of consecutive geometric mesh points; must be finite and greater than 1.
alpha	number	0.3	Width of logarithmic-Gaussian broadening; must be positive when used.
omega0	number	-1.0	Low-frequency crossover; negative selects omega0_ratio*T, while zero is invalid when broadening is used.
omega0_ratio	number	1.0	Multiplier used by the automatic omega0.
diagth	integer	1	Threads for the application OpenMP loop over independent diagonalization tasks; ignored without application OpenMP and separate from BLAS threading.
substeps	boolean	false	Enable interleaved diagonalization for supported QS, QSZ, SPSU2, or SPU1 calculations.
strategy	string	kept	Recalculate kept states or all states; CFS/FDM can force all.
Ninit	non-negative integer	0	Highest Wilson site included in the seed problem; must be below Nmax from data.
reim	boolean	false	Include imaginary spectral weights in output files.
clip_tol_imag	number	1e-10	Non-negative relative tolerance for clipping imaginary values in text output.

substeps requires the ordinary coefficient structure and is not compatible with every polarized, rung, or custom-chain configuration. Unsupported symmetry/backend combinations abort when interleaved recalculation is selected.

Spectral Binning, Patching, And Formatting

Parameter	Type	Default	Meaning
dumpannotated	non-negative integer	0	Emit at least this many low-energy states per iteration to annotated.dat.
dumpabs	boolean	false	Add the accumulated ground-state energy to diagnostic energies.
dumpscaled	boolean	true	Report diagnostics in shell-energy units rather than bandwidth units.
dumpEscale	number	1.0	Final divisor applied to diagnostic energies.
dumpprecision	non-negative integer	8	Significant digits in annotated.dat.
dumpgroups	boolean	true	Group degenerate entries in annotated.dat.
grouptol	number	1e-6	Degeneracy tolerance in current eigenspectrum units used by diagnostic grouping.
dumpdiagonal	non-negative integer	0	Print diagonal singlet matrix elements to standard output.
reportdiagonal	non-negative integer	0	Emit this many states per sector to report.nrg.
reportdiagonallast	boolean	true	Limit report.nrg to the final iteration.
savebins	boolean	false	Save unbroadened native binary spectral bins.
broaden	boolean	true	Save broadened real-frequency text spectra.
emin	number	-1.0	Explicit lower binning limit; non-positive selects a chain-derived limit.
emax	number	-1.0	Explicit upper binning limit; non-positive selects a chain-derived limit.
bins	positive integer	1000	Spectral bins per energy decade; zero is rejected when binning is used.
accumulation	number	0.0	Shift logarithmic-mesh accumulation points away from zero.
linstep	number	0	Linear bin width near a nonzero accumulation point.
discard_trim	number	1e-16	Relative final peak-trimming threshold.
discard_immediately	number	1e-16	Relative on-the-fly peak-trimming threshold.
goodE	number	2.0	Non-FDM patching window: a shell-scale multiplier normally, or a direct unscaled window with absolute=true.
NN1	boolean	false	Use N/N+1 rather than N/N+2 patching.
NN2even	boolean	true	Use even iterations for N/N+2 patching.
NN2avg	boolean	false	Average even and odd N/N+2 results.
NNtanh	number	0.0	Positive values select a smooth tanh patching window.
width_td	integer	16	Minimum column width in td and tdfdm.
width_custom	integer	16	Minimum column width in custom and customfdm.
prec_td	integer	10	Significant digits in td and tdfdm.
prec_custom	integer	10	Significant digits in custom expectation-value output.
prec_xy	integer	10	Significant digits in spectral text output.
resume	boolean	false	Intended to scan for saved unitary files, but the current startup order scans before Nmax is loaded and therefore does not recover a prior run.

dumpabs=true and dumpscaled=true are mutually incompatible. Widths are minimum padding widths, not fixed field boundaries; parse output as whitespace-separated text.

Logging, Diagnostics, HDF5, And Compatibility

Parameter	Type	Default	Meaning
log	string	empty	Character tokens selecting diagnostic logging categories.
logall	boolean	false	Enable every logging category.
silent	boolean	false	Reduce standard-output verbosity.
done	boolean	true	Create DONE after requested phases return.
calc0	boolean	true	Calculate observables for the seed iteration.
lastall	boolean	false	Keep all last-step states for DM-NRG.
lastalloverride	boolean	false	Prevent CFS/FDM from automatically enabling last-step retention.
dumpsubspaces	boolean	false	Write subspaces.dat.
dump_f	boolean	false	Print irreducible f-operator matrix elements.
dumpenergies	boolean	false	Write all diagonalized energies to energies.nrg.
dumpcorr	boolean	false	Add corrected energies to energies.nrg; requires dumpenergies.
dumpcrit	boolean	false	Add truncation criteria to energies.nrg; requires dumpenergies.
dumpstates	boolean	false	Write energy and available vector diagnostics to states.nrg.
dumpenergiesunscaled	boolean	false	Convert energy/state dumps from shell units to bandwidth units.
dumpabsenergies	boolean	false	Write absolute_energies.dat.
removefiles	boolean	true	Remove temporary phase files as they are consumed. The temporary workdir is still removed after a normal run.
checksumrules	boolean	false	Check operator sum rules.
absolute	boolean	false	Run without the usual NRG energy rescaling; generated input must also use data_has_rescaled_energies=false.
diag_mode	string	default	Scheduling mode: default, MPI, OpenMP, or serial.
h5raw	boolean	false	Enable raw.h5 and, when needed, raw-dm.h5.
h5all	boolean	false	Store HDF5 data at every iteration.
h5last	boolean	true	Store HDF5 data at the final iteration.
h5ham	boolean	false	Include Hamiltonian matrices in HDF5 output.
h5ops	boolean	false	Include iteration operator matrices in HDF5 output; a seed group written by h5all includes operators independently.
h5vectors	boolean	false	Include available iteration eigenspectrum vectors in HDF5 output; a seed group written by h5all can include vectors independently.
h5U	boolean	false	Include block transformation matrices in HDF5 output.
h5struct	boolean	false	Include ancestor/subspace structure in HDF5 output.
project	string	empty	Measurement projection. Universal value trivial retains everything; other values are symmetry-specific.
data_has_rescaled_energies	boolean	true	Interpret seed energies using the current rescaled convention; set it to false during generation and runtime for absolute=true.

Common log combinations are @0 for high-level flow, is for matrix-construction diagnostics, eAt for diagonalization, and fr for irreducible operator recalculation. Logging text is diagnostic and not a machine-readable interface.

Eigensolvers And Backends

diag=default selects dsyevd for real data and zheevd for complex data. Real-data choices are dsyev, dsyevd, dsyevr, cuda, and cuda_dsyevd. Complex-data choices are zheev, zheevd, zheevr, cuda, and cuda_zheevd. CUDA choices require a CUDA-enabled build and a usable device.

diagratio applies to the partial dsyevr and zheevr solvers. CFS and FDM calculations require diagratio=1.

Effective Defaults And Interactions

Several declared defaults are sentinels rather than literal runtime values:

Setting	Effective behavior
broaden_min<=0	Use broaden_min_ratio times the final shell scale.
omega0<0	Use omega0_ratio*T.
emin<=0, emax<=0	Derive the binning interval from Wilson-chain scales.
keepenergy<=0	Use fixed-count truncation controlled by keep.
safeguard<=0	Disable extra near-degenerate-state retention.
NNtanh<=0	Use the linear patching window.
positive chitp_ratio	Replace chitp with chitp_ratio/betabar.
any DM-NRG/CFS/FDM algorithm	Enable dm automatically.
CFS or FDM algorithm	Keep all states at the last step unless lastalloverride=true.
positive Tmin_ratio with explicit positive T and no explicit Tmin	Regenerate the chain length from T*Tmin_ratio, replacing an explicit Nmax.
absolute=true	Use data_has_rescaled_energies=false in both generation and runtime so seed and iterative energies use one convention.

Validation is partly feature-dependent. For example, mesh and broadening bounds are checked only when spectra are actually produced. An accepted startup configuration can therefore still fail when a selected algorithm first uses one of its parameters.

See Output format reference for the files controlled by the output parameters and Getting started for a complete minimal calculation.