Sigma
code overview
Sigma
is the second half of the GW code. It should be run after calculating
epsmat[.h5]
/esp0mat[.h5]
with epsilon
. It gives the
quasiparticle selfenergies and dispersion relation for quasielectron and
quasihole states. The main result is written to the standard output and to the
sigma_hp.log
file.
Summary of input and output files
Required input files

sigma.inp
: Input parameters. 
epsmat[.h5]
: Inverse dielectric matrix (q\ne0). Created usingepsilon
. The file has ah5
extension if the code is compiled with HDF5 support (for specification, seeepsmat.h5.spec
). 
eps0mat.[h5]
: Inverse dielectric matrix (q\rightarrow0). Created usingepsilon
. The file has a.h5
extension if the code is compiled with HDF5 support (for specification, seeepsmat.h5.spec
). 
WFN_inner[.h5]
: Wavefunctions used to expand the Green's function G in \Sigma=iGW, and, wheneverWFN_outer
is abset, file used to load the states n\rangle and m\rangle used to compute the selfenergy matrix element \langle n\Sigmam \rangle. For a given kpoint inWFN_inner[.h5]
, all other kpoints connected by any qpoint inepsmat[.h5]
should also be inWFN_inner[.h5]
. The file will be read in HDF5 format (i.e. from file with.h5
extension) if the code is compiled with HDF5 support and theuse_wfn_hdf5
is set in input. Information of spinor wavefunctions is initialized automatically. 
RHO
: Charge density \rho(G) (only needed for generalized plasmonpole model), from SCF calculation on whichWFN_inner[.h5]
is based. 
vxc.dat
: Matrix elements of the exchangecorrelation potential, from a meanfield calculation or a previousSigma
run.VXC
file, which stores the whole exchangecorrelation matrix in reciprocal space, V_{xc}(G), may be used instead via keyworddont_use_vxcdat
.
Additional input
WFN_outer
: Outer wavefunctions between which the selfenergy operator and exchangecorrelation potential are sandwiched, i.e., the file used to load the states n\rangle and m\rangle used to compute the selfenergy matrix element \langle n\Sigmam \rangle. If absent, the inner wavefunctions fromWFN_inner[.h5]
will be used instead. Note thatVXC
should be consistent with outer wfn whileRHO
with inner wfn. If outer wfn is generated using a hybrid functional,VXC
contains the local part of exchangecorrelation potential. In this case setbare_exchange_fraction
insigma.inp
to compensate for the nonlocal part, or usevxc.dat
instead ofVXC
.
The file below will be read only if
eqp_corrections
is set in
sigma.inp
.
eqp.dat
: A list of quasiparticle energy corrections for the bands inWFN_inner[.h5]
. The corrected eigenvalues are used for constructing the selfenergy operator.
The file below will be read only if
eqp_outer_corrections
is set in
sigma.inp
.

eqp_outer.dat
: A list of quasiparticle energy corrections for the bands inWFN_outer
. The corrected eigenvalues determine the energies at which the selfenergy operator is calculated. 
vxc2.dat
: Matrix elements of the exchangecorrelation potential, from a meanfield calculation or a previous Sigma run. This file is analogous tovxc.dat
, but used for a oneshot hybridfunctionallike calculation instead of aSigma
calculation.VXC2
file, which stores the whole exchangecorrelation matrix in reciprocal space, V_{xc}(G), may be used instead via keyworddont_use_vxc2dat
.
Auxiliary files

x.dat
: Matrix elements of the bare exchange, generated by a previousSigma
run to speed up subsequent calculations. Read ifuse_xdat
keyword is present, written otherwise. 
VXC
: Exchangecorrelation potential (whose matrix elements are subtracted from DFT eigenvalues). Produced by a meanfield code, from the SCF calculation on whichWFN_inner[.h5]
is based (orWFN_outer
, if present). Used only ifvxc.dat
is not present or keyworddont_use_vxcdat
is set. 
VXC2
: Exchangecorrelation potential (whose matrix elements are added to the hybridfunctionallike DFT eigenvalues). Produced by a meanfield code, from the SCF calculation on whichWFN_inner[.h5]
is based (orWFN_outer
, if present). Used only ifvxc2.dat
is not present or keyworddont_use_vxc2dat
is set.
Output files
The file below will be read only if
eqp_corrections
is set in
sigma.inp
.

eqp0.dat
: Contains the onshell QP energies, E^\mathrm{mf}  V_\mathrm{xc}  \Sigma(E_0). This is not the recommended quantity to use for QP properties. This is Eqn. 36 from Hybertsen & Louie PRB 34 5390. 
eqp1.dat
: Contains the offshell solution to the linearized Dyson's equation, E^\mathrm{qp}_0 + (d\Sigma/dE) / (1  d\Sigma/dE) (E^\mathrm{qp}_0  E_0), or a full linear interpolation if more freq. points where computed. This is the recommended quantity to use for QP properties. If you only evaluate \Sigma(\omega) at two frequencies, this is Eqn. 37 from Hybertsen & Louie PRB 34 5390. If there are more frequencies available, the code uses them to find a better linearized solution. For GW calculations without plasmonpole models, the code reports how many solutions to Dyson's equation were found. 
sigma_hp.log
: The log file containing quasiparticle energy values for desired states. For a fullfrequency calculation only the value for Sigma calculated at energy closest to the outer wavefunction eigenvalue is shown. The filespectrum.dat
contains the full \Sigma(\omega) spectra.