Excitonic effects in metallic systems ?

[Yunfeng]

a new version of the routine fermi_level.F has been posted in the repository (rev. 388). This version should solve your problem. Please download the latest source by using svn and check in the devel/04_03_2009 folder for the new updated source.

Dear Andrea,

Thank you very much! The Fermi_not_converged problem has been solved! With the newer patch [rev.389], the code went further and stopped at

" <24m-22s> [05] Bethe-Salpeter Kernel
[ERROR] STOP signal received while in :[05] Bethe-Salpeter Kernel
[ERROR]Fractional e/h occupations found. BS coupling forced."

For your convenience, I attached the input again

********************************************************************
# GPL Version 3.2.1 Revision 387
# http://www.yambo-code.org
#

em1s # [R Xs] Static Inverse Dielectric Matrix
optics # [R OPT] Optics
bse # [R BSK] Bethe Salpeter Equation.
bss # [R BSS] Bethe Salpeter Equation solver
BSresKmod= "xc" # [BSK] Resonant Kernel mode. (`x`;`c`;`d`,`u`)
% BSEBands
1 | 6 | # [BSK] Bands range
%
BSENGBlk= 51 RL # [BSK] Screened interaction block size
BSENGexx= 2085 RL # [BSK] Exchange components
% QpntsRXs
1 | 133 | # [Xs] Transferred momenta
%
% BndsRnXs
1 | 60 | # [Xs] Polarization function bands

%
NGsBlkXs= 51 RL # [Xs] Response block size
% LongDrXs
1.000000 | 0.000000 | 0.000000 | # [Xs] [cc] Electric Field
%
BSSmod= "h" # [BSS] Solvers `h/d/i/t`
% BEnRange
0.00000 | 10.00000 | eV # [BSS] Energy range
%
% BDmRange
0.02000 | 0.80000 | eV # [BSS] Damping range
%
BEnSteps= 500 # [BSS] Energy steps
% BLongDir
1.000000 | 0.000000 | 0.000000 | # [BSS] [cc] Electric Field
%
********************************************************************

Sincerely, Yunfeng

[andrea marini]

Dear Andrea,

Thank you very much! The Fermi_not_converged problem has been solved! With the newer patch [rev.389], the code went further and stopped at

" <24m-22s> [05] Bethe-Salpeter Kernel
[ERROR] STOP signal received while in :[05] Bethe-Salpeter Kernel
[ERROR]Fractional e/h occupations found. BS coupling forced."

Dear Yunfeng,

if I remember correctly your system is a metal. As a consequence occupations are fractional and Yambo stops because to complete the solution of the Bethe-Salpeter equation it would need the antiresonant (negative electron-hole energies) part of the Kernel. This part is not included in the GPL distro and, for this reason, the code did not go further.

However the point here is, why do you want to solve the Bethe-Salpeter equation for a metal ?. I mean, except in very specific cases (see here or here) excitons and, more in general, deformations of the optical spectra due to the electron-hole attraction, are absent in metals because of strong screening by free carriers (Drude tail).

In practice this means that, as a consequence of the metallic character, the static dielectric function diverges in the long wavelength limit. This divergence is removed only if the density of electrons at the fermi level is zero (is this your case ?).

Andrea

[Yunfeng]

...I wish the Earth quake had no/minimal influence on your life and all the people in Italy.

Maybe a silly question: why are you able to calculate the absorption spectra for Cu and Ag, which are actually common metal? Also as I mentioned to you, with an older version of Yambo and present version, I can run Yambo and obtain a fairly good spectra with a 8x8x8 K-point mesh.

Sincerely, Yunfeng

[andrea marini]

...I wish the Earth quake had no/minimal influence on your life and all the people in Italy.

Well... in Rome we had some shaking but no damages. Unfortunately our brothers in the center of Italy were less lucky. Let's hope the number of deaths will not increase too much

Maybe a silly question: why are you able to calculate the absorption spectra for Cu and Ag, which are actually common metal? Also as I mentioned to you, with an older version of Yambo and present version, I can run Yambo and obtain a fairly good spectra with a 8x8x8 K-point mesh.

In my paper about Dynamical excitonic effects I study the role played by a dynamical screened interaction. This was to prove a partial cancellation with quasiparticle dynamical effects. Yambo uses the "standard" approach: no dynamical screening, no quasiparticle dynamical effects.

Regarding your 8x8x8 K-point mesh: was it metallic ? If yes, why didn't you have fractional occupations (maybe you were still using the buggy fermi_level routine) ?

Cheers

Andrea

[Yunfeng]

Regarding your 8x8x8 K-point mesh: was it metallic ? If yes, why didn't you have fractional occupations (maybe you were still using the buggy fermi_level routine) ?

Dear Andrea,

I have tried both version. Both versions recognized it as a metal and yielded optical spectra:)

Sincerely, Yunfeng

[andrea marini]

Regarding your 8x8x8 K-point mesh: was it metallic ? If yes, why didn't you have fractional occupations (maybe you were still using the buggy fermi_level routine) ?

I have tried both version. Both versions recognized it as a metal and yielded optical spectra:)

Sorry to repeat ... but... do you have fractional occupations ? What is the number of electrons at the Fermi level ? Please attach any report file of the 8x8x8 grid calculation.

Andrea

[Yunfeng]

The report file of newer version is attached below.

***********************************************************************************************************************
::: ::: ::: :::: :::: ::::::::: ::::::::
:+: :+: :+: :+: +:+:+: :+:+:+ :+: :+: :+: :+:
+:+ +:+ +:+ +:+ +:+ +:+:+ +:+ +:+ +:+ +:+ +:+
+#++: +#++:++#++: +#+ +:+ +#+ +#++:++#+ +#+ +:+
+#+ +#+ +#+ +#+ +#+ +#+ +#+ +#+ +#+
#+# #+# #+# #+# #+# #+# #+# #+# #+#
### ### ### ### ### ######### ########

GPL Version 3.2.1 Revision 387
http://www.yambo-code.org

YAMBO@node005.internal.net x 004 CPUs * 04/05/2009 18:43

[01] Job Setup
==============

CORE databases in .
Additional I/O in .
Communications in .
Input file is yambo.in
Report file is ./r_optics_bse_em1s_bss
Log file is ./l_optics_bse_em1s_bss

[RD./SAVE//s.db1]-------------------------------------------
Bands : 150
K-points : 50
G-vectors [RL space]: 2085
Components [wavefunctions]: 264
Symmetries [spatial]: 24
Spinor components : 1
Spin polarizations : 1
Temperature [ev]: 0.000000
Electrons : 4.000000
WF G-vectors : 401
Max atoms/species : 1
No. of atom species : 1
- S/N 004577 ---------------------------- v.03.02.01 r.387 -

(...)

[02.03] Input (E)nergies[ev] & Occupations
==========================================

Fermi Energy[ev] - T[ev/K] : 11.20038 0.00000 0.00000
States summary : Full Metallic Empty
0001-0001 0002-0003 0004-0150
Electrons - <f_met> : 4.000000 0.980000
X BZ K-points : 512

(...)

[05.01] Screneed interaction header I/O
=======================================

[RD./SAVE//db.em1s]-----------------------------------------
Brillouin Zone Q/K grids (IBZ/BZ): 50 512 50 512
RL vectors (WF): 405
Electronic Temperature [ev]: 0.000000
Static diel. fun. energies :
wavefunctions :
X matrix size : 59
X band range : 1 60
X e/h energy range [ev]:-1.000000 -1.000000
X Time ordering :t
X xc-Kernel :none
X Drude frequency : 0.000 0.000
X poles [o/o]: 100.0000
Rl vectors in the sum : 405
[r,Vnl] included :no
Longitudinal Gauge :no
Field direction :0.1000E-4 0.000 0.000
BZ energy Random IM :no
BZ energy RIM points :0
:: Current Q-pt index : 1
:: X energy range [ev]: 0.000 0.000
:: X damping range [ev]:0.1000E-2 0.1000E-2
:: Number of frequencies : 1
- S/N 004577 ---------------------------- v.03.02.01 r.387 -
[P 01] Kernel filling [o/o] 25.00001
[P 02] Kernel filling [o/o] 25.00000
[P 03] Kernel filling [o/o] 25.00000
[P 04] Kernel filling [o/o] 25.00000

[WARNING]Exchange FFT size is too big. RL vectors reduced to 211
[FFT-BSK] Mesh size: 9 9 9

[RD./SAVE//s.wf]--------------------------------------------
Bands in each block : 150
Blocks : 1
- S/N 004577 ---------------------------- v.03.02.01 r.387 -

[05.02] Main loop
=================

[WR./SAVE//db.BS_Q1]----------------------------------------
Brillouin Zone Q/K grids (IBZ/BZ): 50 512 50 512
RL vectors (WF): 405
BS kernel wavefunctions :
Static diel. fun. energies :
wavefunctions :
BSK|Identifier : 52
|Dimension : 3958
|Bands : 1 6
|Exchange [res]:yes
|Correlation [res]:yes
|Kernel`s coupling :no
|Exchange [cpl]:no
|W interaction is bare :no
|Correlation [cpl]:no
|ALDA kernel in R-space :no
|RL vectors [exchange]: 211
|RL vectors [correlation]: 59
|E/h energy range [ev]:-1.000000 -1.000000
|Coupling range [o/o]: 100.0000 100.0000
W |Interaction is diagonal :no
|Matrix size : 59
|Bands : 1 60
|e/h energy range [ev]:-1.000000 -1.000000
|Poles [o/o]: 100.0000
|Rl vectors in the sum : 405
|[r,Vnl] included :no
|Longitudinal Gauge :no
|Field direction :0.1000E-4 0.000 0.000
|Columbian Cutoff :none
|xc-Kernel :none
RIM|RL components [col]:0
|Random points [col]:0
- S/N 004577 ---------------------------- v.03.02.01 r.387 -

CpuTiming [Min/Max/Average]: 01m-12s/01m-15s/01m-13s

(...)

[07] Game Over & Game summary
=============================

YAMBO@node005.internal.net x 004 CPUs * 04/05/2009 18:43 [start]
04/05/2009 18:46 [end]

Cpu Timing [Min/Max/Average]: 02m-42s/02m-45s/02m-43s

.-ACKNOWLEDGMENT
|
| The users of YAMBO have little formal obligations with respect to
| the YAMBO group (those specified in the GNU General Public
| License, http://www.gnu.org/copyleft/gpl.txt). However, it is
| common practice in the scientific literature, to acknowledge the
| efforts of people that have made the research possible. In this
| spirit, please find below the reference we kindly ask you to use
| in order to acknowledge YAMBO:
|
| Yambo: An ab initio tool for excited state calculations
| A. Marini, C. Hogan, M. Gr\"uning, D. Varsano
| Computer Physics Communications (2009), in press.
| http://dx.doi.org/10.1016/j.cpc.2009.02.003
|

.-Input file : yambo.in
| optics # [R OPT] Optics
| bse # [R BSK] Bethe Salpeter Equation.
| em1s # [R Xs] Static Inverse Dielectric Matrix
| bss # [R BSS] Bethe Salpeter Equation solver
| FFTGvecs= 405 RL # [FFT] Plane-waves
| BSresKmod= "xc" # [BSK] Resonant Kernel mode. (`x`;`c`;`d`,`u`)
| % BSEBands
| 1 | 6 | # [BSK] Bands range
| %
| BSENGBlk= 59 RL # [BSK] Screened interaction block size
| BSENGexx= 211 RL # [BSK] Exchange components
| % QpntsRXs
| 1 | 50 | # [Xs] Transferred momenta
| %
| % BndsRnXs
| 1 | 60 | # [Xs] Polarization function bands
| %
| NGsBlkXs= 59 RL # [Xs] Response block size
| % LongDrXs
| 0.1000E-4 | 0.000 | 0.000 | # [Xs] [cc] Electric Field
| %
| BSSmod= "h" # [BSS] Solvers `h/d/i/t`
| % BEnRange
| 0.00000 | 10.00000 | eV # [BSS] Energy range
| %
| % BDmRange
| 0.02000 | 0.80000 | eV # [BSS] Damping range
| %
| BEnSteps= 500 # [BSS] Energy steps
| % BLongDir
| 0.1000E-4 | 0.000 | 0.000 | # [BSS] [cc] Electric Field
| %

[andrea marini]

The report file of newer version is attached below.

[02.03] Input (E)nergies[ev] & Occupations
==========================================

Fermi Energy[ev] - T[ev/K] : 11.20038 0.00000 0.00000
States summary : Full Metallic Empty
0001-0001 0002-0003 0004-0150
Electrons - <f_met> : 4.000000 0.980000
X BZ K-points : 512

Dear Yunfeng,

I must correct my previous statement. In general a metal can have integer occupations (0,1,2). In this case the code does not stop. However Yambo, in order to converge the Fermi level of a metal with particularly complicated grids, can add some small temperature. As a consequence you have fractional occupations and the code stops.

Still my point remains. If you remove from the BSE equation the correlation, by using, BSresKmod= "x" do you see any difference in the final spectra ? If your system is a metal, my guess is no. What you see is, then, the effect of the exchange only. But no correlation = no excitonic effects.

Cheers

Andrea

[Yunfeng]

Still my point remains. If you remove from the BSE equation the correlation, by using, BSresKmod= "x" do you see any difference in the final spectra ? If your system is a metal, my guess is no. What you see is, then, the effect of the exchange only. But no correlation = no excitonic effects.

In case of the 8x8x8, the spectra difference is very small.

A simple question is: with my input and using BSresKmod= "x", does yambo integrate over all k points within the whole BZ? or equivalently which equation we are using in terms of your paper?

As I'm also using
yambo -o c
and plot the spectra at gama point and found they are the same. Maybe here is some physics, which I didn't know before. Does in theory the above two methods will yield the same results?

Sincerely, Yunfeng

[myrta gruning]

Dear Yunfeng,

The choice BSresKmod= "x" corresponds to consider just the exchange interaction term \bar V (described in eq. 20) and in eq. 22 of the yambo paper within the square brackets. The naming "exchange interaction" can be a bit confusing because this is just a Hartree-like term.

With yambo o -c you get the optics in the random-phase approximation, in which the response function is obtained assuming that the total potential of the system is approximatively given by the external potential + the Hartree term (no exchange-correlation terms).
Within the RPA, the X(q,\omega) can be calculated for different transfer momenta q (QpntsRXd variable). The q=0 transferred momentum corresponds to what you called "spectra at gamma point". The transferred momentum q is not related to the integration on the k-point sampling (see eq. 8). Note also that from the solution of BSE we get the lim q->0 X(q,\omega) (see eq. 17).

So in the case of q=0 transferred momenta for the RPA, if you are including the same number of reciprocal vector G to describe the local fields (or you are at convergence), the underlying physics is the same as the BSE with BSresKmod= "x". What does change is the way the equation is solved. In one case in the basis of electron-hole pairs, and in the other case in reciprocal space (you can also look to the analogous case of the TDDFT/ALDA described in the yambo paper sec 2.3)

I hope this may help
cheers,
m