Real Axis and Lifetimes - Revision history

Davide: /* The materials */ Fixing links

2024-09-26T11:37:04Z

The materials: Fixing links

← Older revision		Revision as of 11:37, 26 September 2024
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	* Lattice constant 7.50 [a.u.]		* Lattice constant 7.50 [a.u.]
	* Plane waves cutoff 16 Hartree (240 RL vectors)		* Plane waves cutoff 16 Hartree (240 RL vectors)
	* Al database files: [~~http~~://~~www~~.yambo-code.~~org~~/educational/tutorials/files/Aluminum.tar.gz Aluminum.tar.gz]		* Al database files: [https://media.yambo-code.eu/educational/tutorials/files/Aluminum.tar.gz Aluminum.tar.gz]

	'''LiF'''		'''LiF'''
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	* Lattice constant 7.61 [a.u.]		* Lattice constant 7.61 [a.u.]
	* Plane waves cutoff 40 Hartree (1800 RL vectors)		* Plane waves cutoff 40 Hartree (1800 RL vectors)
	LiF database files: [~~http~~://~~www~~.yambo-code.~~org~~/educational/tutorials/files/LiF.tar.gz LiF.tar.gz]		LiF database files: [https://media.yambo-code.eu/educational/tutorials/files/LiF.tar.gz LiF.tar.gz]

	= Electronic Lifetimes in Aluminum =		= Electronic Lifetimes in Aluminum =

Davide: /* Electronic Lifetimes in Aluminum */

2024-02-05T13:06:37Z

Electronic Lifetimes in Aluminum

← Older revision		Revision as of 13:06, 5 February 2024
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	The result of the code is the file ''o-01_Lifetimes.qp'' that contains the electronic linewidths. These can be plotted using the columns 3 and 4.		The result of the code is the file ''o-01_Lifetimes.qp'' that contains the electronic linewidths. These can be plotted using the columns 3 and 4.

	Now we can perform a quadratic fit of by using a simple gnuplot script		Now we can perform a quadratic fit of by using a simple gnuplot script.
			Put the following instructions inside the file ''plot_lifetimes.gnuplot''
			outfile='o-01_Lifetimes.qp'
	c(x)=ax*2		c(x)=ax*2
	v(x)=bx*2		v(x)=bx*2
	fit [0:] c(x) ~~'o-01_Lifetimes.qp'~~ u 3:4 via a		fit [0:] c(x) outfile u 3:4 via a
	fit [:0] v(x) ~~'o-01_Lifetimes.qp'~~ u 3:4 via b		fit [:0] v(x) outfile u 3:4 via b
	set ylabel "QP widths [meV]"		set ylabel "QP widths [meV]"
	set xlabel "Energy [eV]"		set xlabel "Energy [eV]"
	p ~~'o-01_Lifetimes.qp'~~ u 3:4 w p t "QP widths"		p outfile u 3:4 w p t "QP widths"
	rep [0:] c(x) t "quadratic fit (conduction)"		rep [0:] c(x) t "quadratic fit (conduction)"
	rep [:0] v(x) t "quadratic fit (valence)"		rep [:0] v(x) t "quadratic fit (valence)"
			enter gnuplot and load the scrip
			$ gnuplot
			gnuplot> load "plot_lifetimes.gnuplot"

	The result is displayed in the following picture:		The result is displayed in the following picture:

Marini: /* The materials */

2019-11-05T18:50:10Z

The materials

← Older revision		Revision as of 18:50, 5 November 2019
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	In the second section we will use LiF to test the accuracy of the PPA by comparing the results with the real-axis calculation. We will also discuss a non-perturbative solver of the Dyson equation in order to get a more deep insight in the definition of the QP energy and lifetime.		In the second section we will use LiF to test the accuracy of the PPA by comparing the results with the real-axis calculation. We will also discuss a non-perturbative solver of the Dyson equation in order to get a more deep insight in the definition of the QP energy and lifetime.

	== The materials ==		=The materials =

	'''Al'''		'''Al'''

Marini: /* Exercises */

2019-11-05T18:49:49Z

Exercises

← Older revision		Revision as of 18:49, 5 November 2019
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	From the plot of the imaginary part of the self-energy we see that it correctly changes sign at the Fermi level. We also notice that the self-energy spectral function is characterized by a series of poles far away from the Fermi level. As a consequence the real part of the self-energy is dominated by the frequency dependence of the Hilbert transformation. This frequency dependence, together with the position of the poles, instead, explains the success of the PPA.		From the plot of the imaginary part of the self-energy we see that it correctly changes sign at the Fermi level. We also notice that the self-energy spectral function is characterized by a series of poles far away from the Fermi level. As a consequence the real part of the self-energy is dominated by the frequency dependence of the Hilbert transformation. This frequency dependence, together with the position of the poles, instead, explains the success of the PPA.

	=== Exercises ===		== Exercises ==

	* Confirm the QP energy found with the secant solver by finding "by hand" the QP energy using the plot of the self-energy		* Confirm the QP energy found with the secant solver by finding "by hand" the QP energy using the plot of the self-energy
	* What would be (approximatively) the energy dependence of the self-energy in the PPA compared with the full calculation ?		* What would be (approximatively) the energy dependence of the self-energy in the PPA compared with the full calculation ?

Marini at 18:49, 5 November 2019

2019-11-05T18:49:26Z

← Older revision		Revision as of 18:49, 5 November 2019
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	<span id="08"></span>		<span id="08"></span>

	== ~~[08]~~ QPs in real-axis GW (Newton solver) (yambo -g n -d -k hartree) ==		== QPs in real-axis GW (Newton solver) (yambo -g n -d -k hartree) ==

	We can now go beyond the PPA by removing the '''-p p''' command line option. The calculation can be done by using		We can now go beyond the PPA by removing the '''-p p''' command line option. The calculation can be done by using
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	[[File:PPA vs RA Z.png]]		[[File:PPA vs RA Z.png]]

	== ~~[10]~~ QPs in real-axis GW (Secant solver) (yambo -g s -d -k hartree) ==		== QPs in real-axis GW (Secant solver) (yambo -g s -d -k hartree) ==

	The QP equation is a non-linear equation whose solution must be found using a suitable numerical algorithm. The mostly used, based on the linearization of the self-energy operator is the Newton method. Yambo can also perform a search of the QP energies using a non-linear iterative method based on the '''Secant iterative method'''.		The QP equation is a non-linear equation whose solution must be found using a suitable numerical algorithm. The mostly used, based on the linearization of the self-energy operator is the Newton method. Yambo can also perform a search of the QP energies using a non-linear iterative method based on the '''Secant iterative method'''.
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	<span id="11"></span>		<span id="11"></span>
	== ~~[11]~~ The frequency dependent Green's functions (yambo -g g -d -k hartree) ==		== The frequency dependent Green's functions (yambo -g g -d -k hartree) ==

	By typing		By typing

Marini: /* [08] QPs in real-axis GW (Newton solver) (yambo -g n -d -k hartree) */

2019-11-05T17:04:15Z

[08] QPs in real-axis GW (Newton solver) (yambo -g n -d -k hartree)

← Older revision		Revision as of 17:04, 5 November 2019
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	In this case Yambo needs to calculate the response function on a large energy range. The number of frequencies, therefore, is much larger then in the case of the PPA. As a consequence the calculation is more cumbersome and long. At the end of the run we can directly compare the results with the PPA case. In particular we can compare the columns 3:5 and the columns 3:11.		In this case Yambo needs to calculate the response function on a large energy range. The number of frequencies, therefore, is much larger then in the case of the PPA. As a consequence the calculation is more cumbersome and long. At the end of the run we can directly compare the results with the PPA case. In particular we can compare the columns 3:5 and the columns 3:11.

	[[File:life_PPA_vs_RA.png]] [[File:~~PPA_vs_RA_Z~~.png]]		[[File:life_PPA_vs_RA.png]]

			[[File:PPA vs RA Z.png]]

	== [10] QPs in real-axis GW (Secant solver) (yambo -g s -d -k hartree) ==		== [10] QPs in real-axis GW (Secant solver) (yambo -g s -d -k hartree) ==

Marini: /* [08] QPs in real-axis GW (Newton solver) (yambo -g n -d -k hartree) */

2019-11-05T17:03:11Z

[08] QPs in real-axis GW (Newton solver) (yambo -g n -d -k hartree)

← Older revision		Revision as of 17:03, 5 November 2019
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	[[File:life_PPA_vs_RA.png]] [[File:PPA_vs_RA_Z.png]]		[[File:life_PPA_vs_RA.png]] [[File:PPA_vs_RA_Z.png]]
	~~<span id="10"></span>~~
	== [10] QPs in real-axis GW (Secant solver) (yambo -g s -d -k hartree) ==		== [10] QPs in real-axis GW (Secant solver) (yambo -g s -d -k hartree) ==

Marini: /* [11] The frequency dependent Green's functions (yambo -g g -d -k hartree) */

2019-11-05T17:02:12Z

[11] The frequency dependent Green's functions (yambo -g g -d -k hartree)

← Older revision		Revision as of 17:02, 5 November 2019
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	[[File:life_Real_Sigma.png]] [[File:life_Im_Sigma.png]]		[[File:life_Real_Sigma.png]] [[File:life_Im_Sigma.png]]

	From the plot of the imaginary part of the self-energy we see that it correctly changes sign at the Fermi level. We also notice that the self-energy spectral function is characterized by a series of poles far away from the Fermi level. As a consequence the real part of the self-energy is dominated by the frequency dependence of the Hilbert transformation. This frequency dependence, together with the position of the poles, instead, explains the success of the PPA.		From the plot of the imaginary part of the self-energy we see that it correctly changes sign at the Fermi level. We also notice that the self-energy spectral function is characterized by a series of poles far away from the Fermi level. As a consequence the real part of the self-energy is dominated by the frequency dependence of the Hilbert transformation. This frequency dependence, together with the position of the poles, instead, explains the success of the PPA.

Marini at 17:00, 5 November 2019

2019-11-05T17:00:53Z

← Older revision		Revision as of 17:00, 5 November 2019
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	Another crucial consequence of the relatively high renormalization factors is that they point to a possible good performance of the PPA, in this case.		Another crucial consequence of the relatively high renormalization factors is that they point to a possible good performance of the PPA, in this case.

	=~~= Exercise ==~~		<span id="08"></span>

	* Explain why an high renormalization factor is in favour of a good performance of the PPA.		== [08] QPs in real-axis GW (Newton solver) (yambo -g n -d -k hartree) ==

	~~<span id="08"></span>~~
	== [08] QPs in real-axis GW (Newton solver)~~: [[03_real_axis.php\|03_real_axis]]~~ (yambo -g n -d -k hartree) ==

	We can now go beyond the PPA by removing the '''-p p''' command line option. The calculation can be done by using		We can now go beyond the PPA by removing the '''-p p''' command line option. The calculation can be done by using
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	[[File:life_PPA_vs_RA.png]] [[File:PPA_vs_RA_Z.png]]		[[File:life_PPA_vs_RA.png]] [[File:PPA_vs_RA_Z.png]]
	<span id="10"></span>		<span id="10"></span>
	== [10] QPs in real-axis GW (Secant solver)~~: [[04_real_axis_secant.php\|04_real_axis_secant]]~~ (yambo -g s -d -k hartree) ==		== [10] QPs in real-axis GW (Secant solver) (yambo -g s -d -k hartree) ==

	The QP equation is a non-linear equation whose solution must be found using a suitable numerical algorithm. The mostly used, based on the linearization of the self-energy operator is the Newton method. Yambo can also perform a search of the QP energies using a non-linear iterative method based on the '''Secant iterative method'''.		The QP equation is a non-linear equation whose solution must be found using a suitable numerical algorithm. The mostly used, based on the linearization of the self-energy operator is the Newton method. Yambo can also perform a search of the QP energies using a non-linear iterative method based on the '''Secant iterative method'''.
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	<span id="11"></span>		<span id="11"></span>
	== [11] The frequency dependent Green's functions ~~[[05_rx_greenfunc.php\|05_rx_greenfunc]]~~ (yambo -g g -d -k hartree) ==		== [11] The frequency dependent Green's functions (yambo -g g -d -k hartree) ==

	By typing		By typing
Line 147:		Line 144:
	From the plot of the imaginary part of the self-energy we see that it correctly changes sign at the Fermi level. We also notice that the self-energy spectral function is characterized by a series of poles far away from the Fermi level. As a consequence the real part of the self-energy is dominated by the frequency dependence of the Hilbert transformation. This frequency dependence, together with the position of the poles, instead, explains the success of the PPA.		From the plot of the imaginary part of the self-energy we see that it correctly changes sign at the Fermi level. We also notice that the self-energy spectral function is characterized by a series of poles far away from the Fermi level. As a consequence the real part of the self-energy is dominated by the frequency dependence of the Hilbert transformation. This frequency dependence, together with the position of the poles, instead, explains the success of the PPA.

	== ~~Exercise~~ ==		=== Exercises ===

	* Confirm the QP energy found with the secant solver by finding "by hand" the QP energy using the plot of the self-energy		* Confirm the QP energy found with the secant solver by finding "by hand" the QP energy using the plot of the self-energy
	* What would be (approximatively) the energy dependence of the self-energy in the PPA compared with the full calculation ?		* What would be (approximatively) the energy dependence of the self-energy in the PPA compared with the full calculation ?

Marini: /* Exercise */

2019-11-05T16:59:48Z

Exercise

← Older revision		Revision as of 16:59, 5 November 2019
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	[[File:life_08_PPA_E_minus_Eo.png]]		[[File:life_08_PPA_E_minus_Eo.png]]

	~~== Exercise ==~~		By adapting the gnuplot fit procedure used before now perform a linear fit of the positive and negative energy dependence of the QP energies to find the gap renormalization and the bands stretching

	* Perform a linear fit of the positive and negative energy dependence of the QP energies to find the gap renormalization and the bands stretching

	Using columns 3 versus 11 we can plot the renormalization factors. From the quite high mean value (around 0.9) we can infer that LiF is, indeed, a weakly correlated material.		Using columns 3 versus 11 we can plot the renormalization factors. From the quite high mean value (around 0.9) we can infer that LiF is, indeed, a weakly correlated material.