CRPA of SrVO3 - Revision history

Kaltakm: /* cRPA Calculation */

2025-03-28T09:10:08Z

cRPA Calculation

← Older revision		Revision as of 09:10, 28 March 2025
Line 140:		Line 140:
	screened Hubbard u = 2.3455 0.0000		screened Hubbard u = 2.3455 0.0000
	screened Hubbard J = 0.4281 -0.0000		screened Hubbard J = 0.4281 -0.0000
			The full interaction matrix is written to {{FILE\|UIJKL}}.
	{{NB\|mind\|The frequency point <math>\omega</math> can be set by {{TAG\|OMEGAMAX}} in the INCAR.}}		{{NB\|mind\|The frequency point <math>\omega</math> can be set by {{TAG\|OMEGAMAX}} in the INCAR.}}
	For instance to evaluate the cRPA interaction matrix at <math>\omega=10</math> eV, add		For instance to evaluate the cRPA interaction matrix at <math>\omega=10</math> eV, add
Line 173:		Line 174:
	bare Hubbard u = 15.0984 -0.0000		bare Hubbard u = 15.0984 -0.0000
	bare Hubbard J = 0.5351 0.0000		bare Hubbard J = 0.5351 0.0000
			Similar to the effectively screened interaction the full output is written to {{FILE\|VIJKL}}.

	=== cRPA calculation on Matsubara axis ===		=== cRPA calculation on Matsubara axis ===

Kaltakm: /* cRPA Calculation */

2025-03-28T09:08:39Z

cRPA Calculation

← Older revision		Revision as of 09:08, 28 March 2025
Line 101:		Line 101:
	{{TAGBL\|LWRITE_WANPROJ}} = .TRUE. # write wannier projection file		{{TAGBL\|LWRITE_WANPROJ}} = .TRUE. # write wannier projection file
	#{{TAGBL\|LFINITE_TEMPERATURE}} = T # T>0 formalism can be avoided here, because U computed only at omega=0		#{{TAGBL\|LFINITE_TEMPERATURE}} = T # T>0 formalism can be avoided here, because U computed only at omega=0

	{{NB\|warning\|As of version 6.2.0 run this tutorial successfully by adding following lines to INCAR. For older version copy wannier90.win.CRPA to wannier90.win and omit following lines in INCAR.}}		{{NB\|warning\|As of version 6.2.0 run this tutorial successfully by adding following lines to INCAR. For older version copy wannier90.win.CRPA to wannier90.win and omit following lines in INCAR.}}

	{{TAGBL\|NUM_WANN}} = 3		{{TAGBL\|NUM_WANN}} = 3
	{{TAGBL\|WANNIER90_WIN}} = "		{{TAGBL\|WANNIER90_WIN}} = "

Kaltakm: /* cRPA Calculation */

2025-03-28T09:08:05Z

cRPA Calculation

← Older revision		Revision as of 09:08, 28 March 2025
Line 119:		Line 119:
	The cRPA interaction values for <math>\omega=0</math> can be found in the {{TAG\|OUTCAR}}:		The cRPA interaction values for <math>\omega=0</math> can be found in the {{TAG\|OUTCAR}}:
	spin components: 1 1, frequency: 0.0000 0.0000		spin components: 1 1, frequency: 0.0000 0.0000

	screened Coulomb repulsion U_iijj between MLWFs:		screened Coulomb repulsion U_iijj between MLWFs:
	1 2 3		1 2 3
Line 125:		Line 125:
	2 2.3455 3.3459 2.3455		2 2.3455 3.3459 2.3455
	3 2.3455 2.3455 3.3459		3 2.3455 2.3455 3.3459

	screened Coulomb repulsion U_ijji between MLWFs:		screened Coulomb repulsion U_ijji between MLWFs:
	1 2 3		1 2 3
Line 131:		Line 131:
	2 0.4281 3.3459 0.4281		2 0.4281 3.3459 0.4281
	3 0.4281 0.4281 3.3459		3 0.4281 0.4281 3.3459

	screened Coulomb repulsion U_ijij between MLWFs:		screened Coulomb repulsion U_ijij between MLWFs:
	1 2 3		1 2 3
Line 137:		Line 137:
	2 0.4281 3.3459 0.4281		2 0.4281 3.3459 0.4281
	3 0.4281 0.4281 3.3459		3 0.4281 0.4281 3.3459

	averaged interaction parameter		averaged interaction parameter
	screened Hubbard U = 3.3459 0.0000		screened Hubbard U = 3.3459 0.0000

Kaltakm: /* cRPA Calculation */

2025-03-28T09:07:20Z

cRPA Calculation

← Older revision		Revision as of 09:07, 28 March 2025
Line 151:		Line 151:

	In addition, the bare Coulomb interaction matrix is calculated for a high {{TAG\|VCUTOFF}} and low energy cutoff {{TAG\|ENCUTGW}} and written in that order to the {{TAG\|OUTCAR}} file. Look for the lines similar to:		In addition, the bare Coulomb interaction matrix is calculated for a high {{TAG\|VCUTOFF}} and low energy cutoff {{TAG\|ENCUTGW}} and written in that order to the {{TAG\|OUTCAR}} file. Look for the lines similar to:

	spin components: 1 1		spin components: 1 1

	bare Coulomb repulsion V_iijj between MLWFs:		bare Coulomb repulsion V_iijj between MLWFs:
	1 2 3		1 2 3
Line 159:		Line 158:
	2 15.0984 16.3485 15.0984		2 15.0984 16.3485 15.0984
	3 15.0984 15.0984 16.3485		3 15.0984 15.0984 16.3485

	bare Coulomb repulsion V_ijji between MLWFs:		bare Coulomb repulsion V_ijji between MLWFs:
	1 2 3		1 2 3
Line 165:		Line 164:
	2 0.5351 16.3485 0.5351		2 0.5351 16.3485 0.5351
	3 0.5351 0.5351 16.3485		3 0.5351 0.5351 16.3485

	bare Coulomb repulsion V_ijij between MLWFs:		bare Coulomb repulsion V_ijij between MLWFs:
	1 2 3		1 2 3

Kaltakm: /* Optional: Analytic continuation */

2025-03-28T08:35:47Z

Optional: Analytic continuation

← Older revision		Revision as of 08:35, 28 March 2025
Line 239:		Line 239:
	idx=[0,40,80 ]		idx=[0,40,80 ]
	# store one-site bare interaction		# store one-site bare interaction
	v = np.sum( np.loadtxt('VIJKL').T[4][idx] )/3		v = np.sum( np.loadtxt('VIJKL').T[4][idx] )/len(idx)
	for i in range(nomega):		for i in range(nomega):
	raw = np.loadtxt( 'UIJKL.{omega:d}'.format(omega=i+1) )		raw = np.loadtxt( 'UIJKL.{omega:d}'.format(omega=i+1) )
	u[i] = np.sum( raw.T[4][idx] + 1j * raw.T[5][idx] ) / 3		u[i] = np.sum( raw.T[4][idx] + 1j * raw.T[5][idx] ) / len(idx)
	# extract omega points		# extract omega points
	!grep "omega =" UIJKL.{?,??} \| awk '{print $5}' > omegas.dat		!grep "omega =" UIJKL.{?,??} \| awk '{print $5}' > omegas.dat

Kaltakm: /* Optional: Analytic continuation */

2025-03-28T08:26:42Z

Optional: Analytic continuation

Kaltakm: /* cRPA calculation on Matsubara axis */

2025-03-27T16:35:31Z

cRPA calculation on Matsubara axis

← Older revision		Revision as of 16:35, 27 March 2025
Line 226:		Line 226:

	The complete matrix at zero frequency is also written to {{FILE\|UIJKL}}, while the result at the first frequency point of the minimax grid{{cite\|Kaltak:PRB:2020}} is found in {{FILE\|UIJKL}}.1 and so on.		The complete matrix at zero frequency is also written to {{FILE\|UIJKL}}, while the result at the first frequency point of the minimax grid{{cite\|Kaltak:PRB:2020}} is found in {{FILE\|UIJKL}}.1 and so on.
	{{NB\|mind\|The number of frequency points should be large enough to guarantee for an accurate Fourier transformation of the cRPA polarizability matrix from the imaginary time to imaginary frequency domain. See [[ACFDT/RPA calculations#Low_scaling_ACFDT.2FRPA_algorithm\|ACFDT/RPA calculations]] for more information.}}

	==== Optional: Analytic continuation ====		==== Optional: Analytic continuation ====

Kaltakm: /* Optional: Analytic continuation */

2025-03-27T16:34:49Z

Optional: Analytic continuation

← Older revision		Revision as of 16:34, 27 March 2025
Line 263:		Line 263:
	</syntaxhighlight>		</syntaxhighlight>
	[[File:SrVO3 U omega acont.png\|480px]]		[[File:SrVO3 U omega acont.png\|480px]]
	{{NB\|tip\|Increase {{TAG\|NOMEGA}} points ~~might~~ to resolve more details on the real frequency axis.}}		{{NB\|tip\|Increase {{TAG\|NOMEGA}} points to resolve more details on the real frequency axis.}}

	== Off-centre Coulomb integrals ==		== Off-centre Coulomb integrals ==

Kaltakm at 15:09, 27 March 2025

2025-03-27T15:09:42Z

@@ Line 227: / Line 227: @@
 The complete matrix at zero frequency is also written to {{FILE|UIJKL}}, while the result at the first frequency point of the minimax grid{{cite|Kaltak:PRB:2020}} is found in {{FILE|UIJKL}}.1 and so on.
 {{NB|mind|The number of frequency points should be large enough to guarantee for an accurate Fourier transformation of the cRPA polarizability matrix from the imaginary time to imaginary frequency domain. See [[ACFDT/RPA calculations#Low_scaling_ACFDT.2FRPA_algorithm|ACFDT/RPA calculations]] for more information.}}
 == Off-centre Coulomb integrals ==

Kaltakm: /* cRPA calculation on Matsubara axis */

2025-03-27T13:41:02Z

cRPA calculation on Matsubara axis

← Older revision		Revision as of 13:41, 27 March 2025
Line 199:		Line 199:
	{{TAGBL\|NCRPA_BANDS}} = 21 22 23 # remove bands 21-23 in screening, currently required for space-time algo		{{TAGBL\|NCRPA_BANDS}} = 21 22 23 # remove bands 21-23 in screening, currently required for space-time algo
	{{TAGBL\|NOMEGA}} = 8 # use 8 imaginary frequency points		{{TAGBL\|NOMEGA}} = 8 # use 8 imaginary frequency points
			{{TAGBL\|NOMEGA_DUMP}} = 0 # write WFULLxxxx.tmp files at omega=0, used for off-centre Coulomb integrals in next step


	Run VASP and make a copy of the output file		Run VASP and make a copy of the output file

← Older revision		Revision as of 09:08, 28 March 2025
Line 101:		Line 101:
	{{TAGBL\|LWRITE_WANPROJ}} = .TRUE. # write wannier projection file		{{TAGBL\|LWRITE_WANPROJ}} = .TRUE. # write wannier projection file
	#{{TAGBL\|LFINITE_TEMPERATURE}} = T # T>0 formalism can be avoided here, because U computed only at omega=0		#{{TAGBL\|LFINITE_TEMPERATURE}} = T # T>0 formalism can be avoided here, because U computed only at omega=0

	{{NB\|warning\|As of version 6.2.0 run this tutorial successfully by adding following lines to INCAR. For older version copy wannier90.win.CRPA to wannier90.win and omit following lines in INCAR.}}		{{NB\|warning\|As of version 6.2.0 run this tutorial successfully by adding following lines to INCAR. For older version copy wannier90.win.CRPA to wannier90.win and omit following lines in INCAR.}}

	{{TAGBL\|NUM_WANN}} = 3		{{TAGBL\|NUM_WANN}} = 3
	{{TAGBL\|WANNIER90_WIN}} = "		{{TAGBL\|WANNIER90_WIN}} = "

← Older revision		Revision as of 08:26, 28 March 2025
Line 230:		Line 230:
	To obtain the effective interaction on the real frequency axis from the imaginary axis (stored in {{FILE\|UIJKL}}.*) following python code can be used in a [https://jupyter.org/ jupyter notebook]:		To obtain the effective interaction on the real frequency axis from the imaginary axis (stored in {{FILE\|UIJKL}}.*) following python code can be used in a [https://jupyter.org/ jupyter notebook]:
	<syntaxhighlight lang="python" line>		<syntaxhighlight lang="python" line>
	import numpy as np		import numpy as np
	from scipy.interpolate import AAA		from scipy.interpolate import AAA
	import matplotlib.pyplot as plt		import matplotlib.pyplot as plt
	# results stored in NOMEGA dimensional array		# results stored in NOMEGA dimensional array
	nomega=24		nomega=24
	u = np.zeros( nomega, dtype='complex' )		u = np.zeros( nomega, dtype='complex' )
	# one-site indices		# one-site indices
	idx=[0,40,80 ]		idx=[0,40,80 ]
	# store one-site bare interaction		# store one-site bare interaction
	v = np.sum( np.loadtxt('VIJKL').T[4][idx] )/3		v = np.sum( np.loadtxt('VIJKL').T[4][idx] )/3
	for i in range(nomega):		for i in range(nomega):
	raw = np.loadtxt( 'UIJKL.{omega:d}'.format(omega=i+1) )		raw = np.loadtxt( 'UIJKL.{omega:d}'.format(omega=i+1) )
	u[i] = np.sum( raw.T[4][idx] + 1j * raw.T[5][idx] ) / 3		u[i] = np.sum( raw.T[4][idx] + 1j * raw.T[5][idx] ) / 3
	# extract omega points		# extract omega points
	!grep "omega =" UIJKL.{?,??} \| awk '{print $5}' > omegas.dat		!grep "omega =" UIJKL.{?,??} \| awk '{print $5}' > omegas.dat
	omegas=np.loadtxt( 'omegas.dat' )*1j		omegas=np.loadtxt( 'omegas.dat' )*1j
	# use AAA algorithm for analytic continuation		# use AAA algorithm for analytic continuation
	u_cont = AAA(omegas,u )		u_cont = AAA(omegas,u )
	# plot real part of U and bare interaction V		# plot real part of U and bare interaction V
	z = np.linspace( 0, 200, num=1000)		z = np.linspace( 0, 200, num=1000)
	fig, ax = plt.subplots()		fig, ax = plt.subplots()
	ax.plot( z, u_cont(z).real, '-', color='r', label='U')		ax.plot( z, u_cont(z).real, '-', color='r', label='U')
	ax.axhline(y=v, color='b', linestyle='-', label='V')		ax.axhline(y=v, color='b', linestyle='-', label='V')
	ax.legend()		ax.legend()
	# add low-frequency regime as an inset		# add low-frequency regime as an inset
	zlow=np.linspace( 0, 20, num=1000)		zlow=np.linspace( 0, 20, num=1000)
	inset_ax = ax.inset_axes([0.35, 0.1, 0.6, 0.6]) # [left, bottom, width, height]		inset_ax = ax.inset_axes([0.35, 0.1, 0.6, 0.6]) # [left, bottom, width, height]
	inset_ax.plot(zlow, u_cont(zlow), color='red')		inset_ax.plot(zlow, u_cont(zlow), color='red')
	plt.xlabel('$\omega$ [eV]')		plt.xlabel('$\omega$ [eV]')
	plt.show()		plt.show()
	</syntaxhighlight>		</syntaxhighlight>
	[[File:SrVO3 U omega acont.png\|480px]]		[[File:SrVO3 U omega acont.png\|480px]]