spectral_localizer_bloch Module Reference

Exact spectral flattening of a translation-invariant AO torus in primitive Bloch blocks. More...

Functions/Subroutines
subroutine, public	localizer_flatten_bloch (h, s, grid, nspin, energy, scale, tolerance, metric_tolerance, gap_tolerance, para_env, flattened, gap, metric_ratio, residuals, status)
	Flatten all Bloch bands, then return to the original distributed real-cell/spin AO basis.

Detailed Description

Exact spectral flattening of a translation-invariant AO torus in primitive Bloch blocks.

Author

Thomas D. Kuehne, tkueh.nosp@m.ne@c.nosp@m.p2k.o.nosp@m.rg

Function/Subroutine Documentation

localizer_flatten_bloch()

subroutine, public spectral_localizer_bloch::localizer_flatten_bloch	(	type(localizer_matrix_type), intent(inout)	h,
		type(localizer_matrix_type), intent(inout)	s,
		integer, dimension(3), intent(in)	grid,
		integer, intent(in)	nspin,
		real(dp), intent(in)	energy,
		real(dp), intent(in)	scale,
		real(dp), intent(in)	tolerance,
		real(dp), intent(in)	metric_tolerance,
		real(dp), intent(in)	gap_tolerance,
		type(mp_para_env_type), pointer	para_env,
		type(localizer_matrix_type), intent(out)	flattened,
		real(dp), intent(out)	gap,
		real(dp), intent(out)	metric_ratio,
		real(dp), dimension(4), intent(out)	residuals,
		integer, intent(out)	status )

Flatten all Bloch bands, then return to the original distributed real-cell/spin AO basis.

Parameters

h	Original complex Hamiltonian in spin/cell/atom order, unchanged
s	Original complex metric in the same order, unchanged
grid	Full Gamma-centered torus dimensions
nspin	Number of physical spin blocks (one or two)
energy	Absolute query energy
scale	Positive flattened energy
tolerance	Structure, covariance and eigensystem tolerance
metric_tolerance	Minimum global overlap eigenvalue ratio
gap_tolerance	Minimum original electronic distance from the query
para_env	Communicator; independent eigensystems are distributed across its ranks
flattened	Newly allocated covariant shifted Hamiltonian only on success
gap	Original electronic gap, not a flattened localizer gap
metric_ratio	Global minimum/maximum overlap eigenvalue ratio across all k-points
residuals	Covariance, metric orthonormality, eigenproblem and final Hermiticity residuals
status	0 success, 1 unresolved gap, -1 invalid layout/data, -2 metric, -4 eigensolver, -6 excessive residual, -7 broken translation covariance

Note

No occupied-state projection, symmetry reduction or modification of coordinate operators.

Definition at line 54 of file spectral_localizer_bloch.F.

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