Local Wilson-loop linear algebra, independent of the electronic-structure representation. WCC are arg(eigenvalue)/(2*pi), as in Z2Pack. The occupied subspace must be isolated. More...

Functions/Subroutines
subroutine, public	chern_from_wcc (wcc, invariant, winding, status, closure_tol)
	First Chern number from determinant Wilson-phase winding on a closed surface. Both transverse endpoints must be present. This is not a Z2 half-surface. The sign follows Z2Pack: increasing transverse coordinate, fixed loop orientation.
logical function, public	surface_resolved (wcc)
	Conservative neighbouring-line movement and largest-gap separation checks.
subroutine, public	wilson_step (product, overlap, minimum_sv, status, sv_tol)
	Multiply by the unitary polar factor of an overlap. Reject rank-deficient links.
subroutine, public	wilson_spectrum (product, wcc, berry, status)
	Sorted Wilson eigenphases in reduced units and total Berry phase in radians.
subroutine, public	z2_from_wcc (wcc, invariant, status, pair_tol)
	Largest-gap crossing parity for an ordered time-reversal half-surface. Endpoint degeneracy is necessary but does not establish time-reversal symmetry. Sampling convergence and an isolated fixed-rank subspace must be checked by the caller.
real(kind=dp) function, public	wcc_distance (a, b)
	Minimum maximal cyclic matching distance between two WCC sets.

Detailed Description

Local Wilson-loop linear algebra, independent of the electronic-structure representation. WCC are arg(eigenvalue)/(2*pi), as in Z2Pack. The occupied subspace must be isolated.

Function/Subroutine Documentation

◆ chern_from_wcc()

subroutine, public topology_wilson::chern_from_wcc	(	real(kind=dp), dimension(:, :), intent(in)	wcc,
		integer, intent(out)	invariant,
		real(kind=dp), intent(out)	winding,
		integer, intent(out)	status,
		real(kind=dp), intent(in)	closure_tol )

First Chern number from determinant Wilson-phase winding on a closed surface. Both transverse endpoints must be present. This is not a Z2 half-surface. The sign follows Z2Pack: increasing transverse coordinate, fixed loop orientation.

Parameters

wcc	Wilson centres, band index first and transverse line second
invariant	candidate integer, meaningful only for status zero
winding	unrounded winding
status	0 success, -1 invalid data, -2 unclosed surface, -3 unresolved phase step
closure_tol	maximal endpoint WCC mismatch

Definition at line 36 of file topology_wilson.F.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ surface_resolved()

logical function, public topology_wilson::surface_resolved ( real(kind=dp), dimension(:, :), intent(in) wcc )

Conservative neighbouring-line movement and largest-gap separation checks.

Parameters

wcc	centres, band index first and surface-line index second

Returns: whether the sampled surface is locally resolved (not a proof between samples)

Definition at line 75 of file topology_wilson.F.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ wilson_step()

subroutine, public topology_wilson::wilson_step	(	complex(kind=dp), dimension(:, :), intent(inout)	product,
		complex(kind=dp), dimension(:, :), intent(in)	overlap,
		real(kind=dp), intent(out)	minimum_sv,
		integer, intent(out)	status,
		real(kind=dp), intent(in)	sv_tol )

Multiply by the unitary polar factor of an overlap. Reject rank-deficient links.

Parameters

product	running Wilson matrix
overlap	overlap between adjacent occupied subspaces
minimum_sv	smallest singular value of this link
status	zero on success; negative for invalid/singular input; positive LAPACK failure
sv_tol	rank tolerance

Definition at line 114 of file topology_wilson.F.

Here is the caller graph for this function:

◆ wilson_spectrum()

subroutine, public topology_wilson::wilson_spectrum	(	complex(kind=dp), dimension(:, :), intent(in)	product,
		real(kind=dp), dimension(:), intent(out)	wcc,
		real(kind=dp), intent(out)	berry,
		integer, intent(out)	status )

Sorted Wilson eigenphases in reduced units and total Berry phase in radians.

Parameters

product	Wilson matrix
wcc	sorted centres in [0,1)
berry	Berry phase in [-pi,pi)
status	zero on success

Definition at line 150 of file topology_wilson.F.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ z2_from_wcc()

subroutine, public topology_wilson::z2_from_wcc	(	real(kind=dp), dimension(:, :), intent(in)	wcc,
		integer, intent(out)	invariant,
		integer, intent(out)	status,
		real(kind=dp), intent(in)	pair_tol )

Largest-gap crossing parity for an ordered time-reversal half-surface. Endpoint degeneracy is necessary but does not establish time-reversal symmetry. Sampling convergence and an isolated fixed-rank subspace must be checked by the caller.

Parameters

wcc	Wilson centres, band index first and surface-line index second
invariant	Z2 parity, or -1 if checks fail
status	0 success, -1 invalid input, -2 missing Kramers pairs, -3 ambiguous crossing
pair_tol	tolerance on boundary Kramers degeneracy, in reduced units

Definition at line 182 of file topology_wilson.F.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ wcc_distance()

real(kind=dp) function, public topology_wilson::wcc_distance	(	real(kind=dp), dimension(:), intent(in)	a,
		real(kind=dp), dimension(:), intent(in)	b )

Minimum maximal cyclic matching distance between two WCC sets.

Parameters

a	first WCC set
b	second WCC set

Returns: distance, or huge if sizes differ

Definition at line 228 of file topology_wilson.F.

Here is the call graph for this function:

Here is the caller graph for this function:

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ chern_from_wcc()

◆ surface_resolved()

◆ wilson_step()

◆ wilson_spectrum()

◆ z2_from_wcc()

◆ wcc_distance()