Gauge-covariant C1/C2 plaquette kernels, independent of the state representation. More...

Functions/Subroutines
subroutine, public	polar_link (overlap, link, minimum, status, tolerance)
	Polar-unitarize a physical link, retaining its minimum singular value.
subroutine, public	link_plaquette (u_mu, u_nu_at_mu, u_mu_at_nu, u_nu, p)
	Oriented plaquette U_mu(x) U_nu(x+mu) U_mu(x+nu)^dagger U_nu(x)^dagger.
subroutine, public	curvature_density (plaquettes, ndim, phase_limit, value, maximum, status)
	Local contribution to C1 or C2. Report unrounded values and reject unresolved phases.

Detailed Description

Gauge-covariant C1/C2 plaquette kernels, independent of the state representation.

Note: C2 is the second Chern character pairing, not generally the second Chern class.

Function/Subroutine Documentation

subroutine, public topology_curvature::polar_link	(	complex(kind=dp), dimension(:, :), intent(in)	overlap,
		complex(kind=dp), dimension(:, :), intent(out)	link,
		real(kind=dp), intent(out)	minimum,
		integer, intent(out)	status,
		real(kind=dp), intent(in)	tolerance )

Polar-unitarize a physical link, retaining its minimum singular value.

Parameters

overlap	Raw selected-state overlap matrix
link	Unitary polar factor
minimum	Smallest singular value of the raw overlap
status	Zero on success; nonzero for an invalid or singular link
tolerance	Minimum allowed singular value

Definition at line 31 of file topology_curvature.F.

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subroutine, public topology_curvature::link_plaquette	(	complex(kind=dp), dimension(:, :), intent(in)	u_mu,
		complex(kind=dp), dimension(:, :), intent(in)	u_nu_at_mu,
		complex(kind=dp), dimension(:, :), intent(in)	u_mu_at_nu,
		complex(kind=dp), dimension(:, :), intent(in)	u_nu,
		complex(kind=dp), dimension(:, :), intent(out)	p )

Oriented plaquette U_mu(x) U_nu(x+mu) U_mu(x+nu)^dagger U_nu(x)^dagger.

Parameters

u_mu	Link in direction mu based at x
u_nu_at_mu	Link in direction nu based at x+mu
u_mu_at_nu	Link in direction mu based at x+nu
u_nu	Link in direction nu based at x
p	Oriented unitary plaquette based at x

Definition at line 55 of file topology_curvature.F.

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subroutine, public topology_curvature::curvature_density	(	complex(kind=dp), dimension(:, :, :), intent(in)	plaquettes,
		integer, intent(in)	ndim,
		real(kind=dp), intent(in)	phase_limit,
		real(kind=dp), intent(out)	value,
		real(kind=dp), intent(out)	maximum,
		integer, intent(out)	status )

Local contribution to C1 or C2. Report unrounded values and reject unresolved phases.

Parameters

plaquettes	Order 12 for C1; 12,13,14,23,24,34 for C2; all based at the same vertex
ndim	Parameter dimension, 2 or 4
phase_limit	Maximum allowed principal plaquette phase, strictly between zero and pi
value	Unrounded local contribution
maximum	Maximum absolute plaquette phase
status	Zero on success, negative invalid/unresolved input, positive LAPACK failure

Definition at line 72 of file topology_curvature.F.

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