Factory functions for spin coupling terms

Collaboration diagram for Factory functions for spin coupling terms:

Functions
RealExpr	Pomerol::LatticePresets::SplusSminus (std::string const &Label1, std::string const &Label2, RealType J, unsigned short Orbital)
ComplexExpr	Pomerol::LatticePresets::SplusSminus (std::string const &Label1, std::string const &Label2, ComplexType J, unsigned short Orbital)
RealExpr	Pomerol::LatticePresets::SminusSplus (std::string const &Label1, std::string const &Label2, RealType J, unsigned short Orbital)
ComplexExpr	Pomerol::LatticePresets::SminusSplus (std::string const &Label1, std::string const &Label2, ComplexType J, unsigned short Orbital)
RealExpr	Pomerol::LatticePresets::SzSz (std::string const &Label1, std::string const &Label2, RealType J, unsigned short NOrbitals=1)
ComplexExpr	Pomerol::LatticePresets::SzSz (std::string const &Label1, std::string const &Label2, ComplexType J, unsigned short NOrbitals=1)
RealExpr	Pomerol::LatticePresets::SS (std::string const &Label1, std::string const &Label2, RealType J, unsigned short NOrbitals=1)
ComplexExpr	Pomerol::LatticePresets::SS (std::string const &Label1, std::string const &Label2, ComplexType J, unsigned short NOrbitals=1)

Detailed Description

Function Documentation

SminusSplus() [1/2]

ComplexExpr Pomerol::LatticePresets::SminusSplus	(	std::string const &	Label1,
		std::string const &	Label2,
		ComplexType	J,
		unsigned short	Orbital
	)

Make a fermionic \(S_- S_+\)-coupling term \(J S_{-,i\alpha} S_{+,j\alpha} = J c^\dagger_{i\alpha\downarrow} c_{i\alpha\uparrow} c^\dagger_{j\alpha\uparrow} c_{j\alpha\downarrow}\) with a complex exchange constant \(J\).

Parameters

[in]	Label1	The first lattice site \(i\).
[in]	Label2	The second lattice site \(j\).
[in]	J	Exchange constant \(J\).
[in]	Orbital	Orbital index \(\alpha\).

SminusSplus() [2/2]

RealExpr Pomerol::LatticePresets::SminusSplus	(	std::string const &	Label1,
		std::string const &	Label2,
		RealType	J,
		unsigned short	Orbital
	)

Make a fermionic \(S_- S_+\)-coupling term \(J S_{-,i\alpha} S_{+,j\alpha} = J c^\dagger_{i\alpha\downarrow} c_{i\alpha\uparrow} c^\dagger_{j\alpha\uparrow} c_{j\alpha\downarrow}\) with a real exchange constant \(J\).

Parameters

[in]	Label1	The first lattice site \(i\).
[in]	Label2	The second lattice site \(j\).
[in]	J	Exchange constant \(J\).
[in]	Orbital	Orbital index \(\alpha\).

SplusSminus() [1/2]

ComplexExpr Pomerol::LatticePresets::SplusSminus	(	std::string const &	Label1,
		std::string const &	Label2,
		ComplexType	J,
		unsigned short	Orbital
	)

Make a fermionic \(S_+ S_-\)-coupling term \(J S_{+,i\alpha} S_{-,j\alpha} = J c^\dagger_{i\alpha\uparrow} c_{i\alpha\downarrow} c^\dagger_{j\alpha\downarrow} c_{j\alpha\uparrow}\) with a complex exchange constant \(J\).

Parameters

[in]	Label1	The first lattice site \(i\).
[in]	Label2	The second lattice site \(j\).
[in]	J	Exchange constant \(J\).
[in]	Orbital	Orbital index \(\alpha\).

SplusSminus() [2/2]

RealExpr Pomerol::LatticePresets::SplusSminus	(	std::string const &	Label1,
		std::string const &	Label2,
		RealType	J,
		unsigned short	Orbital
	)

Make a fermionic \(S_+ S_-\)-coupling term \(J S_{+,i\alpha} S_{-,j\alpha} = J c^\dagger_{i\alpha\uparrow} c_{i\alpha\downarrow} c^\dagger_{j\alpha\downarrow} c_{j\alpha\uparrow}\) with a real exchange constant \(J\).

Parameters

[in]	Label1	The first lattice site \(i\).
[in]	Label2	The second lattice site \(j\).
[in]	J	Exchange constant \(J\).
[in]	Orbital	Orbital index \(\alpha\).

SS() [1/2]

ComplexExpr Pomerol::LatticePresets::SS	(	std::string const &	Label1,
		std::string const &	Label2,
		ComplexType	J,
		unsigned short	NOrbitals = 1
	)

Make a fermionic \(\mathbf{S S}\)-coupling term

\[ J \mathbf{S}_{i} \mathbf{S}_{j} = J \sum_\alpha \left[ S_{z,i\alpha} S_{z,j\alpha} + \frac{1}{2} S_{+,i\alpha} S_{-,j\alpha} + \frac{1}{2} S_{-,i\alpha} S_{+,j\alpha}\right] \]

with a complex exchange constant \(J\).

Parameters

[in]	Label1	The first lattice site \(i\).
[in]	Label2	The second lattice site \(j\).
[in]	J	Exchange constant \(J\).
[in]	NOrbitals	Number of orbitals \(\alpha\) to sum over.

SS() [2/2]

RealExpr Pomerol::LatticePresets::SS	(	std::string const &	Label1,
		std::string const &	Label2,
		RealType	J,
		unsigned short	NOrbitals = 1
	)

Make a fermionic \(\mathbf{S S}\)-coupling term

\[ J \mathbf{S}_{i} \mathbf{S}_{j} = J \sum_\alpha \left[ S_{z,i\alpha} S_{z,j\alpha} + \frac{1}{2} S_{+,i\alpha} S_{-,j\alpha} + \frac{1}{2} S_{-,i\alpha} S_{+,j\alpha}\right] \]

with a real exchange constant \(J\).

Parameters

[in]	Label1	The first lattice site \(i\).
[in]	Label2	The second lattice site \(j\).
[in]	J	Exchange constant \(J\).
[in]	NOrbitals	Number of orbitals \(\alpha\) to sum over.

SzSz() [1/2]

ComplexExpr Pomerol::LatticePresets::SzSz	(	std::string const &	Label1,
		std::string const &	Label2,
		ComplexType	J,
		unsigned short	NOrbitals = 1
	)

Make a fermionic \(S_z S_z\)-coupling term

\[ J S_{z,i} S_{z,j} = \frac{J}{4} \sum_\alpha (n_{i\alpha\uparrow} - n_{i\alpha\downarrow}) (n_{j\alpha\uparrow} - n_{j\alpha\downarrow}) \]

with a complex exchange constant \(J\).

Parameters

[in]	Label1	The first lattice site \(i\).
[in]	Label2	The second lattice site \(j\).
[in]	J	Exchange constant \(J\).
[in]	NOrbitals	Number of orbitals \(\alpha\) to sum over.

SzSz() [2/2]

RealExpr Pomerol::LatticePresets::SzSz	(	std::string const &	Label1,
		std::string const &	Label2,
		RealType	J,
		unsigned short	NOrbitals = 1
	)

Make a fermionic \(S_z S_z\)-coupling term

\[ J S_{z,i} S_{z,j} = \frac{J}{4} \sum_\alpha (n_{i\alpha\uparrow} - n_{i\alpha\downarrow}) (n_{j\alpha\uparrow} - n_{j\alpha\downarrow}) \]

with a real exchange constant \(J\).

Parameters

[in]	Label1	The first lattice site \(i\).
[in]	Label2	The second lattice site \(j\).
[in]	J	Exchange constant \(J\).
[in]	NOrbitals	Number of orbitals \(\alpha\) to sum over.