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pomerol  2.1
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Factory functions for Coulomb interaction terms
Collaboration diagram for Factory functions for Coulomb interaction terms:

Functions

RealExpr Pomerol::LatticePresets::CoulombS (std::string const &Label, RealType U, RealType Eps, unsigned short NOrbitals=1)
 
ComplexExpr Pomerol::LatticePresets::CoulombS (std::string const &Label, ComplexType U, ComplexType Eps, unsigned short NOrbitals=1)
 
RealExpr Pomerol::LatticePresets::CoulombP (std::string const &Label, RealType U, RealType U_p, RealType J, RealType Eps, unsigned short NOrbitals=3)
 
ComplexExpr Pomerol::LatticePresets::CoulombP (std::string const &Label, ComplexType U, ComplexType U_p, ComplexType J, ComplexType Eps, unsigned short NOrbitals=3)
 
RealExpr Pomerol::LatticePresets::CoulombP (std::string const &Label, RealType U, RealType J, RealType Eps, unsigned short NOrbitals=3)
 
ComplexExpr Pomerol::LatticePresets::CoulombP (std::string const &Label, ComplexType U, ComplexType J, ComplexType Eps, unsigned short NOrbitals=3)
 

Detailed Description

Function Documentation

◆ CoulombP() [1/4]

ComplexExpr Pomerol::LatticePresets::CoulombP ( std::string const &  Label,
ComplexType  U,
ComplexType  J,
ComplexType  Eps,
unsigned short  NOrbitals = 3 
)

Make a Hubbard-Kanamori interaction term of the following form,

\[ U \sum_{\alpha, \sigma > \sigma'} n_{i\alpha\sigma}n_{i\alpha\sigma'} + (U-2J) \sum_{\alpha\neq\alpha',\sigma > \sigma'} n_{i\alpha\sigma} n_{i\alpha'\sigma'} + \frac{U-3J}{2} \sum_{\alpha\neq\alpha',\sigma} n_{i\alpha\sigma} n_{i\alpha'\sigma} - J \sum_{\alpha\neq\alpha',\sigma > \sigma'} (c^\dagger_{i\alpha \sigma} c^\dagger_{i\alpha'\sigma'}c_{i\alpha'\sigma}c_{i\alpha\sigma'} + c^\dagger_{i\alpha'\sigma}c^\dagger_{i\alpha'\sigma'}c_{i\alpha\sigma}c_{i\alpha\sigma'}) + \varepsilon \sum_{\alpha,\sigma} n_{i\alpha\sigma} \]

with complex interaction constants \(U\), \(J\) and a complex energy level \(\varepsilon\). The number of orbitals must be at least 2.

Parameters
[in]LabelLattice site \(i\).
[in]UHubbard-Kanamori interaction constant \(U\).
[in]JHund's coupling \(J\).
[in]EpsEnergy level \(\varepsilon\).
[in]NOrbitalsNumber of orbitals \(\alpha, \alpha'\) to sum over.

◆ CoulombP() [2/4]

ComplexExpr Pomerol::LatticePresets::CoulombP ( std::string const &  Label,
ComplexType  U,
ComplexType  U_p,
ComplexType  J,
ComplexType  Eps,
unsigned short  NOrbitals = 3 
)

Make a Hubbard-Kanamori interaction term of the following form,

\[ U \sum_{\alpha, \sigma > \sigma'} n_{i\alpha\sigma}n_{i\alpha\sigma'} + U' \sum_{\alpha\neq\alpha',\sigma > \sigma'} n_{i\alpha\sigma} n_{i\alpha'\sigma'} + \frac{U'-J}{2} \sum_{\alpha\neq\alpha',\sigma} n_{i\alpha\sigma} n_{i\alpha'\sigma} - J \sum_{\alpha\neq\alpha',\sigma > \sigma'} (c^\dagger_{i\alpha \sigma} c^\dagger_{i\alpha'\sigma'}c_{i\alpha'\sigma}c_{i\alpha\sigma'} + c^\dagger_{i\alpha'\sigma}c^\dagger_{i\alpha'\sigma'}c_{i\alpha\sigma}c_{i\alpha\sigma'}) + \varepsilon \sum_{\alpha,\sigma} n_{i\alpha\sigma} \]

with complex interaction constants \(U\), \(U_p\), \(J\) and a complex energy level \(\varepsilon\). The number of orbitals must be at least 2.

Parameters
[in]LabelLattice site \(i\).
[in]UHubbard-Kanamori interaction constant \(U\).
[in]U_pHubbard-Kanamori interaction constant \(U_p\).
[in]JHund's coupling \(J\).
[in]EpsEnergy level \(\varepsilon\).
[in]NOrbitalsNumber of orbitals \(\alpha, \alpha'\) to sum over.

◆ CoulombP() [3/4]

RealExpr Pomerol::LatticePresets::CoulombP ( std::string const &  Label,
RealType  U,
RealType  J,
RealType  Eps,
unsigned short  NOrbitals = 3 
)

Make a Hubbard-Kanamori interaction term of the following form,

\[ U \sum_{\alpha, \sigma > \sigma'} n_{i\alpha\sigma}n_{i\alpha\sigma'} + (U-2J) \sum_{\alpha\neq\alpha',\sigma > \sigma'} n_{i\alpha\sigma} n_{i\alpha'\sigma'} + \frac{U-3J}{2} \sum_{\alpha\neq\alpha',\sigma} n_{i\alpha\sigma} n_{i\alpha'\sigma} - J \sum_{\alpha\neq\alpha',\sigma > \sigma'} (c^\dagger_{i\alpha \sigma} c^\dagger_{i\alpha'\sigma'}c_{i\alpha'\sigma}c_{i\alpha\sigma'} + c^\dagger_{i\alpha'\sigma}c^\dagger_{i\alpha'\sigma'}c_{i\alpha\sigma}c_{i\alpha\sigma'}) + \varepsilon \sum_{\alpha,\sigma} n_{i\alpha\sigma} \]

with real interaction constants \(U\), \(J\) and a real energy level \(\varepsilon\). The number of orbitals must be at least 2.

Parameters
[in]LabelLattice site \(i\).
[in]UHubbard-Kanamori interaction constant \(U\).
[in]JHund's coupling \(J\).
[in]EpsEnergy level \(\varepsilon\).
[in]NOrbitalsNumber of orbitals \(\alpha, \alpha'\) to sum over.

◆ CoulombP() [4/4]

RealExpr Pomerol::LatticePresets::CoulombP ( std::string const &  Label,
RealType  U,
RealType  U_p,
RealType  J,
RealType  Eps,
unsigned short  NOrbitals = 3 
)

Make a Hubbard-Kanamori interaction term of the following form,

\[ U \sum_{\alpha, \sigma > \sigma'} n_{i\alpha\sigma}n_{i\alpha\sigma'} + U' \sum_{\alpha\neq\alpha',\sigma > \sigma'} n_{i\alpha\sigma} n_{i\alpha'\sigma'} + \frac{U'-J}{2} \sum_{\alpha\neq\alpha',\sigma} n_{i\alpha\sigma} n_{i\alpha'\sigma} - J \sum_{\alpha\neq\alpha',\sigma > \sigma'} (c^\dagger_{i\alpha \sigma} c^\dagger_{i\alpha'\sigma'}c_{i\alpha'\sigma}c_{i\alpha\sigma'} + c^\dagger_{i\alpha'\sigma}c^\dagger_{i\alpha'\sigma'}c_{i\alpha\sigma}c_{i\alpha\sigma'}) + \varepsilon \sum_{\alpha,\sigma} n_{i\alpha\sigma} \]

with real interaction constants \(U\), \(U_p\), \(J\) and a real energy level \(\varepsilon\). The number of orbitals must be at least 2.

Parameters
[in]LabelLattice site \(i\).
[in]UHubbard-Kanamori interaction constant \(U\).
[in]U_pHubbard-Kanamori interaction constant \(U_p\).
[in]JHund's coupling \(J\).
[in]EpsEnergy level \(\varepsilon\).
[in]NOrbitalsNumber of orbitals \(\alpha, \alpha'\) to sum over.

◆ CoulombS() [1/2]

ComplexExpr Pomerol::LatticePresets::CoulombS ( std::string const &  Label,
ComplexType  U,
ComplexType  Eps,
unsigned short  NOrbitals = 1 
)

Make a Coulomb interaction term of the following form,

\[ U \sum_\alpha n_{i\alpha\uparrow} n_{i\alpha\downarrow} + \varepsilon \sum_{\alpha,\sigma} n_{i\alpha\sigma} \]

with a complex interaction constant \(U\) and a complex energy level \(\varepsilon\).

Parameters
[in]LabelLattice site \(i\).
[in]UInteraction constant \(U\).
[in]EpsEnergy level \(\varepsilon\).
[in]NOrbitalsNumber of orbitals \(\alpha\) to sum over.

◆ CoulombS() [2/2]

RealExpr Pomerol::LatticePresets::CoulombS ( std::string const &  Label,
RealType  U,
RealType  Eps,
unsigned short  NOrbitals = 1 
)

Make a Coulomb interaction term of the following form,

\[ U \sum_\alpha n_{i\alpha\uparrow} n_{i\alpha\downarrow} + \varepsilon \sum_{\alpha,\sigma} n_{i\alpha\sigma} \]

with a real interaction constant \(U\) and a real energy level \(\varepsilon\).

Parameters
[in]LabelLattice site \(i\).
[in]UInteraction constant \(U\).
[in]EpsEnergy level \(\varepsilon\).
[in]NOrbitalsNumber of orbitals \(\alpha\) to sum over.