Fermionic single-particle Matsubara Green's function. More...
#include <GreensFunction.hpp>
Public Member Functions | |
| GreensFunction (StatesClassification const &S, Hamiltonian const &H, FieldOperator const &F1, FieldOperator const &F2, DensityMatrix const &DM) | |
| GreensFunction (GreensFunction const &GF) | |
| void | prepare () |
| void | compute () |
| Actually computes the parts. More... | |
| ParticleIndex | getIndex (std::size_t Position) const |
| ComplexType | operator() (long MatsubaraNumber) const |
| ComplexType | operator() (ComplexType z) const |
| ComplexType | of_tau (RealType tau) const |
| bool | isVanishing () const |
| Is this Green's function identically zero? More... | |
 Public Member Functions inherited from Pomerol::Thermal | |
| Thermal (RealType beta) | |
| Public Member Functions inherited from Pomerol::ComputableObject | |
| ComputableObject ()=default | |
| StatusEnum | getStatus () const |
| Return the current computation status. More... | |
| void | setStatus (StatusEnum Status_in) |
Data Fields | |
| RealType | PoleResolution = 1e-8 |
| Lehmann representation: Maximal distance between energy poles to be consider coinciding. More... | |
| RealType | CoefficientTolerance = 1e-8 |
| Lehmann representation: Maximal magnitude of a term coefficient to be considered negligible. More... | |
| Data Fields inherited from Pomerol::Thermal | |
| RealType const | beta |
| Inverse temperature \(\beta\). More... | |
| ComplexType const | MatsubaraSpacing |
| Spacing between (imaginary) Matsubara frequencies, \(i\pi/\beta\). More... | |
Friends | |
| class | GFContainer |
Additional Inherited Members | |
| Public Types inherited from Pomerol::ComputableObject | |
| enum | StatusEnum { Constructed , Prepared , Computed } |
| Computation status of the object. More... | |
| Protected Attributes inherited from Pomerol::ComputableObject | |
| StatusEnum | Status = Constructed |
| Current computation status. More... | |
Detailed Description
Fermionic single-particle Matsubara Green's function.
This class gives access to the GF values both in imaginary time representation,
\[ G(\tau) = -Tr[\mathcal{T}_\tau \hat\rho F_1(\tau) F_2(0)] \]
and at the imaginary Matsubara frequencies \(\omega_n = \pi(2n+1)/\beta\),
\[ G(i\omega_n) = \int_0^\beta d\tau e^{i\omega_n\tau} G(\tau). \]
Here, the operators \(F_1\) and \(F_2\) can be either creation or annihilation operators of fermions. It is actually a container class for a collection of GreensFunctionPart's (most of the real calculations take place in the parts).
Definition at line 50 of file GreensFunction.hpp.
Constructor & Destructor Documentation
◆ GreensFunction() [1/2]
| Pomerol::GreensFunction::GreensFunction | ( | StatesClassification const & | S, |
| Hamiltonian const & | H, | ||
| FieldOperator const & | F1, | ||
| FieldOperator const & | F2, | ||
| DensityMatrix const & | DM | ||
| ) |
Constructor.
- Parameters
-
[in] S Information about invariant subspaces of the Hamiltonian. [in] H The Hamiltonian. [in] F1 The first operator \(F_1\). [in] F2 The second operator \(F_2\). [in] DM Many-body density matrix \(\hat\rho\).
◆ GreensFunction() [2/2]
| Pomerol::GreensFunction::GreensFunction | ( | GreensFunction const & | GF | ) |
Copy-constructor.
- Parameters
-
[in] GF GreensFunction object to be copied.
Member Function Documentation
◆ compute()
| void Pomerol::GreensFunction::compute | ( | ) |
Actually computes the parts.
◆ getIndex()
| ParticleIndex Pomerol::GreensFunction::getIndex | ( | std::size_t | Position | ) | const |
Returns the single-particle index of either \(F_1\) or \(F_2\).
- Parameters
-
[in] Position Select \(F_1\) for Position==0 and \(F_2\) for Position==1. Throws for other values of this argument.
◆ isVanishing()
|
inline |
Is this Green's function identically zero?
Definition at line 118 of file GreensFunction.hpp.
◆ of_tau()
|
inline |
Return the GF value calculated at a given imaginary time \(\tau\).
- Parameters
-
[in] tau Imaginary time point.
Definition at line 138 of file GreensFunction.hpp.
◆ operator()() [1/2]
|
inline |
Return the GF value calculated at a given complex frequency \(z\).
- Parameters
-
[in] z The complex frequency.
Definition at line 127 of file GreensFunction.hpp.
◆ operator()() [2/2]
|
inline |
Return the GF value calculated at a given Matsubara frequency.
- Parameters
-
[in] MatsubaraNumber Index of the Matsubara frequency \(n\) ( \(\omega_n=\pi(2n+1)/\beta\)).
Definition at line 123 of file GreensFunction.hpp.
◆ prepare()
| void Pomerol::GreensFunction::prepare | ( | ) |
Select all relevant parts of \(F_1\) and \(F_2\) and allocate resources for the GreensFunctionPart's.
Friends And Related Function Documentation
◆ GFContainer
|
friend |
Definition at line 52 of file GreensFunction.hpp.
Field Documentation
◆ CoefficientTolerance
| RealType Pomerol::GreensFunction::CoefficientTolerance = 1e-8 |
Lehmann representation: Maximal magnitude of a term coefficient to be considered negligible.
Definition at line 75 of file GreensFunction.hpp.
◆ PoleResolution
| RealType Pomerol::GreensFunction::PoleResolution = 1e-8 |
Lehmann representation: Maximal distance between energy poles to be consider coinciding.
Definition at line 73 of file GreensFunction.hpp.
The documentation for this class was generated from the following file:
- pomerol/GreensFunction.hpp
