Dynamical susceptibility. More...
#include <Susceptibility.hpp>
Public Member Functions | |
| Susceptibility (StatesClassification const &S, Hamiltonian const &H, MonomialOperator const &A, MonomialOperator const &B, DensityMatrix const &DM) | |
| Susceptibility (Susceptibility const &Chi) | |
| void | prepare () |
| void | compute () |
| Actually computes the parts. More... | |
| void | subtractDisconnected () |
| void | subtractDisconnected (ComplexType ave_A, ComplexType ave_B) |
| void | subtractDisconnected (EnsembleAverage &EA_A, EnsembleAverage &EA_B) |
| ComplexType | operator() (long MatsubaraNumber) const |
| ComplexType | operator() (ComplexType z) const |
| ComplexType | of_tau (RealType tau) const |
| bool | isVanishing () const |
| Is this susceptibility 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... | |
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
Dynamical susceptibility.
This class represents a dynamical susceptibility in the Matsubara space,
\[ \chi(i\omega_n) = \int_0^\beta Tr[\mathcal{T}_\tau \hat\rho A(\tau) B(0)] e^{i\omega_n\tau} d\tau \]
and its connected part,
\[ \tilde{\chi}(i\omega_n) = \chi(i\omega_n) - \beta \langle\hat A \rangle \langle\hat B \rangle. \]
Here, \(\beta\) is inverse temperature and \(\langle\hat A\rangle, \langle\hat B\rangle\) are EnsembleAverage's of boson-like monomial operators \(\hat A, \hat B\).
It is actually a container class for a collection of SusceptibilityPart's (most of the real calculations take place in the parts).
Definition at line 55 of file Susceptibility.hpp.
Constructor & Destructor Documentation
◆ Susceptibility() [1/2]
| Pomerol::Susceptibility::Susceptibility | ( | StatesClassification const & | S, |
| Hamiltonian const & | H, | ||
| MonomialOperator const & | A, | ||
| MonomialOperator const & | B, | ||
| DensityMatrix const & | DM | ||
| ) |
Constructor.
- Parameters
-
[in] S Information about invariant subspaces of the Hamiltonian. [in] H The Hamiltonian. [in] A Monomial operator \(\hat A\). [in] B Monomial operator \(\hat B\). [in] DM Many-body density matrix \(\hat\rho\).
◆ Susceptibility() [2/2]
| Pomerol::Susceptibility::Susceptibility | ( | Susceptibility const & | Chi | ) |
Copy-constructor.
- Parameters
-
[in] Chi Susceptibility object to be copied.
Member Function Documentation
◆ compute()
| void Pomerol::Susceptibility::compute | ( | ) |
Actually computes the parts.
◆ isVanishing()
|
inline |
Is this susceptibility identically zero?
Definition at line 138 of file Susceptibility.hpp.
◆ of_tau()
|
inline |
Return the susceptibility value calculated at a given imaginary time \(\tau\).
- Parameters
-
[in] tau Imaginary time point.
Definition at line 160 of file Susceptibility.hpp.
◆ operator()() [1/2]
|
inline |
Return the susceptibility value calculated at a given complex frequency \(z\).
- Parameters
-
[in] z The complex frequency.
Definition at line 147 of file Susceptibility.hpp.
◆ operator()() [2/2]
|
inline |
Return the susceptibility value calculated at a given Matsubara frequency.
- Parameters
-
[in] MatsubaraNumber Index of the Matsubara frequency \(n\) ( \(\omega_n=2\pi n/\beta\)).
Definition at line 143 of file Susceptibility.hpp.
◆ prepare()
| void Pomerol::Susceptibility::prepare | ( | ) |
Select all relevant parts of \(\hat A\) and \(\hat B\) and allocate resources for the SusceptibilityPart's.
◆ subtractDisconnected() [1/3]
| void Pomerol::Susceptibility::subtractDisconnected | ( | ) |
Activate subtraction of the disconnected part \(\langle\hat A \rangle \langle\hat B \rangle\). \(\langle\hat A \rangle\) and \(\langle\hat B \rangle\) are computed by this class.
◆ subtractDisconnected() [2/3]
| void Pomerol::Susceptibility::subtractDisconnected | ( | ComplexType | ave_A, |
| ComplexType | ave_B | ||
| ) |
Activate subtraction of the disconnected part \(\langle\hat A \rangle \langle\hat B \rangle\). Precomputed ensemble averages must be provided by the caller.
- Parameters
-
[in] ave_A Precomputed value of \(\langle\hat A \rangle\). [in] ave_B Precomputed value of \(\langle\hat B \rangle\).
◆ subtractDisconnected() [3/3]
| void Pomerol::Susceptibility::subtractDisconnected | ( | EnsembleAverage & | EA_A, |
| EnsembleAverage & | EA_B | ||
| ) |
Activate subtraction of the disconnected part \(\langle\hat A \rangle \langle\hat B \rangle\). EnsembleAverage objects must must be provided by the caller.
- Parameters
-
[in] EA_A Predefined EnsembleAverage class for the operator \(\hat A\). [in] EA_B Predefined EnsembleAverage class for the operator \(\hat B\).
Field Documentation
◆ CoefficientTolerance
| RealType Pomerol::Susceptibility::CoefficientTolerance = 1e-8 |
Lehmann representation: Maximal magnitude of a term coefficient to be considered negligible.
Definition at line 84 of file Susceptibility.hpp.
◆ PoleResolution
| RealType Pomerol::Susceptibility::PoleResolution = 1e-8 |
Lehmann representation: Maximal distance between energy poles to be consider coinciding.
Definition at line 82 of file Susceptibility.hpp.
The documentation for this class was generated from the following file:
- pomerol/Susceptibility.hpp
