dyson.solvers.dynamic.corrvec

dyson.solvers.dynamic.corrvec#

Correction vector Green’s function solver [1].

Classes

CorrectionVector(*args, **kwargs)

Correction vector Green's function solver.
class dyson.solvers.dynamic.corrvec.CorrectionVector(*args: Any, **kwargs: Any)[source]#

Bases: DynamicSolver

Correction vector Green’s function solver.

Parameters:

  • matvec – The matrix-vector operation for the self-energy supermatrix.

  • diagonal – The diagonal of the self-energy supermatrix.

  • nphys – The number of physical degrees of freedom.

  • grid – Real frequency grid upon which to evaluate the Green’s function.

reduction: Reduction = 'none'#
component: Component = 'full'#
ordering: Ordering = 'ordered'#
conv_tol: float = 1e-08#
classmethod from_self_energy(static: Array, self_energy: Lehmann, overlap: Array | None = None, **kwargs: Any) → CorrectionVector[source]#

Create a solver from a self-energy.

Parameters:

  • static – Static part of the self-energy.

  • self_energy – Self-energy.

  • overlap – Overlap matrix for the physical space.

  • kwargs – Additional keyword arguments for the solver.

Returns:

Solver instance.

classmethod from_expression(expression: BaseExpression, **kwargs: Any) → CorrectionVector[source]#

Create a solver from an expression.

Parameters:

  • expression – Expression to be solved.

  • kwargs – Additional keyword arguments for the solver.

Returns:

Solver instance.

matvec_dynamic(vector: Array, grid_index: int) → Array[source]#

Perform the matrix-vector operation for the dynamic self-energy supermatrix.

\[\mathbf{x}_\omega = \left(\omega - \mathbf{H} - i\eta\right) \mathbf{r}\]
Parameters:

  • vector – The vector to operate on.

  • grid_index – Index of the real frequency grid.

Returns:

The result of the matrix-vector operation.

matdiv_dynamic(vector: Array, grid_index: int) → Array[source]#

Approximately perform a matrix-vector division for the dynamic self-energy supermatrix.

\[\mathbf{x}_\omega = \frac{\mathbf{r}}{\omega - \mathbf{H} - i\eta}\]
Parameters:

  • vector – The vector to operate on.

  • grid_index – Index of the real frequency grid.

Returns:

The result of the matrix-vector division.

Notes

The inversion is approximated using the diagonal of the matrix.

get_state_bra(orbital: int) → Array[source]#

Get the bra vector corresponding to a fermion operator acting on the ground state.

Parameters:

orbital – Orbital index.

Returns:

Bra vector.

get_state_ket(orbital: int) → Array[source]#

Get the ket vector corresponding to a fermion operator acting on the ground state.

Parameters:

orbital – Orbital index.

Returns:

Ket vector.

kernel(*args: Any, **kwargs: Any) → Any#

Run the solver.

property matvec: Callable[[Array], Array]#

Get the matrix-vector operation for the self-energy supermatrix.

property diagonal: Array#

Get the diagonal of the self-energy supermatrix.

property grid: RealFrequencyGrid#

Get the real frequency grid.

property nphys: int#

Get the number of physical degrees of freedom.

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