Stored Hamiltonian \(H\times\vec{v}\)

The module ed_hamiltonian_normal_stored_hxv implements the construction of the sector Hamiltonian sparse matrices and the related matrix-vector products algorithms, serial or parallel and according to actual quantum numbers, as defined by the value of the variable ed_total_ud distinguishing between conservation of total or orbital resolved spin occupations.

Description

Constructs each terms of the sector Hamiltonian storing them into different sparse_matrix instances, implement the corresponding matrix-vector products using stored sparse matrices.

Quick access

Routines:

ed_buildh_normal_main(), ed_buildh_normal_orbs(), spmatvec_normal_main(), spmatvec_normal_orbs(), spmatvec_mpi_normal_main(), spmatvec_mpi_normal_orbs()

Used modules

• ed_hamiltonian_normal_common: Global variables related to sector Hamiltonian construction. It contains the vector_transpose_mpi() implementing the MPI Allv-2-Allv parallel matrix transposition.

Subroutines and functions

subroutine  ed_hamiltonian_normal_stored_hxv/ed_buildh_normal_main([hmat])

Builds the sector Hamiltonian \(H\) and save each term in a suitable sparse matrix instance for ed_total_ed = True. If the dimension dim of the sector are smaller than lanc_dim_threshold the global matrix is dumped to the optional variable hmat.

The sparse matrices are:

• \(H_d \rightarrow\) sph0d : diagonal part of the electronic Hamiltonian

• \(H_\uparrow \rightarrow\) sph0ups : \(\uparrow\) spin terms of the eletronic Hamiltonian

• \(H_\downarrow \rightarrow\) sph0dws : \(\downarrow\) spin terms of the eletronic Hamiltonian

• \(H_{nd} \rightarrow\) sph0nd : non-diagonal part of the eletronic Hamiltonian

• \(H_{ph} \rightarrow\) sph0_ph : phonon part of the of the global Hamiltonian

• \(H_{e-eph} \rightarrow\) sph0e_eph : electron part of the electron-phonon term of the global Hamiltonian

• \(H_{ph_eph} \rightarrow\) sph0e_ph : phonon part of the electron-phonon term of the global Hamiltonian

Options:

hmat (•, •) [real] – optional dense matrix

subroutine  ed_hamiltonian_normal_stored_hxv/ed_buildh_normal_orbs([hmat])

Builds the sector Hamiltonian \(H\) and save each term in a suitable sparse matrix instance for ed_total_ed = False. If the dimension dim of the sector are smaller than lanc_dim_threshold the global matrix is dumped to the optional variable hmat.

The sparse matrices are:

• \(H_d \rightarrow\) sph0d : diagonal part of the electronic Hamiltonian

• \(\vec{H}_\uparrow \rightarrow\) sph0ups : \(\uparrow\) spin terms of the eletronic Hamiltonian

• \(\vec{H}_\downarrow \rightarrow\) sph0dws : \(\downarrow\) spin terms of the eletronic Hamiltonian

• \(H_{nd} \rightarrow\) sph0nd : non-diagonal part of the eletronic Hamiltonian

• \(H_{ph} \rightarrow\) sph0_ph : phonon part of the of the global Hamiltonian

• \(H_{e-eph} \rightarrow\) sph0e_eph : electron part of the electron-phonon term of the global Hamiltonian

• \(H_{ph_eph} \rightarrow\) sph0e_ph : phonon part of the electron-phonon term of the global Hamiltonian

where \(\vec{H}_\sigma = [H^1_\sigma,\dots,H^{Norb}_\sigma]\) are the orbital and spin resolved Hamiltonian matrices.

Options:

hmat (•, •) [real] – optional dense matrix

subroutine  ed_hamiltonian_normal_stored_hxv/spmatvec_normal_main(nloc, v, hv)

Serial version of the matrix-vector product \(\vec{w}=H\times\vec{v}\) used in Arpack/Lanczos algorithm for ed_total_ud = True This procedures applies one by one each term of the global Hamiltonian to an input vector using the stored sparse matrices.

Options:

nloc [integer] – Global dimension of the problem. size(v)=Nloc=size(Hv)

Parameters:

• v (nloc) [real] – input vector (passed by Arpack/Lanczos) \(\vec{v}\)

• hv (nloc) [real] – output vector (required by Arpack/Lanczos) \(\vec{w}\)

subroutine  ed_hamiltonian_normal_stored_hxv/spmatvec_normal_orbs(nloc, v, hv)

Serial version of the matrix-vector product \(\vec{w}=H\times\vec{v}\) used in Arpack/Lanczos algorithm for ed_total_ud = False This procedures applies one by one each term of the global Hamiltonian to an input vector using the stored sparse matrices.

Options:

nloc [integer] – Global dimension of the problem. size(v)=Nloc=size(Hv)

Parameters:

• v (nloc) [real] – input vector (passed by Arpack/Lanczos) \(\vec{v}\)

• hv (nloc) [real] – output vector (required by Arpack/Lanczos) \(\vec{w}\)

subroutine  ed_hamiltonian_normal_stored_hxv/spmatvec_mpi_normal_main(nloc, v, hv)

MPI parallel version of the matrix-vector product \(\vec{w}=H\times\vec{v}\) used in P-Arpack/P-Lanczos algorithm for ed_total_ud = True. This procedures applies one by one each term of the global Hamiltonian to a part of the vector own by the thread using the stored sparse matrices.

Options:

nloc [integer] – Local dimension of the vector chunk. size(v)=Nloc with \(\sum_p\) Nloc = Dim

Parameters:

• v (nloc) [real] – input vector part (passed by P-Arpack/P-Lanczos) \(\vec{v}\)

• hv (nloc) [real] – output vector (required by P-Arpack/P-Lanczos) \(\vec{w}\)

subroutine  ed_hamiltonian_normal_stored_hxv/spmatvec_mpi_normal_orbs(nloc, v, hv)

MPI parallel version of the matrix-vector product \(\vec{w}=H\times\vec{v}\) used in P-Arpack/P-Lanczos algorithm for ed_total_ud = False. This procedures applies one by one each term of the global Hamiltonian to a part of the vector own by the thread using the stored sparse matrices.

Options:

nloc [integer] – Local dimension of the vector chunk. size(v)=Nloc with \(\sum_p\) Nloc = Dim

Parameters:

• v (nloc) [real] – input vector part (passed by P-Arpack/P-Lanczos) \(\vec{v}\)

• hv (nloc) [real] – output vector (required by P-Arpack/P-Lanczos) \(\vec{w}\)