grogu/src/grogu_magn/jij.py

# Copyright (c) [2024] [Daniel Pozsar]
#
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# SOFTWARE.

if __name__ == "__main__":
    import argparse
    import sys
    from itertools import permutations, product
    from timeit import default_timer as timer

    import numpy as np
    import numpy.linalg as nl
    import sisl
    import tqdm
    from mpi4py import MPI
    from scipy.special import roots_legendre

    from grogu_magn.useful import hsk, make_atran, make_contour, make_kset

    start = timer()

    # Some input parsing
    parser = argparse.ArgumentParser()
    parser.add_argument(
        "--kset",
        dest="kset",
        default=2,
        type=int,
        help="k-space resolution of Jij calculation",
    )
    parser.add_argument(
        "--kdirs",
        dest="kdirs",
        default="xyz",
        help="Definition of k-space dimensionality",
    )
    parser.add_argument(
        "--eset",
        dest="eset",
        default=42,
        type=int,
        help="Number of energy points on the contour",
    )
    parser.add_argument(
        "--eset-p",
        dest="esetp",
        default=10,
        type=int,
        help="Parameter tuning the distribution on the contour",
    )
    parser.add_argument("--input", dest="infile", required=True, help="Input file name")
    parser.add_argument(
        "--output", dest="outfile", required=True, help="Output file name"
    )
    parser.add_argument(
        "--Ebot",
        dest="Ebot",
        default=-20.0,
        type=float,
        help="Bottom energy of the contour",
    )
    parser.add_argument(
        "--npairs",
        dest="npairs",
        default=1,
        type=int,
        help="Number of unitcell pairs in each direction for Jij calculation",
    )
    parser.add_argument(
        "--adirs", dest="adirs", default=False, help="Definition of pair directions"
    )
    parser.add_argument(
        "--use-tqdm",
        dest="usetqdm",
        default="not",
        help="Use tqdm for progressbars or not",
    )
    parser.add_argument(
        "--cutoff",
        dest="cutoff",
        default=100.0,
        type=float,
        help="Real space cutoff for pair generation in Angs",
    )
    parser.add_argument(
        "--pairfile",
        dest="pairfile",
        default=False,
        help="File to read pair information",
    )
    args = parser.parse_args()
    # ----------------------------------------------------------------------

    # MPI init
    comm = MPI.COMM_WORLD
    size = comm.Get_size()
    rank = comm.Get_rank()
    root_node = 0
    if rank == root_node:
        print("Number of nodes in the parallel cluster: ", size)
    # ----------------------------------------------------------------------

    # importing the necessary structures from SIESTA output
    dat = sisl.get_sile(args.infile)
    dh = dat.read_hamiltonian()
    # update datastructure of the hamiltonian
    # this is needed for quick Hk building
    dh.hup = (
        dh.tocsr(0)
        .toarray()
        .reshape(dh.no, dh.n_s, dh.no)
        .transpose(0, 2, 1)
        .astype("complex128")
    )
    dh.hdo = (
        dh.tocsr(1)
        .toarray()
        .reshape(dh.no, dh.n_s, dh.no)
        .transpose(0, 2, 1)
        .astype("complex128")
    )
    dh.sov = (
        dh.tocsr(2)
        .toarray()
        .reshape(dh.no, dh.n_s, dh.no)
        .transpose(0, 2, 1)
        .astype("complex128")
    )
    # ----------------------------------------------------------------------

    # generate k space sampling
    kset = make_kset(dirs=args.kdirs, NUMK=args.kset)
    wk = 1 / len(kset)  # weight of a kpoint in BZ integral
    kpcs = np.array_split(kset, size)
    if "k" in args.usetqdm:
        kpcs[root_node] = tqdm.tqdm(kpcs[root_node], desc="k loop")
    # ----------------------------------------------------------------------
    # define pairs

    if args.pairfile:
        # if pair file is specified read in pair information from pairfile
        if rank == root_node:
            # read in pair on root node file in a format of five integer columns
            # first two integers define sublattice
            # second three define distance vectors of unitcells
            dummy = np.loadtxt(args.pairfile, dtype=int)
            atran = [
                (dummy[p, 0], dummy[p, 1], [dummy[p, 2], dummy[p, 3], dummy[p, 4]])
                for p in range(len(dummy))
            ]
        else:
            atran = None
        # syncronize atran over all nodes
        atran = comm.bcast(atran, root=root_node)
    else:
        # if pairfile is not specified generate pair as defined by npairs and adirs
        # Take pair directions for k directions if adirs is not set
        args.adirs = args.adirs if args.adirs else args.kdirs
        # definition of pairs in terms of integer coordinates refering
        # to unicell distances and atomic positions
        atran = make_atran(len(dh.atoms), args.adirs, dist=args.npairs)
    pairs = []
    for i, j, uc in atran:
        if nl.norm(np.dot(uc, dh.cell)) < args.cutoff:
            pairs.append(
                dict(
                    offset=uc,  # lattice vector offset between the unitcells the two atoms are
                    aiij=[i, j],  # indecies of the atoms in the unitcell
                    noij=[
                        dh.atoms.orbitals[i],
                        dh.atoms.orbitals[j],
                    ],  # number of orbitals on the appropriate atoms
                    slij=[
                        slice(
                            *(lambda x: [min(x), max(x) + 1])(dh.a2o(i, all=True))
                        ),  # slices for
                        slice(*(lambda x: [min(x), max(x) + 1])(dh.a2o(j, all=True))),
                    ],  # appropriate orbitals
                    rirj=[
                        dh.axyz()[i],
                        dh.axyz()[j],
                    ],  # real space vectors of atoms in the unit cell
                    Rij=np.dot(
                        uc, dh.cell
                    ),  # real space distance vector between unit cells
                    rij=np.dot(uc, dh.cell)
                    - dh.axyz()[i]
                    + dh.axyz()[j],  # real space vector between atoms
                    Jijz=[],  # in this empty list are we going to gather the integrad of the energy integral
                    Jij=0,  # the final results of the calculation are going to be here on the root node
                )
            )

    if rank == root_node:
        print("Number of pairs beeing calculated: ", len(pairs))

    comm.Barrier()
    # ----------------------------------------------------------------------

    # make energy contour
    # we are working in eV now  !
    # and sisil shifts E_F to 0 !
    cont = make_contour(emin=args.Ebot, enum=args.eset, p=args.esetp)
    eran = cont.ze
    # ----------------------------------------------------------------------

    # generating onsite matrix and overalp elements of all the atoms in the unitcell
    # onsite of the origin supercell
    orig_indx = np.arange(0, dh.no) + dh.sc_index([0, 0, 0]) * dh.no
    # spin up
    uc_up = dh.tocsr(dh.UP)[:, orig_indx].toarray()
    # spin down
    uc_down = dh.tocsr(dh.DOWN)[:, orig_indx].toarray()
    Hs = []
    # get number of atoms in the unit cell
    for i in range(len(dh.atoms)):
        at_indx = dh.a2o(i, all=True)
        Hs.append(uc_up[:, at_indx][at_indx, :] - uc_down[:, at_indx][at_indx, :])

    # ----------------------------------------------------------------------

    # sampling the integrand on the contour and the BZ

    for pair in pairs:
        noi, noj = pair["noij"]
        pair["Guij"] = np.zeros((args.eset, noi, noj), dtype="complex128")
        pair["Gdji"] = np.zeros((args.eset, noj, noi), dtype="complex128")
        pair["Guij_tmp"] = np.zeros((args.eset, noi, noj), dtype="complex128")
        pair["Gdji_tmp"] = np.zeros((args.eset, noj, noi), dtype="complex128")

    for k in kpcs[rank]:
        HKU, HKD, SK = hsk(dh, k)
        Gku = nl.inv(SK * eran.reshape(args.eset, 1, 1) - HKU)
        Gkd = nl.inv(SK * eran.reshape(args.eset, 1, 1) - HKD)
        for pair in pairs:
            phase = np.exp(1j * np.dot(np.dot(k, dh.rcell), pair["Rij"]))
            si, sj = pair["slij"]
            pair["Guij_tmp"] += Gku[:, si, sj] * phase * wk
            pair["Gdji_tmp"] += Gkd[:, sj, si] / phase * wk

    # summ reduce partial results of mpi nodes
    for pair in pairs:
        comm.Reduce(pair["Guij_tmp"], pair["Guij"], root=root_node)
        comm.Reduce(pair["Gdji_tmp"], pair["Gdji"], root=root_node)

    if rank == root_node:
        for pair in pairs:
            i, j = pair["aiij"]
            # The Szunyogh-Lichtenstein formula
            pair["Jijz"] = np.trace(
                (Hs[i] @ pair["Guij"]) @ (Hs[j] @ pair["Gdji"]), axis1=1, axis2=2
            )
            # evaluation of the contour integral
            pair["Jij"] = np.trapz(np.imag(pair["Jijz"] * cont.we) / (2 * np.pi))
        end = timer()

        # ----------------------------------------------------------------------
        # and saveing output of the calculation
        np.savetxt(
            args.outfile,
            np.array(
                [
                    [nl.norm(p["rij"]), p["Jij"] * sisl.unit_convert("eV", "Ry") * 1000]
                    + p["aiij"]
                    + list(p["offset"])
                    + list(p["rij"])
                    for p in pairs
                ],
                dtype=object,
            ),
            header=str(args)
            + "\nnumber of cores = "
            + str(size)
            + "\ntime of calculation = "
            + str(end - start)
            + "\nnorm(rij),Jij[mRy],aiij,offset,rij",
            fmt="%s",
        )