1.7. Use eigenvectors

In this tutorial, we will study how to read the eigenvectors. In the standard mode, setting EigenVecIO = "Out" makes HPhi write the calculated eigenvectors as output/zvo_eigenvec_[index]_rank_[rank].dat, where [index] is the index of the states (e.g., the ground state has [index] = 0) and [rank] is the rank of the process. In the MPI parallelization with \(N_{\text{para}}\) processes, HPhi splits the whole Hilbert space into the \(N_{\text{para}}\) blocks and each process treats one of them. The file format is described in the reference manual . For example, the following python function (samples/tutorial-1.7/read_gs.py) reads the vector:

def read_gs(*, index=0, rank=0):
    import numpy as np
    from os.path import join
    from struct import unpack

    filename = join("output",
    with open(filename, "rb") as f:
        nelems = unpack("L", f.read(8))[0]
        ret = np.zeros(nelems, dtype=np.complex128)
        for i in range(nelems):
            re = unpack("d", f.read(8))[0]
            im = unpack("d", f.read(8))[0]
            ret[i] = complex(re, im)
        return ret

1.7.1. Exercise

Check the orthogonality of the eigenvectors calculated by the LOBCG method by calculating the norm and the inner product of some of the eigenvectors.

Hint : In the standard mode, the exct keyword controls the number of eigenvectors to be calculated.

Solution : See samples/tutorial-1.7/solution.py. This script firstly generates the input file for calculating the ground state and the first excited state of the \(L=8\) AFH chain with the LOBCG method, next invokes HPhi, then reads the vectors, and finally calculates the norms and the inner product.