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eigval0

Computes the groud state energy of a Hermitian operator on a block by using an iterative Lanczos algorithm. This function is a shortcut for the eigvals_lanczos function. We refer to eigvals_lanczos for further details on the algorithm and the convergence criterion.

The algorithm can be run either on-the-fly (matrix-free) or using a sparse matrix in the compressed-sparse-row format (see CSRMatrix).

Sources: sparse_diag.hpp · sparse_diag.cpp

Definition

On-the-fly

eigval0(ops::OpSum, block::Block;   precision::Float64 = 1e-12, 
        max_iterations::Int64 = 1000, random_seed::Int64 = 42)::Float64

double eigval0(OpSum const &ops, Block const &block, double precision = 1e-12,
               int64_t max_iterations = 1000, int64_t random_seed = 42);

Sparse matrix

eigval0(ops::CSRMatrix, block::Block; precision::Float64 = 1e-12, 
    max_iterations::Int64 = 1000, random_seed::Int64 = 42)::Float64

double eigval0(CSRMatrix<idx_t, coeff_t> const &ops,
    Block const &block, double precision = 1e-12,
    int64_t max_iterations = 1000, int64_t random_seed = 42);

Parameters

Name Description Default
ops OpSum or CSRMatrix defining a Hermitian operator
block block on which the operator is defined
precision accuracy of the computed ground state 1e-12
max_iterations maximum number of iterations 1000
random_seed random seed for setting up the initial vector 42

Returns

Type Description
real number lowest lying eigenvalue of ops

Usage Example

let 
    N = 8
    nup = N ÷ 2
    block = Spinhalf(N, nup)

    # Define the nearest-neighbor Heisenberg model
    ops = OpSum()
    for i in 1:N
        ops += "J" * Op("SdotS", [i, mod1(i+1, N)])
    end
    ops["J"] = 1.0

    # on-the-fly
    e0 = eigval0(ops, block)

    # sparse matrix
    spmat = csr_matrix(ops, block)
    e0 = eigval0(spmat, block)
end

int N = 8;
int nup = N / 2;
auto block = Spinhalf(N, nup);

// Define the nearest-neighbor Heisenberg model
auto ops = OpSum();
for (int i=0; i<N; ++i) {
  ops += "J" * Op("SdotS", {i, (i+1) % N});
}
ops["J"] = 1.0;

// On-the-fly
double e0 = eigval0(ops, block);

// sparse matrix
auto spmat = csr_matrix(ops, block);
double e0s = eigval0(spmat, block);