4.1.5. Parameters for the numerical condition

• 2S

  Type : Positive integer (1 as a default)

  Description : The \(2 S\) at each site in the localized spin system is specified. (E.g. 1 for the \(1/2\) system)

• Restart

  Type : String (choose from "None", "Restart_out", "Restart_in", "Restart". "None" as a default)

  Description : The condition of the restart is specified. "None" for omitting file IOs for the restart, "Restart_out" for starting calculation from scratch and generating a restart-file after the calculation finishes, "Restart_in" for starting calculation with the restart-file generated in the previous run, "Restart" for "Restart_out" + "Restart_in".

• anczos_max

  Type : Positive integer (default value: 2000)

  Description : The upper limit of the Lanczos/LOBCG/BiCG step and the number of steps for TPQ/Time=evolution are specified with this parameter.

• initial_iv

  Type : Integer (default value: -1)

  Description : An initial vector is specified with this parameter.

  • Lanczos method

    • For the canonical ensemble and initial_iv \(\geq 0\)

      The non-zero components of an initial vector are specified with this parameter.

    • For the grand canonical ensemble or initial_iv \(< 0\)

      The seed of the random generator is given by this parameter and the random vector is used as the initial vector.

  • TPQ method

    The seed of the random generator is given by this parameter and the random vector is used as the initial vector.

  See Algorithm for details of setting an initial vector.

• exct

  Type : Positive integer (default value: 1)

  Description : The number of eigenvectors obtained from the ground energy by the Lanczos method are specified.

  When exct=2, the eigenvector of the first-excited state is obtained. When method="CG", the number of states to be calculated is specified.

  Note: The condition nvec \(>=\) exct must be satisfied.

• LanczosEps

  Type : Positive integer (default value: 14)

  Description : The convergence criterion for the Lanczos method is specified with this parameter. If the difference between the old and the new target eigenvalue falls below \(10^{- LanczosEps|}\), the Lanczos step will finish. For method="CG", we assume the calculation is converged when the 2-norm of the residual vector becomes smaller than \(10^{-{\tt LanczosEps}/2}\).

• LanczosTarget

  Type : Positive integer (default value: 2)

  Description : The target eigenenergy for the convergence criterion is specified. If it is set to 1, the target eigenenergy becomes the ground state.

• LargeValue

  Type : Double (the default value is provided below)

  Description : (Only for TPQ) \(l\) as \(l=\hat{\mathcal H}/N_{s}\) is used in the TPQ calculation. Usually, the largest eigenvalue of the Hamiltonian is used as \(l\). Thus, the default value of \(l\) is taken as the summation of the absolute values of each coefficient in the Hamiltonian divided by the number of sites.

• NumAve

  Type : Positive integer (default value: 5)

  Description : (Only for TPQ) The number of independent runs for the TPQ method is specified with this parameter.

• ExpecInterval

  Type : Positive integer (default value: 20)

  Description : (Only for TPQ) The interval of calculating correlation functions in the TPQ iteration is specified.

  Note: A small interval increases the time cost of calculations.

• OutputMode

  Type : Choose from "none", "correlation", and "full" (correlation as default)

  Description : Indices of correlation functions are specified with this keyword. "none" indicates correlation functions will not be calculated. When outputmode="correlation", the correlation function supported by the utility fourier is computed. For more details, see the document in doc/fourier/. If "full" is selected, \(\langle c_{i \sigma}^{\dagger}c_{j \sigma'} \rangle\) is computed at all \(i, j, \sigma, \sigma'\), and \(\langle c_{i_1 \sigma_1}^{\dagger}c_{i_2 \sigma_2} c_{i_3 \sigma_3}^{\dagger}c_{i_4 \sigma_4} \rangle\) is computed at all \(i_1, i_2, i_3, i_4, \sigma_1, \sigma_2, \sigma_3, \sigma_4\).

  In a spin system, the indices are specified as those of the Bogoliubov representation (see Bogoliubov representation ).

• InitialVecType

  Type : Character (choose from "C", "R". "C" as a default)

  Description : The type of the initial eigenvector is specified. C for the complex number, and R for the real number.

• EigenVecIO

  Type : String (choose from "None", "Out", "In". "None" as a default)

  Description : The I/O of the eigenvector is specified. "None" for omitting the IO of the eigenvector, "Out" for writing the eigenvector to a file, "In" for reading the eigenvector from a file and using it in the subsequent calculation (such as the Green’s function).