Auxiliary Functions

Description

Hosts a number of auxiliary procedures required in different parts of the code. Specifically, it implements: creation/annihilation fermionic operators, binary decomposition of integer representation of Fock states and setup the local impurity Hamiltonian

Quick access

Routines:

ed_set_hloc(), ed_set_suffix(), scatter_vector_mpi(), allgather_vector_mpi(), ed_reset_suffix(), c(), cdg(), bdecomp(), ed_search_variable(), search_chemical_potential()

Used modules

• ed_input_vars: Contains all global input variables which can be set by the user through the input file. A specific preocedure ed_read_input() should be called to read the input file using parse_input_variable() procedure from SciFortran. All variables are automatically set to a default, looked for and updated by reading into the file and, sequentially looked for and updated from command line (std.input) using the notation variable_name=variable_value(s) (case independent).

• ed_vars_global: Contains all variables, arrays and derived types instances shared throughout the code. Specifically, it contains definitions of the effective_bath, the gfmatrix and the sector data structures.

• sf_timer

• sf_linalg

  • eye()

• sf_spin

• sf_misc

  • assert_shape()

• sf_iotools

  • free_unit()

  • reg()

  • txtfy()

• sf_arrays

  • arange()

  • linspace()

Subroutines and functions

interface  ed_aux_funx/ed_set_hloc(hloc, nlat)

This subroutine sets the local Hamiltonian of the impurity problem. The local hamiltonian can have different shapes:

• [nspin . norb , nspin . norb ]: single-impurity case, rank-2 array

• [nspin , nspin , norb , norb ]: single-impurity case, rank-4 array

• [nlat. nspin . norb, nlat. nspin . norb ]: real-space DMFT case, rank-2 array.

• [nlat , nspin . norb , nspin . norb ]: real-space RDMFT case, rank-3 array.

• [nlat , nspin , nspin , norb , norb ]: real-space RDMFT case, rank-5 array.

In the case of real-space DMFT, the number of impurities nlat must be provided.

Parameters:

• hloc (various shapes) [complex, in] – The local Hamiltonian array

• nlat [integer] – Number of impurities for real-space DMFT

interface  ed_aux_funx/ed_set_suffix(indx)

This subroutine sets a suffix for the output files generated by the library as stored in the global variable ed_file_suffix. The suffix can be of type:

• integer: will be converted to string and padded with zeros

• real: will be converted to string

• character[len=*]

Parameters:

indx [integer, real, character(len=*)]

interface  ed_aux_funx/scatter_vector_mpi(mpicomm, v, vloc)

Scatter the vector \(\vec{V}\) into the smaller parts \(\vec{V}_{t}\) on each thread such that \(\sum_{t}{\rm size}(\vec{V}_t) = {\rm size}(\vec{V})\)

Parameters:

• mpicomm [integer]

• v (•) [real, complex] – size[N]

• vloc (•) [real, complex] – size[Nloc]

interface  ed_aux_funx/allgather_vector_mpi(mpicomm, vloc, v)

All threads gather the other portions \(\vec{V}_{t}\) of the vector \(\vec{V}\) and reduce it into a local copy.

Parameters:

• mpicomm [integer]

• vloc (•) [real, complex] – size[Nloc]

• v (•) [real, complex] – size[N]

subroutine  ed_aux_funx/ed_reset_suffix()

This subroutine resets the suffix set by ed_set_suffix() to an empty string

subroutine  ed_aux_funx/c(pos, in, out, fsgn)

Fermionic destruction operator, used in the construction of the sector Hamiltonian. The c() operator set the bit at position pos to 0 in the bit representation of the integer in. Further it evaluates the corresponding fermionic sign fsign as \(\sum_{i<pos}(-1)^{i}\). The obtained bitset identifies a new integer Out.

Parameters:

• pos [integer, in]

• in [integer, in]

• out [integer, inout]

• fsgn [real, inout]

subroutine  ed_aux_funx/cdg(pos, in, out, fsgn)

Fermionic creation operator, used in the construction of the sector Hamiltonian. The cdg() operator set the bit at position pos to 1 in the bit representation of the integer in. Further it evaluates the corresponding fermionic sign fsign as \(\sum_{i<pos}(-1)^{i}\). The obtained bitset identifies a new integer Out.

Parameters:

• pos [integer, in]

• in [integer, in]

• out [integer, inout]

• fsgn [real, inout]

function  ed_aux_funx/bdecomp(i, ntot)

Binary decomposition of the integer i with ntot bits. The input integers represents a Fock state \(|i-1\rangle\) with \(i=1,\dots,2^{2N_s}\). The resulting vector ivec describes the state \(|n_1,n_2,\dots,n_{N_{tot}}\rangle\) with \(n_i=0,1\).

Parameters:

• i [integer]

• ntot [integer]

Return:

ivec (ntot) [integer]

subroutine  ed_aux_funx/ed_search_variable(var, ntmp, converged)

This function checks the value of the read density ntmp against the desired value nread (if different from zero) and adjusts var accordingly (in a monotonous way).

The updated xmu is saved in search_variable_iteration"//reg(ed_file_suffix)//".ed

The converged xmu is saved in var_compressibility.restart

If a file var_compressibility.used is present, its value is read

Parameters:

• var [real, inout] – the variable to be adjusted

• ntmp [real, in] – the density value at the given iteration

• converged [logical, inout] – whether the DMFT loop has achieved a sufficiently small error independently on the density

subroutine  ed_aux_funx/search_chemical_potential(var, ntmp, converged)

This function checks the value of the read density ntmp against the desired value nread (if different from zero) and adjusts xmu accordingly (in a monotonous way).

The updated xmu is saved in search_mu_iteration"//reg(ed_file_suffix)//".ed

The converged xmu is saved in xmu.restart

If a file var_compressibility.used is present, its value is read

NOTE: this function is accessible to the user as edipack2/ed_search_chemical_potential()

Parameters:

• var [real, inout] – the chemical potential

• ntmp [real, in] – the density value at the given iteration

• converged [logical, inout] – reset convergence