Bath dynamical functions

Description

A comprehensive set of procedures to evaluate the non-interacting impurity Green’s functions \(\hat{G}^{\rm And}\) and hybridizations \(\hat{F}^{\rm And}\) in the complex frequency domain given the effective_bath instance.

Quick access

Routines:

delta_bath_function(), fdelta_bath_function(), g0and_bath_function(), f0and_bath_function(), invg0_bath_function(), invf0_bath_function()

Used modules

• sf_constants

  • zero

• sf_iotools

  • free_unit()

  • reg()

  • file_length()

  • txtfy()

  • str()

• sf_linalg

  • eye()

  • inv()

  • diag()

  • zeye()

  • inv_her()

  • kron()

• sf_spin

  • pauli_sigma_z()

• 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.

• ed_aux_funx: 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

• ed_bath_aux: Implements a number of auxiliary procedures used to construct replica/general bath

• ed_bath_dim: Returns or check the dimensions to which the user should allocate the bath array.

• ed_bath_user: Implements functions the user can use to enforce specific symmetry operations on the bath array.

• ed_bath_dmft: A class for the the effective_bath data structure describing the effective bath in the code.

• ed_bath_replica: In these module we implement the functions to set the matrix basis \(\{ \hat{O}_i \}_{i=1,\dots,N_{sym}}\) and the initial variational parameters \(\vec{\lambda}\) used to decompose each local bath hamiltonian for the replica and general bath types.

Subroutines and functions

interface  ed_bath_functions/delta_bath_function(x, dmft_bath_[, axis])

Evaluates the normal hybridization function \(\Delta(x)\).

Output:

• delta : complex rank-5 array with dimension [ nspin , nspin , norb , norb , size(x) ]

Parameters:

• x (•) [complex, in] – complex array for the frequency

• dmft_bath [effective_bath] – the current effective_bath instance

Options:

axis [character(len=*)] – string indicating the desired axis, 'm' for Matsubara (default), 'r' for Real-axis

interface  ed_bath_functions/fdelta_bath_function(x, dmft_bath_[, axis])

Evaluates the anomalouse hybridization function \(\Theta(x)\).

Output:

• fdelta : complex rank-5 array with dimension [ nspin , nspin , norb , norb , size(x) ]

Parameters:

• x (•) [complex, in] – complex array for the frequency

• dmft_bath [effective_bath] – the current effective_bath instance

Options:

axis [character(len=*)] – string indicating the desired axis, 'm' for Matsubara (default), 'r' for Real-axis

interface  ed_bath_functions/g0and_bath_function(x, dmft_bath_[, axis])

Evaluates the normal non-interacting Green’s function \(G_0(x)\).

Output:

• g0and : complex rank-5 array with dimension [ nspin , nspin , norb , norb , size(x) ]

Parameters:

• x (•) [complex, in] – complex array for the frequency

• dmft_bath [effective_bath] – the current effective_bath instance

Options:

axis [character(len=*)] – string indicating the desired axis, 'm' for Matsubara (default), 'r' for Real-axis

interface  ed_bath_functions/f0and_bath_function(x, dmft_bath_[, axis])

Evaluates the anomalous non-interacting Green’s function \(F_0(x)\).

Output:

• f0and : complex rank-5 array with dimension [ nspin , nspin , norb , norb , size(x) ]

Parameters:

• x (•) [complex, in] – complex array for the frequency

• dmft_bath [effective_bath] – the current effective_bath instance

Options:

axis [character(len=*)] – string indicating the desired axis, 'm' for Matsubara (default), 'r' for Real-axis

interface  ed_bath_functions/invg0_bath_function(x, dmft_bath_[, axis])

Evaluates the inverse of the normal non-interacting Green’s function \(G^{-1}_0(x)\).

Output:

• g0and : complex rank-5 array with dimension [ nspin , nspin , norb , norb , size(x) ]

Parameters:

• x (•) [complex, in] – complex array for the frequency

• dmft_bath [effective_bath] – the current effective_bath instance

Options:

axis [character(len=*)] – string indicating the desired axis, 'm' for Matsubara (default), 'r' for Real-axis

interface  ed_bath_functions/invf0_bath_function(x, dmft_bath_[, axis])

Evaluates the inverse of the anomalous non-interacting Green’s function \(F^{-1}_0(x)\).

Output:

• f0and : complex rank-5 array with dimension [ nspin , nspin , norb , norb , size(x) ]

Parameters:

• x (•) [complex, in] – complex array for the frequency

• dmft_bath [effective_bath] – the current effective_bath instance

Options:

axis [character(len=*)] – string indicating the desired axis, 'm' for Matsubara (default), 'r' for Real-axis