Parameters

Pre-processor flags

• ADAPTIVE_GRID

  If defined, use optimization routine to find the best scale factor \(A\) of the frequency grid;

  If undefined, just rescale the grid.

  Warning: Can be expensive and unreliable in the presence of numerical artifacts.

• ANALYTIC_TAILS

  0 for false; 1 for true.

  If true, the analytic expression for the bare bubble is used to treat the high-frequency asymptotics during bubble computations in the finite-\(T\) MF.

• BARE_SE_FEEDBACK

  If defined, only bare selfenergy is used. Only makes sense if STATIC_FEEDBACK is defined. Useful for benchmarks with previous Keldysh fRG schemes.

• CONTOUR_BASIS

  0 for false, 1 for true.

  If true, no Keldysh rotation is performed and the contour basis is used instead to parametrize the Keldysh components of all correlation functions. Useful for comparisons with results that use this convention. Not as well tested and thus not recommended for production runs.

• DEBUG_SYMMETRIES

  0 for false; 1 for true.

  Performs computations without use of symmetries if true. Useful for debugging purposes.

• GRID

  Controls which frequency grid is to be used.

  0 for the non-linear grid, 1 for the hybrid grid, 2 for the polar grid.

  Recommendation: 0.

• KATANIN

  If defined, the Katanin extension is used during fRG computations.

• KELDYSH_FORMALISM

  Determines whether calculations shall be done in the Keldysh or Matsubara formalism.

  0 for Matsubara formalism (MF); 1 for Keldysh formalism (KF).

• MAX_DIAG_CLASS

  Defines the diagrammatic classes that will be considered.

  1 for only \(K_1\), 2 for \(K_1\) and \(K_2\) and 3 for the full dependencies.

  Useful for debugging purposes and for computations in second-order perturbation theory, or if STATIC_FEEDBACK is defined, when only \(K_1\) is required.

• NDEBUG

  If defined, assert functions are switched off. Recommended setting for production runs.

• PARTICLE_HOLE_SYMM

  0 for false; 1 for true.

  If true, particle-hole symmetry is assumed.

• PT2_FLOW

  If defined, only compute the flow equations up to \(O(U^2)\). Only makes sense for pure \(K_1\) calculations. Useful as a consistency check together with independent PT2 calculations.

• REG

  Specifies the mfRG flow regulator to be used.

  \(2\): \(\Delta\)-flow, \(3\): \(\omega\)-flow, \(4\): \(U\)-flow, \(5\): \(T\)-flow.

• REPARAMETRIZE_FLOWGRID

  If defined, the flow parameter is reparametrized. Only recommended for the \(\Delta\)-flow.

• SBE_DECOMPOSITION

  0 for false; 1 for true.

  If true, the SBE decomposition is used to parametrize the vertex and the flow equations. Only implemented in the MF!

• SELF_ENERGY_FLOW_CORRECTIONS

  0 for false; 1 for true.

  If true, corrections to the flow equations for the vertex from the self-energy, starting at \(\ell=3\), are included.

• STATIC_FEEDBACK

  If defined, use static \(K_1\) inter-channel feedback. Only makes sense for pure \(K_1\) calculations.

• SWITCH_SUM_N_INTEGRAL

  0 for false; 1 for true.

  If true, the sum over internal Keldysh indices is done before the frequency integration.

  Recommended setting: 1.

• USE_ANDERSON_ACCELERATION

  0 for false; 1 for true.

  If true, Anderson acceleration is used to converge parquet iterations and self-energy iterations in mfRG faster.

• USE_MPI

  If defined, MPI is used for parallelization across multiple nodes.

• USE_SBEb_MFRG_EQS

  Determines which version of the SBE approximation shall be used.

  0 for SBEa, 1 for SBEb.

  Warning: Only implemented in the MF!

• VECTORIZED_INTEGRATION

  0 for false; 1 for true.

  If true, integrals are performed with vector-valued integrands. For Keldysh, vectorization over Keldysh indices. For Matsubara at finite \(T\), vectorization over the Matsubara sum.

• ZERO_TEMP

  0 for false; 1 for true.

  If true, temperature \(T = 0\) is assumed.

Global parameters

• converged_tol

  Tolerance for loop convergence in mfRG.

• COUNT

  Used to set the number of frequency points in the MF. For details, see the definitions in the file frequency_parameters.hpp.

• Delta_factor_K1

  Scale factor for the frequency grid of the \(K_1\) vertex class.

• Delta_factor_SE

  Scale factor for the frequency grid of the self-energy.

• Delta_factor_K2_w

  Scale factor for the frequency grid of the bosonic frequency of the \(K_2\) and \(K_{2'}\) vertex classes.

• Delta_factor_K2_v

  Scale factor for the frequency grid of the fermionic frequency of the \(K_2\) and \(K_{2'}\) vertex classes.

• Delta_factor_K3_w

  Scale factor for the frequency grid of the bosonic frequency of the \(K_3\) vertex class.

• Delta_factor_K3_v

  Scale factor for the frequency grid of the fermionic frequencies of the \(K_3\) vertex class.

• EQUILIBRIUM

  If true, use equilibrium FDTs for propagators.

• glb_mu

  Chemical potential – w.l.o.g. ALWAYS set to 0.0 for the AM!

• integrator_tol

  Integrator tolerance.

• inter_tol

  Tolerance for closeness to grid points when interpolating.

• INTERPOLATION

  Interpolation method to me used.

  linear: linear interpolation on the frequency grid.

  linear_on_aux: linear interpolation on the grid for the auxiliary frequency \(\Omega\).

  cubic: Interpolation with cubic splines (warning: expensive!).

• Lambda_ini

  Initial value of the regulator \(\Lambda\) for an mfRG flow.

• Lambda_fin

  Final value of the regulator \(\Lambda\) for an mfRG flow.

• Lambda_scale

  Scale of the log substitution, relevant in the hybridization flow.

• dLambda_initial

  Initial step size for ODE solvers with adaptive step size control.

• nBOS

  Number of bosonic frequency points for the \(K_1\) vertex class.

• nFER

  Number of fermionic frequency points for the self-energy.

• nBOS2

  Number of bosonic frequency points for the \(K_2\) and \(K_{2'}\) vertex classes.

• nFER2

  Number of fermionic frequency points for the \(K_2\) and \(K_{2'}\) vertex classes.

• nBOS3

  Number of bosonic frequency points for the \(K_3\) vertex class.

• nFER3

  Number of fermionic frequency points for the \(K_3\) vertex class.

• U_NRG

  Vector with the values of \(U\) in units of \(\Delta\) that an mfRG flow should cover. Serve as checkpoints for the flow. Useful for benchmarking purposes if data from other methods at precise parameter points are available.

• VERBOSE

  If true, detailed information about all computational steps is written into the log file.

  Recommended setting for production runs: false

• nmax_Selfenergy_iterations

  Maximal number of self-energy iterations to be done during an mfRG flow for \(\ell \geq 3\).

  Default value: 10

• tol_selfenergy_correction_abs

  Absolute tolerance for self-energy iterations in mfRG.

  Default value: \(10^{-9}\)

• tol_selfenergy_correction_rel

  Relative tolerance for self-energy iterations in mfRG.

  Default value: \(10^{-5}\)