dyson_mat() [1/2]

template<typename T >

void cntr::dyson_mat	(	herm_matrix< T > &	G,
		T	mu,
		function< T > &	H,
		herm_matrix< T > &	Sigma,
		T	beta,
		const int	SolveOrder,
		const int	method,
		const bool	force_hermitian
	)

Dyson solver (integral-differential form) for a Green's function \(G\)

Purpose

One solves the Dyson equation of the following form: \( [ id/dt + \mu - H(t) ] G(t,t^\prime) - [\Sigma*G](t,t^\prime) = \delta(t,t^\prime)\) for a hermitian matrix \(G(t, t^\prime)\) on a Matsubara axis. There are 3 possible methods for solution: Fourier, steep, and fixpoint.

Parameters

&G	[herm_matrix<T>] solution
mu	[T] chemical potential
&Sigma	[herm_matrix<T>] self-energy
&H	[function<T>] time-dependent function
SolveOrder	[int] integrator order
beta	[double] inverse temperature
method	[int] Solution method on the Matsubara axis with 0: Fourier, 1: steep, 2: fixpoint
force_hermitian	[bool] force hermitian solution, if 'true'

Definition at line 1393 of file cntr_dyson_impl.hpp.

References force_matsubara_hermitian().

                                                                                     {
  assert(method <= 2 && "UNKNOWN CNTR_MAT_METHOD");
  assert(SolveOrder <= MAX_SOLVE_ORDER);

  const int fourier_order = 3;
  const double tol=1.0e-12;
  int maxiter;

  switch(method){
  case 0:
    dyson_mat_fourier(G, Sigma, mu, H, beta, fourier_order);
    break;
  case 1:
    maxiter = 40;
    dyson_mat_steep(G, Sigma, mu, H, integration::I<T>(SolveOrder), beta, maxiter, tol);
    break;
  case 2:
    maxiter=6;
    dyson_mat_fixpoint(G, Sigma, mu, H, integration::I<T>(SolveOrder), beta, maxiter);
    break;
  }
  if(force_hermitian){
    force_matsubara_hermitian(G);
  }
}

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