Solver options and accessors

The solver consists of one main object with a constructor and a solve() method, and accessors. The options of the constructor and solve() method are used to give more information as to the desired run, such as number of Matsubara frequencies, number of Monte-Carlo cycles, or which observables have to be measured. The accessors are members of the solver class which are used both to set the inputs of the solver (like the non-interacting Green’s function G0_iw or the dynamical interactions D0_iw) and to read out the observables at the end of the computation (such as G_tau, G_iw or nn_iw).

The options of the constructor are:

Parameter Name	Type	Default	Documentation
beta	double	–	Inverse temperature
gf_struct	gf_struct_t	–	Structure of the GF (names, sizes of blocks)
n_tau	int	10001	Number of time slices for $Delta(\tau)$/$G(\tau)$/$F(\tau)$
n_tau_k	int	10001	Number of time slices for $K(\tau)$
n_tau_jperp	int	10001	Number of time slices for $J_\perp(\tau)$
n_tau_nn	int	101	Number of Legendre coefficients for G(l)
n_w_b_nn	int	32	Number of bosonic Matsub. freqs for $nn(i\omega)$, $\mathcal{D}_0(i\omega)$, $J_\perp$
n_iw	int	1025	Number of fermionic Matsubara frequencies for $G_0(i\omega)$, $G$, $F$, $\Sigma$

The options of the solve() method and the solver accessors are summarized below. They are identical in the C++ and Python interface.

C++ interface

Python interface

class triqs_ctseg.SolverCore

Main solver class

Worker which runs the quantum Monte-Carlo simulation.

D0_iw: Density-density retarded interactions $mathcal{D}^{sigmasigma’}_{0,ab}(iOmega)$

Delta_tau: Hybridization function $Delta^sigma_{ab}(tau)$

F_2w: 3-point improved estimator (see [[measure_g2w]])

F_3w: 4-point improved estimator (see [[measure_g3w]])

F_iw: Improved estimator function $F^sigma_{ab}(iomega)$ (see [[measure_gw]])

F_l: Improved estimator function in Legendre basis $G^sigma_{ab}(n)$ (see [[measure_gl]])

F_tau: Improved estimator function $F^sigma_{ab}(tau)$ (see [[measure_gt]])

G0_iw: Weiss field $mathcal{G}^{sigma}_{0,ab}(iomega)$

G_2w: 3-point correlation function $chi^{sigmasigma’}_{abc}(iomega,iOmega)$ (see [[measure_g2w]])

G_3w: 4-point correlation function $chi^{sigmasigma’}_{abcd}(iomega,iomega’,iOmega)$ (see [[measure_g3w]])

G_iw: Impurity Green’s function $G^sigma_{ab}(iomega)$ (see [[measure_gw]])

G_l: Impurity Green’s function in Legendre basis $G^sigma_{ab}(n)$ (see [[measure_gl]])

G_tau: Impurity Green’s function $G^sigma_{ab}(tau)$ (see [[measure_gt]])

Jperp_iw: Dynamical spin-spin interaction, perpendicual components: $mathcal{J}_perp(iOmega)$

Jperp_tau: Dynamical spin-spin interactions $mathcal{J}_perp(tau)$

K_tau: Dynamical kernel $K(tau)$

Kperpprime_tau: Derivative of the dynamical kernel $partial_tau K_perp(tau)$

Kprime_tau: Derivative of the dynamical kernel $partial_tau K(tau)$

Sigma_iw: Impurity self-energy $Sigma^sigma_{ab}(iomega)$ (see [[measure_gw]])

average_sign: Monte Carlo sign

chipm_tau: Spin spin correlation function $langle s_+(tau) s_-(0)rangle$ (see [[measure_chipmt]])

histogram: histogram of hybridization perturbation order (see [[measure_hist]])

histogram_composite: histogram of $mathcal{J}_perp$ perturbation order (see [[measure_hist_composite]])

nn: density-density static correlation $langle n^sigma_a n^{sigma’}_b rangle$ (see [[measure_nn]])

nn_iw: Density-density correlation function $mathrm{FT}left[langle n^sigma_{a}(tau) n^{sigma’}_{b}(0)rangleright]$ (see [[measure_nnw]])

nn_tau: Density-density correlation function $langle n^sigma_{a}(tau) n^{sigma’}_{b}(0)rangle$ (see [[measure_nnt]])

sanity_check(): Signature : (triqs_ctseg::solve_params_t p, int n_w, int n_w_b) -> None

solve()

solve method: starts the Metropolis algorithm

Steps:

extract $\Delta^\sigma_{ab}(\tau)$ and $\mu^\sigma_a$ from

$\mathcal{G}^\sigma_{ab}(i\omega)$

if $\mathcal{D}^{\sigma\sigma'}_{0,ab}(i\Omega)\neq 0$, extract

$K(^{\sigma\sigma'}_{ab}\tau)$ and $partial_tau K^{sigmasigma’}_{ab}(tau)$ from $\mathcal{D}^{\sigma\sigma'}_{0,ab}(i\Omega)$

if $\mathcal{J}_{\perp,a}(i\Omega)\neq 0$, extract $partial_tau

K_{perp,a}(tau)$ from $\mathcal{J}_{\perp,a}(i\Omega)$ - add the moves and measures according to the parameters supplied by the user

start the Monte-Carlo simulation

finalize the Monte Carlo simulation

state_histogram: histogram of the boundary states of the trace (see [[measure_statehist]])