Parameter: isort

Definition

Key control flag. It is used to determine whether we should use the orthogonal polynomials trick to improve the accuracy and suppress the numerical noises.

Type

Integer

Default value

1

Component

Only for the GARDENIA, NARCISSUS, LAVENDER, CAMELLIA, and MANJUSHAKA components.

Behavior

There are six possible values for isort parameter so far:

• isort = 1, the standard method is used to measure $G(\tau)$.

• isort = 2, the Legendre orthogonal polynomials trick is used to measure $G(\tau)$.

• isort = 3, the Chebyshev orthogonal polynomials trick is used to measure $G(\tau)$.

• isort = 4, the standard method is used to measure $G(\tau)$ and $F(\tau)$.

• isort = 5, the Legendre orthogonal polynomials trick is used to measure $G(\tau)$ and $F(\tau)$.

• isort = 6, the Chebyshev orthogonal polynomials trick is used to measure $G(\tau)$ and $F(\tau)$.

Here $G(\tau)$ is the imaginary-time Green's function and $F(\tau)$ auxiliary imaginary-time function which can be used to calculate $\Sigma(i\omega_n)$ analytically.

\[\Sigma(i\omega_n) = \frac{F(i\omega_n)}{G(i\omega_n)}\]

If the orthogonal polynomials trick is used, the $G(\tau)$ and $F(\tau)$ are expanded using orthogonal polynomials. And then the expansion coefficients are measured during Monte Carlo sampling procedure. Finally, according the expansion coefficients the $G(\tau)$ and $F(\tau)$ can be calculated analytically.

The expansion series are defined by the chmax, chgrd, lemax, and legrd parameters.

The GARDENIA and NARCISSUS components support all of the six possible values of isort. However, in the LAVENDER, CAMELLIA, and MANJUSHAKA components, isort must be less than or equal to 3. In order words, the improved estimator for self-energy function was not implemented in the LAVENDER, CAMELLIA, and MANJUSHAKA components.

Comment

See chmax, chgrd, lemax, and legrd parameters for more details.