Main Features
Now the ACFlow toolkit supports six analytic continuation methods as introduced before. It includes seven different analytic continuation solvers, namely
MaxEntBarRatNevanACStochACStochSKStochOMStochPX
Just as their names suggested, the MaxEnt solver implements the maximum entropy method. The BarRat solver implements the barycentric rational function approximation. The NevanAC solver implements the Nevanlinna analytical continuation. The StochAC and StochSK solvers implement the K. S. D. Beach's algorithm and A. W. Sandvik's algorithm of the stochastic analytic continuation, respectively. The StochOM solver implements the stochastic optimization method. The StochPX solver implements the stochastic pole expansion method. The ACFlow toolkit also provides a convenient library, which can be used to prepare and carry out analytic continuation calculations flexibly. The major features of the present ACFlow toolkit (v2.0.0 and above) are summarized in Table 1.
| Features | MaxEnt | BarRat | NevanAC | StochAC | StochSK | StochOM | StochPX |
|---|---|---|---|---|---|---|---|
| Matrix-valued Green's function | Y | Y | N | N | N | N | Y |
| Fragment input grid | Y | N | Y | Y | Y | Y | Y |
| Imaginary time grid | Y | N | N | Y | Y | Y | N |
| Matsubara frequency grid | Y | Y | Y | Y | Y | Y | Y |
| Linear mesh | Y | Y | Y | Y | Y | Y | Y |
| Nonlinear mesh | Y | Y | Y | Y | Y | Y | Y |
| Fermionic kernel | Y | Y | Y | Y | Y | Y | Y |
| Bosonic kernel | Y | Y | N | Y | Y | Y | Y |
| Self-defined model function | Y | N | N | N | N | N | N |
| Constrained analytic continuation | N | N | N | Y | Y | Y | Y |
| Self-adaptive parameterization | N | N | N | Y | N | N | Y |
| Regeneration of input data | Y | Y | Y | Y | Y | Y | Y |
| Kramers-Kronig transformation | Y | Y | Y | Y | Y | Y | Y |
| Parallel computing | N | N | N | Y | Y | Y | Y |
| Parallel tempering | N | N | N | Y | N | N | N |
| Interactive mode | Y | Y | Y | Y | Y | Y | Y |
| Script mode | Y | Y | Y | Y | Y | Y | Y |
| Standard mode | Y | Y | Y | Y | Y | Y | Y |
Table 1 | Major features of the ACFlow toolkit. MaxEnt, BarRat, NevanAC, StochAC, StochSK, StochOM, and StochPX are the seven analytic continuation solvers as implemented in this toolkit.
In Table 1, Y means yes while N means no. Interactive mode, Script mode, and Standard model are three running modes supported by the ACFlow toolkit. We will introduce them later. The MaxEnt solver supports the historic, classic, bryan, and chi2kink algorithms to determine the $\alpha$ parameter. The StochAC solver is only compatible with a flat model function, while the BarRat, NevanAC, StochSK, StochOM, and StochPX solvers don't rely on any default model functions.
Note that analytic continuation problem is a hotspot in computational physics and many-body physics all the time. Many efforts have been devoted to solve it in recent years. Noticeable achievements include maximum quantum entropy method, Nevanlinna analytical continuation, blocked-mode sampling and grid point sampling in stochastic analytic continuation, constrained stochastic analytic continuation, machine learning assisted analytic continuation, and so on. We would like to incorporate these new progresses into the ACFlow toolkit in the near future. BTW, contributions from the other users are always welcomed.