Migration from sparse-ir/SparseIR.jl version 1 to version 2

Migration from sparse-ir/SparseIR.jl version 1 to version 2#

Version 2 has changed the internal implementation to C++, but most of the interfaces remain unchanged. The following points have changed as exceptions:

The domain of the basis functions \(U(\tau)\)#

This has been extended from \([0, \beta]\) to \([-\beta, \beta]\).

  • The fermionic basis functions are anti-periodic, while the bosonic basis functions are periodic. If you use the logistic kernel (default), the fermionic and bosonic basis functions are identical in \((0, \beta)\), while they have opposite signs in \((-\beta, 0)\). To keep consistency with the previous version, \(U_l(\beta)\) and \(U_l(-\beta)\) evaluate to the values at \(\beta-0\) and \(-\beta+0\), respectively. The value at \(-0\) can be evaluated by \(U_l(-0)\).

The domain of the \(\tau\) sampling points#

The \(\tau\) sampling points are now defined in \([-\beta/2, \beta/2]\) instead of \([0, \beta]\). The distribution of the sampling points is symmetric with respect to \(0\). This change has been introduced for preparing a future introduction of zero-temperature basis functions. You can switch to the previous behavior by setting use_positive_taus=True when initializing a TauSampling object or a FiniteTempBasisSet object. This will affect some diagrammatic calculations, e.g., second order perturbation theory: \(G(\tau)G(\beta-\tau) = - G(\tau)G(-\tau)\). See the following example code:

# Version 1: G(tau) * G(beta-tau)
gtau * gtau[::-1]

# Version 2: G(tau) * G(-tau)
-gtau * gtau[::-1]
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