SingleExcitationBra file

The operators \(B=c_{i\sigma_1}(c_{i\sigma_1}^{\dagger})\) to generate the bra single excited state \(B|\phi\rangle\), used to compute the off-diagonal dynamical Green’s function

(4.18)\[G_{BA}(z) = \langle \phi | B^{\dagger} \frac{1}{z-H} A | \phi \rangle ,\]

where the ket operator \(A\) is given in SingleExcitation. If this file is omitted, the ordinary diagonal Green’s function (\(B=A\)) is calculated.

The file format and parameters are the same as the SingleExcitation file; only the keyword for the number of operators is NSingleExcitationBra. An example:

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NSingleExcitationBra    1
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====== Single Excitation Bra ===
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    0     0     0    1.0    0.0

Use rules

  • Headers cannot be omitted; the format and parameters are identical to the SingleExcitation file.

  • The operator written here is \(B\), not \(B^{\dagger}\). The computed quantity is \(\langle\phi|B^{\dagger}(z-H)^{-1}A|\phi\rangle\).

  • The off-diagonal Green’s function is available only with the shifted BiCG method (method="CG") and CalcSpec="Normal" (restart/save spectrum modes are not supported together with a bra operator).

  • The ket (SingleExcitation) and bra operators must map \(|\phi\rangle\) into the same excited Hilbert sector (the same change of particle number and \(S_z\)). All operators within one file must also share the same sector change. Otherwise the program is terminated.

  • Supported model: Hubbard. (A single excitation is not defined for spin systems, and other models are not yet supported for the off-diagonal Green’s function; the program is terminated for them.)