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Optimal gauge choice for complex conjugation projector in projected coupled cluster

Determine whether adopting the complex conjugation projection operator P_K = 1 + K as a gauge-fixing choice in projected coupled cluster theory (specifically PCCSD) is optimal for fixing the complex-conjugation gauge, and identify if a superior gauge choice exists that improves convergence and uniqueness of the projected coupled cluster amplitudes.

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Background

Projected coupled cluster methods can exhibit gauge invariances—numerical invariances of the algebraic equations that leave observables unchanged—especially when the disentangled cluster operator W is truncated. These gauge modes can make PCCSD results non-unique.

In this work the authors fix the complex-conjugation gauge by choosing the projector P_K = 1 + K, but they explicitly note that it is unresolved whether this is the best choice. Clarifying the optimal gauge could help stabilize computations and standardize implementations of complex conjugation–projected coupled cluster.

References

In this work, we choose the projection operator to be $1+K$ to fix the gauge in complex conjugation, but whether it is the best choice still needs to be determined.

— Combining complex conjugation, time-reversal, and spin symmetry projection of coupled cluster wave functions (2405.06776 - Song et al., 10 May 2024) in Discussion, Section "Discussion and Conclusion"