Tensor hypercontraction

[obackhouse]

• Adds tensor hypercontraction
• Fixes some bugs (I think) in density fitting

I added a separate entry to TensorFactorizationQNS and made it now use the 5th and 6th rightmost bits.

[Copilot]

Pull request overview

This PR adds tensor hypercontraction (THC) functionality to decompose 4-center 2-electron integral tensors into products of five rank-2 tensors, and fixes bugs in the existing density fitting implementation related to auxiliary index construction.

Key Changes:

• Introduces THC decomposition via new tensor_hypercontract function that converts 4-center tensors into products of collocation and Coulomb matrices
• Fixes missing aux_space parameter in density fitting Index construction
• Updates TensorFactorizationQNS enum to include THC tag using bit 6

Reviewed changes

Copilot reviewed 6 out of 6 changed files in this pull request and generated 4 comments.

Show a summary per file

File	Description
SeQuant/domain/mbpt/rules/thc.hpp	New header declaring tensor_hypercontract function for THC decomposition
SeQuant/domain/mbpt/rules/thc.cpp	New implementation of THC decomposition with support for symmetric and antisymmetric tensors
SeQuant/domain/mbpt/rules/df.cpp	Bug fixes for auxiliary index construction in density fitting
SeQuant/domain/mbpt/space_qns.hpp	Adds THC quantum number tag and updates mask to include bits 5 and 6
tests/unit/test_mbpt.cpp	Comprehensive tests for THC decomposition covering symmetric and antisymmetric cases
CMakeLists.txt	Registers new THC source and header files in build system

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[ajay-mk]

Please rebase with the latest changes from master.

[evaleev]

@obackhouse It will be nice to extend to the many-particle case (e.g., for rank-reduced CC), but that would require some thought about how to dealing with antisymmetry ... good for now. thanks.