Electron-hole bound pairs, or excitons, are common excitations in
semiconductors. They can spontaneously form and condense'' into a new insulating ground state -- the so-called excitonic insulator -- when the energy of electron-hole Coulomb attraction exceeds the band gap. In the presence of electron-phonon coupling, a periodic lattice distortion often concomitantly occurs with this exciton condensation. However, similar structural transition can also be induced by electron-phonon coupling itself, therefore hindering the clean identification of bulk excitonic insulators based on reductionistic reasoning (e.g. which instability is the driving force’’ of the phase
transition). Using high-resolution synchrotron x-ray diffraction and
angle-resolved photoemission spectroscopy techniques, we identify key
electron-phonon coupling effects in a leading excitonic insulator candidate
Ta2NiSe5. These include an extensive unidirectional lattice fluctuation and an
electronic pseudogap in the normal state, as well as a negative electronic
compressibility in the charge-doped broken-symmetry state. In combination with
first principles and model calculations, we determine a minimal lattice model
and the corresponding interaction parameters that capture the experimental
observations. More importantly, we show how the Coulomb and electron-phonon
coupling effects can be separated on the level of lattice model, and
demonstrate a general framework beyond the reductionist approach in the
investigation of correlated systems with intertwined orders.

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