  We derive a general linear-response many-body theory capable of computing
excitation spectra of trapped interacting bosonic systems, e.g., depleted and
fragmented Bose-Einstein condensates (BECs). To obtain the linear-response
equations we linearize the multiconfigurational time-dependent Hartree for
bosons (MCTDHB) method, which provides a self-consistent description of
many-boson systems in terms of orbitals and a state vector (configurations),
and is in principle numerically-exact. The derived linear-response many-body
theory, which we term LR-MCTDHB, is applicable to systems with interaction
potentials of general form. From the numerical implementation of the LR-MCTDHB
equations and solution of the underlying eigenvalue problem, we obtain
excitations beyond available theories of excitation spectra, such as the
Bogoliubov-de Gennes (BdG) equations. The derived theory is first applied to
study BECs in a one-dimensional harmonic potential. The LR-MCTDHB method
contains the BdG excitations and, also, predicts a plethora of additional
many-body excitations which are out of the realm of standard linear response.
In particular, our theory describes the exact energy of the higher harmonic of
the first (dipole) excitation not contained in the BdG theory. We next study a
BEC in a very shallow one-dimensional double-well potential. We find with
LR-MCTDHB low-lying excitations which are not accounted for by BdG, even though
the BEC has only little fragmentation and, hence, the BdG theory is expected to
be valid. The convergence of the LR-MCTDHB theory is assessed by systematically
comparing the excitation spectra computed at several different levels of
theory.
