Speaker
Description
We characterize the lowest optically active excitation of a one-dimensional extended Hubbard chain with on-site repulsion $U_0$ and nearest-neighbor repulsion $U_1$. Two complementary natural-orbital diagnostics disentangle the character of the excitation: the one-particle-one-hole (1p1h) weight $W_{1p1h}$, which measures how completely a single particle-hole picture accounts for the transition, and the participation ratio $P_{1p1h}$, which counts the effective number of particle-hole channels contributing to it. A depletion of $W_{1p1h}$ signals beyond-1p1h, strongly correlated physics (2p2h and higher) that a single-excitation description cannot capture, whereas a large $P_{1p1h}$ identifies a collective excitation coherently distributed over many channels while remaining within the 1p1h sector. Mapping both quantities across the $U_0U_1$ plane at half filling, we distinguish regimes of nearly single-particle response, collective-but-1p1h behavior, and genuinely correlated beyond-1p1h excitations, and we resolve how the excitation character changes qualitatively across the $U_0 \simeq 2U_1$ quantum critical point separating the spin-density-wave (SDW) and charge-density-wave (CDW) phases. The natural-orbital framework thus yields a compact, basis-independent map of how competing local and non-local interactions reshape the excitations of a correlated system.
