Multi-Triplon Excitations of Hubbard Ladders with Site-Dependent Potentials

We study low-lying spin-singlet excitations of two-leg Hubbard ladders with site-dependent potentials. Using general formulas of the charge disproportionation induced by the site-dependent potentials, we derive the contributions of spin degrees of freedom to the spectral functions such as the dynamical charge structure factor \(N(\boldsymbol{k},\omega )\) and the optical conductivity σ_γ(ω) along the γ (\( = x,y\))-direction of the two-leg ladders. Numerical results obtained by the Lanczos diagonalization method have clarified that the multi-triplon singlet states, including two- and three-triplon excitations, can be detected by observing these quantities. Furthermore, we have found that ladders with random potentials also have non-negligible contributions of these excitations to σ_x(ω).