Optical conductivity of strongly correlated electron systems

We present an exact-diagonalization study of the frequency- and wave-vector-dependent conductivity sigma(q,omega) in small clusters in the two-dimensional t-J model. Unlike the related dynamical density correlation function, sigma(q=0,omega) in the underdoped regime has the exchange constant J as its characteristic energy scale and is dominated by a resonancelike excitation with frequency similar to 1.7 J. We interpret this as transition to a p-like excited state of a spin-bag-type quasiparticle (or, alternatively, a tightly bound spinon-holon pair) and show that a simple calculation based on the string picture explains the numerical results semiquantitatively. For doping levels greater than or equal to 25% t remains the only energy scale of sigma(q=0,omega).