Path-integral theory for light-absorption spectra of many-electron systems in insulating states due to strong long-range Coulomb repulsion: Nonlinear coupling between charge and spin excitations

Abstract

We develop a path-integral formulation which is free from Grassmann algebras to calculate absorption spectra of strongly correlated electron systems. The Coulomb repulsions, including not only the short-range part but also a long-range part, are reduced into a time-dependent one-body Hamiltonian with only two kinds of Ising spin variables per site. The sums over these spin configurations are performed according to the quantum Monte Carlo techniques. By this method we disclose the electron correlation effects on absorption spectra. The method is applied to the one-dimensional half-filled electron systems, where the ground state is an insulating state due to the strong long-range Coulomb repulsion and contains large quantum fluctuations by low-energy collective spin excitations. The absorption spectrum shows an infrared divergencelike structure, which seems to arise from the simultaneous excitation of the charge-transfer exciton and collective spin excitations. The spectrum also contains new peaks on the high energy side which correspond to the multiple excitation of electron-hole pairs. Such a multiple excitation is caused by the electron correlation effect, through which the photogenerated electron and hole can excite other electron-hole pairs. Our result clearly shows that charge and spin of the electron are inseparable in a many-body system in an insulating state caused by the strong long-range Coulomb repulsion.