Real-Time Quantum Dynamics of Interacting Electrons: Self-Organized Nanoscale Structure in a Spin-Electron Coupled System

We investigate the quantum evolution of the excited electronic states combined with the classical dynamics of the order parameter field in a spin-electron coupled system. It is found that the nanoscale spatial structure of the spins evolves spontaneously accompanied by the localization of the electronic wave functions, and the nonadiabatic quantum transitions through a resonant mutual precession analogous to the electron spin resonance (ESR) process.

Figure 1

Time evolution of the double-exchange model (see text). (a) The lower panel shows the time ($T$) dependence of the energy level structure. In the upper panel, the number of electrons in the upper energy band (solid line), in the highest two energy states (broken line), and in the lowest energy states of the upper energy band (dotted line) are shown. Configuration of local spins at $T=28$, 80, 224, and 288 are presented in (b), (c), (d), and (e), respectively. Dot indicates the head of local spin. The local spins marked by ellipses in (d) and (e) are strongly deviated from the ground state. Figures (f), (g), (h) , and (i) show the distribution of excitation energy density measured from the ground state at $T=28$, 80, 224, and 288, respectively. A spline interpolation is used for the contour maps.

Figure 2

Relaxation driven by rapid oscillation. (a) The $y$ component of the local spin which shows the largest deviation from the AFM ground state configuration in stage (I). The inset is the trajectory of the local spin on the $S_x\mathrm{\text{−}}{S}_y$ plane. (b) The electron occupation number at the highest energy states. (c) The same with (a) but in stage (II). (d) The electron occupation number at the lowest energy state (in-gap state) in the upper energy band. (e) The Fourier spectral weight of (a). (f) The same with (e) but $T=132$. (g) The Fourier spectral weight of (c). (h) The same with (f) but $T=600$.

Figure 3

Time evolution of the double-exchange model. The parameter set, $t=1$, $S{J}_H=2$, $S\alpha =0.01$, $S=1$, $\Delta T=0.008$, is used. (a) The same with Fig. 1a. (b) Structure of local spins at $T=2000$. Distribution of energy density at (d) $T=2000$, (e) $T=2100$, and (f) $T=2200$.