Numerical Study on the t-t′—J-J′ Model

Yung‐Chung Chen, Hanks Chien

Elbio R. Dagotto

Recent numerical work on strongly correlated electronic models using the Lanczos approach is reviewed. In particular, static and dynamical properties of the Hubbard and t–J models are presented attempting to make a connection with experiments. We conclude that numerical methods like the Lanczos technique are providing useful information in the study of these models.

Y. T. Wang, H. Q. Lin, James E. Gubernatis

Relative to single-band models, multiband models of strongly interacting electron systems are of growing interest because of their wider range of novel phenomena and their closer match to the electronic structure of real materials. In this brief review we discuss the physics of three multiband models (the three-band Hubbard, the periodic Anderson, and the Falicov-Kimball models) that was obtained by numerical simulations at zero temperature. We first give heuristic descriptions of the three principal numerical methods (the Lanczos, the density matrix renormalization group, and the constrained-path Monte Carlo methods). We then present generalized versions of the models and discuss the measurables most often associated with them. Finally, we summarize the results of their ground state numerical studies. While each model was developed to study specific phenomena, unexpected phenomena, usually of a subtle quantum mechanical nature, are often exhibited. Just as often, the predictions of the numerical simulations differ from those of mean-field theories.

C. Lavalle, Michael Brunner, Fakher F. Assaad +1 more

Antoni Wójcik, R. Parzyński

Our recent approximate analytical results on the evolution of the initial state and the excitation from this state of a band of high Rydberg states by an optical pulse [Phys. Rev. A 55, 2144 (1997)] are compared with more exact numerical results. The difference between the two approaches is that the approximations of representative atom-field couplings and equidistant spacing of high Rydberg states, applied in the analytical model, are removed in the numerical model. We find that the approximate analytical model is not able to reproduce all the results of the more exact numerical model, if the laser pulse is very short (i.e., much shorter that the Kepler period of the resonantly excited high Rydberg state) or very intense (i.e., when the Rabi period for the resonant transition is substantially shorter than the above Kepler period). This mainly concerns the redistribution of the population over different Rydberg states. The analytical model predicts a symmetric distribution centered around the resonantly excited Rydberg state, irrespective of the pulse duration and intensity, while the numerical model allows an asymmetric distribution with its maximum shifted towards lower Rydberg states. Despite the above-stated difference, the analytical model is able to give preliminary results for the total population of all the excited Rydberg states and the evolution of the initial state, imitating at least qualitatively the results of the numerical model in certain time and intensity scales.

Achille Hui