Disordered electronic system as a model of interacting matrices

M. Grilli, Sandro Sorella

Masanori Yamanaka, Mahito Kohmoto

We investigate the effects of randomness in a strongly correlated electron model in one dimension at half-filling. The ground state correlation functions are exactly written by products of 3\ifmmode\times\else\texttimes\fi{}3 transfer matrices and are evaluated numerically. The correlation lengths depend on randomness when the interaction is effectively weak. On the contrary, they are completely insensitive to randomness when the interaction is effectively strong.

Niaz Ali Khan

L P Yang, Y J Wang, Wenhu Xu +2 more

We develop a novel quantum transfer matrix method to study thermodynamic properties of one-dimensional (1D) disordered electronic systems. It is shown that the partition function can be expressed as a product of 2 × 2 local transfer matrices. We demonstrate this method by applying it to the 1D disordered Anderson model. Thermodynamic quantities of this model are calculated and discussed.

Georg Schwiete, K. B. Efetov

Considering disordered electron systems we suggest a scheme that allows us to include an electron-electron interaction into a supermatrix $\ensuremath{\sigma}$-model. The method is based on replacing the initial model of interacting electrons by a fully supersymmetric model. Although this replacement is not exact, it is a good approximation for a weak short range interaction and arbitrary disorder. The replacement makes the averaging over disorder and further manipulations straightforward and we come to a supermatrix $\ensuremath{\sigma}$-model containing an interaction term. The structure of the model is rather similar to the replica one, although the interaction term has a different form. We study the model making perturbation theory and renormalization group calculations. We check the renormalizability of the model in the first loop approximation and in the first order in the interaction. In this limit we reproduce the renormalization group equations known from earlier works. We hope that the new supermatrix $\ensuremath{\sigma}$-model may become a new tool for nonperturbative calculations for disordered systems with interaction.

Sonika Johri