Developing New Methods for Electronic Structure of Atoms Molecules and Clusters.

  In the renormalization group (RG) method, developed by Wilson, states above a certain cutoff are removed from the theory, and the Hamiltonian is modified to produce the same results for all physical measurements that involve the remaining modes. This procedure is called "integrating out the high-energy states", a terminology based on the path-integral representation of statistical mechanics. The parameters that specify the different interaction strengths in the Hamiltonian change ("flow") as the cutoff energy is reduced.
  The RG has been applied with enormous success to classical statistical mechanical systems undergoing second-order phase transitions. It has only recently become possible, due to a combination of theoretical and computational advances, to apply the RG method to systems containing many electrons.
  In collaboration with Prof. Ganpathy Murthy of Boston University, we have developed the RG approach to treat electronic structure problems. In this approach we start by separating the Hamiltonian into a ``free-particle'' part H0 and a part that involves residual electronic interactions V. For instance, H0 might be any type of mean field Hamiltonian, and we used the Hartree-Fock Hamiltonian. Initial results show that the method is very accurate for estimating excitations for atoms. The method is general and has potential applicability for molecular systems.
 

 
 

Renormalization group approach for electronic excitations in atoms", G. Murthy and S. Kais, Chem. Phys. Letters, 290, 199-204 (1998).

 

Real-space renormalization group study of the Hubbard model on a non-bipartite lattice", J. X. Wang, Sabre Kais and R.D. Levine, , International Journal of Molecular Sciences 3,4-16 (2002).

 

Combined effects of disorders and electron-electron interactions upon metal-insulator transition in 2D non-bipartite lattice", J. X. Wang and S. Kais, , Physics Letters A 316, 265-270 (2003).

 

Metal-insulator transition in Hubbard model on a triangular lattice with disorders: Renormalization group approach", J. X. Wang and Sabre Kais, , Int. J. Quantum Chem. 93, 360-374 (2003).