Electronically strongly correlated chains and rings can be investigated very accurately, using both analytical and numerical methods. Examples of such numerical methods are exact diagonalization (ED) techniques and the density matrix renormalization group (DMRG).
In the first paper, appended below, we investigate the phase diagram of the two-channel Kondo lattice model, both at quarter and also at lower filling, with the use of the DMRG and a strong coupling perturbation theory. Of particular interest are, first, the existence of a quantum critical point exactly at quarter filling and, secondly, below quarter filling, the existence of a phase transition as a function of the coupling strength.
In the second paper we describe quantum rings with the use of an extended Hubbard model in a magnetic field, so that the ring contains an Aharonov-Bohm flux. This model is then being solved numerically with the ED technique. It describes, e.g., the magnetic properties of conjugated hydrocarbons like benzene. As a result one finds the possible occurrence (under certain conditions) of a permanent magnetic orbital moment in such quantum rings.
Phase diagram of the two-channel Kondo lattice model in one dimension
T. Schauerte, D. L. Cox, R. M. Noack, P. G. J. van Dongen, and C. D. Batista
Phys. Rev. Lett. 94, 147201 (2005)
Cyclic Hydrocarbons: Nanoscopic (π-)SQUIDs?
M. Himmerich, R. M. Noack, and P. G. J. van Dongen
EPJB, 51, Nr. 1, p.5-15 (2006)