Numerical studies on critical states in two dimensions and quantum phase transitions of correlated electrons in low dimensions

Yasuhiro Hatsugai

Subir Sachdev A

N. H. March

Many-body effects in jellium, M.P. Tosi solids with weak and strong electron correlations, P. Fulde ground and low-lying excited states of interacting electron systems - a survey and some critical analyses, B. Farid failure of Fermi liquid theory in two and three dimensions, G. Baskaran quantum phase transitions in electronic systems, T.R. Kirkpatrick and D. Belitz density matrices, density functional theory and quantum Monte Carlo calculations, N.H. March.

Xin Wan

Samuel Kellar

The study of the Hubbard model in three dimensions contains a variety of phases dependent upon the chosen parameters. This thesis shows that there is the indication of a zero temperature phase transition at a finite doping. The Hubbard model has been used to identify a similar quantum critical point in two dimensions. The presented results continue these investigations. The system demonstrates a strange metal phase at finite temperature which cannot be described in term of the conventional Fermi liquid. While there have been extensive studies over the past three decades for such materials in two dimensions, there are few numerical studies in three dimensions. This study strives to identify the existence of the strange metal beyond two dimensions. In this work we present numerical results based on the dynamical cluster approximation to demonstrate the existence of a strange metal phase in three dimensions.

Subir Sachdev A

Small changes in an external parameter can often lead to dramatic qualitative changes in the lowest energy quantum mechanical ground state of a correlated electron system. In anisotropic crystals, such as the high-temperature superconductors where electron motion occurs primarily on a two-dimensional square lattice, the quantum critical point between two such lowest energy states has nontrivial emergent excitations that control the physics over a significant portion of the phase diagram. Nonzero temperature dynamic properties near quantum critical points are described, using simple theoretical models. Possible quantum phases and transitions in the two-dimensional electron gas on a square lattice are discussed.