Landau Theory of the Mott Transition in the Fully Frustrated Hubbard Model in Infinite Dimensions

We discuss the solution of the Mott transition problem in a fully frustrated lattice with a semicircular density of states in the limit of infinite dimensions from the point of view of a Landau free energy functional. This approach provides a simple relation between the free energy of the lattice model and that of its local description in terms of an impurity model. The character of the Mott transition in infinite dimensions, (as reviewed by Georges Kotliar Krauth and Rozenberg, RMP 68, 1996, 13) follows simply from the form of the free energy functional and the physics of quantum impurity models. At zero temperature, below a critical value of the interaction U, a Mott insulator with a finite gap in the one particle spectrum, becomes unstable to the formation of a narrow band near the Fermi energy. Using the insights provided by the Landau approach we answer questions raised about the dynamical mean field solution of the Mott transition problem, and comment on its applicability to three dimensional transition metal oxides

Local Self-Energy Approach For Electronic Structure Calculations

Using a novel self-consistent implementation of Hedin's GW perturbation theory we calculate space and energy dependent self-energy for a number of materials. We find it to be local in real space and rapidly convergent on second-- to third-- nearest neighbors. Corrections beyond GW are evaluated and shown to be completely localized within a single unit cell. This can be viewed as a fully self consistent implementation of the dynamical mean field theory for electronic structure calculations of real solids using a perturbative impurity solver.Comment: 5 pages, 2 figure

Complex Landau Ginzburg Theory of the Hidden Order in URu_2Si_2

We develop a Landau Ginzburg theory of the hidden order phase and the local moment antiferromagnetic phase of URu_2Si_2. We unify the two broken symmetries in a common complex order parameter and derive many experimentally relevant consequences such as the topology of the phase diagram in magnetic field and pressure. The theory accounts for the appearance of a moment under application of stress and the thermal expansion anomaly across the phase transitions. It identifies the low energy mode which is seen in the hidden order phase near the conmensurate wavector (0,0, 1) as the pseudo-Goldstone mode of the approximate U(1) symmetry.Comment: 4 pages, 3 figure

Band Degeneracy and Mott Transition: Dynamical Mean Field Study

We investigate the Mott transition in infinite dimensions in the orbitally degenerate Hubbard model. We find that the qualitative features of the Mott transition found in the one band model are also present in the orbitally degenerate case. Surprisingly, the quantitative aspects of the transition around density one are not very sensitive to orbital degeneracy, justifying the quantitative success of the one band model which was previously applied to orbitally degenerate systems. We contrast this with quantities that have a sizeable dependence on the orbital degeneracy and comment on the role of the intraatomic exchange J

Construction of Localized Basis for Dynamical Mean Field Theory

Many-body Hamiltonians obtained from first principles generally include all possible non-local interactions. But in dynamical mean field theory the non-local interactions are ignored, and only the effects of the local interactions are taken into account. The truncation of the non-local interactions is a basis dependent approximation. We propose a criterion to construct an appropriate localized basis in which the truncation can be carried out. This involves finding a basis in which a functional given by the sum of the squares of the local interactions with appropriate weight factors is maximized under unitary transformations of basis. We argue that such a localized basis is suitable for the application of dynamical mean field theory for calculating material properties from first principles. We propose an algorithm which can be used for constructing the localized basis. We test our criterion on a toy model and find it satisfactory

Consequences of the local spin self-energy approximation on the heavy Fermion quantum phase transition

We show, using the periodic Anderson model, that the local spin self-energy approximation, as implemented in the extended dynamical mean field theory (EDMFT), results in a first order phase transition which persists to T=0. Around the transition, there is a finite coexistence region of the paramagnetic and antiferromagnetic (AFM) phases. The region is bounded by two critical transition lines which differ by an electron-hole bubble at the AFM ordering wave vector.Comment: 16 pages, 1 figur