Coexistence of solutions in dynamical mean-field theory of the Mott transition

In this paper, I discuss the finite-temperature metal-insulator transition of the paramagnetic Hubbard model within dynamical mean-field theory. I show that coexisting solutions, the hallmark of such a transition, can be obtained in a consistent way both from Quantum Monte Carlo (QMC) simulations and from the Exact Diagonalization method. I pay special attention to discretization errors within QMC. These errors explain why it is difficult to obtain the solutions by QMC close to the boundaries of the coexistence region.Comment: 3 pages, 2 figures, RevTe

Surface Instabilities and Magnetic Soft Matter

We report on the formation of surface instabilities in a layer of thermoreversible ferrogel when exposed to a vertical magnetic field. Both static and time dependent magnetic fields are employed. Under variations of temperature, the viscoelastic properties of our soft magnetic matter can be tuned. Stress relaxation experiments unveil a stretched exponential scaling of the shear modulus, with an exponent of beta=1/3. The resulting magnetic threshold for the formation of Rosensweig-cusps is measured for different temperatures, and compared with theoretical predictions by Bohlius et. al. in J. Phys.: Condens. Matter., 2006, 18, 2671-2684.Comment: accepted to Soft Matte

Quantum Monte Carlo calculation of the finite temperature Mott-Hubbard transition

We present clear numerical evidence for the coexistence of metallic and insulating dynamical mean field theory(DMFT) solutions in a half-filled single-band Hubbard model with bare semicircular density of states at finite temperatures. Quantum Monte Carlo(QMC) method is used to solve the DMFT equations. We discuss important technical aspects of the DMFT-QMC which need to be taken into account in order to obtain the reliable results near the coexistence region. Among them are the critical slowing down of the iterative solutions near phase boundaries, the convergence criteria for the DMFT iterations, the interpolation of the discretized Green's function and the reduction of QMC statistical and systematic errors. Comparison of our results with those of other numerical methods is presented in a phase diagram.Comment: 4 pages, 5 figure

Correlated hopping of electrons: Effect on the Brinkman-Rice transition and the stability of metallic ferromagnetism

We study the Hubbard model with bond-charge interaction (`correlated hopping') in terms of the Gutzwiller wave function. We show how to express the Gutzwiller expectation value of the bond-charge interaction in terms of the correlated momentum-space occupation. This relation is valid in all spatial dimensions. We find that in infinite dimensions, where the Gutzwiller approximation becomes exact, the bond-charge interaction lowers the critical Hubbard interaction for the Brinkman-Rice metal-insulator transition. The bond-charge interaction also favors ferromagnetic transitions, especially if the density of states is not symmetric and has a large spectral weight below the Fermi energy.Comment: 5 pages, 3 figures; minor changes, published versio

Landau Theory of the Finite Temperature Mott Transition

In the context of the dynamical mean-field theory of the Hubbard model, we identify microscopically an order parameter for the finite temperature Mott endpoint. We derive a Landau functional of the order parameter. We then use the order parameter theory to elucidate the singular behavior of various physical quantities which are experimentally accessible.Comment: 4 pages, 2 figure

Linked Cluster Expansion Around Mean-Field Theories of Interacting Electrons

A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field theories at weak (Hartree-Fock) and strong (Hubbard-III) coupling the expansion represents a universal and comprehensive tool for systematic improvements of static mean-field theories. As an example of the general formalism we investigate in detail an analytically tractable series of ring diagrams that correctly capture dynamical fluctuations at weak coupling. We introduce renormalizations of the diagrammatic expansion at various levels and show how the resultant theories are related to other approximations of similar origin. We demonstrate that only fully self-consistent approximations produce global and thermodynamically consistent extensions of static mean field theories. A fully self-consistent theory for the ring diagrams is reached by summing the so-called noncrossing diagrams.Comment: 17 pages, REVTEX, 13 uuencoded postscript figures in 2 separate file

Similarities between the Hubbard and Periodic Anderson Models at Finite Temperatures

The single band Hubbard and the two band Periodic Anderson Hamiltonians have traditionally been applied to rather different physical problems - the Mott transition and itinerant magnetism, and Kondo singlet formation and scattering off localized magnetic states, respectively. In this paper, we compare the magnetic and charge correlations, and spectral functions, of the two systems. We show quantitatively that they exhibit remarkably similar behavior, including a nearly identical topology of the finite temperature phase diagrams at half-filling. We address potential implications of this for theories of the rare earth ``volume collapse'' transition.Comment: 4 pages (RevTeX) including 4 figures in 7 eps files; as to appear in Phys. Rev. Let

Absence of hysteresis at the Mott-Hubbard metal-insulator transition in infinite dimensions

The nature of the Mott-Hubbard metal-insulator transition in the infinite-dimensional Hubbard model is investigated by Quantum Monte Carlo simulations down to temperature T=W/140 (W=bandwidth). Calculating with significantly higher precision than in previous work, we show that the hysteresis below T_{IPT}\simeq 0.022W, reported in earlier studies, disappears. Hence the transition is found to be continuous rather than discontinuous down to at least T=0.325T_{IPT}. We also study the changes in the density of states across the transition, which illustrate that the Fermi liquid breaks down before the gap opens.Comment: 4 pages, 4 eps-figures using epsf.st

The Numerical Renormalization Group Method for correlated electrons

The Numerical Renormalization Group method (NRG) has been developed by Wilson in the 1970's to investigate the Kondo problem. The NRG allows the non-perturbative calculation of static and dynamic properties for a variety of impurity models. In addition, this method has been recently generalized to lattice models within the Dynamical Mean Field Theory. This paper gives a brief historical overview of the development of the NRG and discusses its application to the Hubbard model; in particular the results for the Mott metal-insulator transition at low temperatures.Comment: 14 pages, 7 eps-figures include

Finite temperature numerical renormalization group study of the Mott-transition

Wilson's numerical renormalization group (NRG) method for the calculation of dynamic properties of impurity models is generalized to investigate the effective impurity model of the dynamical mean field theory at finite temperatures. We calculate the spectral function and self-energy for the Hubbard model on a Bethe lattice with infinite coordination number directly on the real frequency axis and investigate the phase diagram for the Mott-Hubbard metal-insulator transition. While for T<T_c approx 0.02W (W: bandwidth) we find hysteresis with first-order transitions both at U_c1 (defining the insulator to metal transition) and at U_c2 (defining the metal to insulator transition), at T>T_c there is a smooth crossover from metallic-like to insulating-like solutions.Comment: 10 pages, 9 eps-figure