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This paper deals with the theory of the density of states of pure type-II superconductors in high magnetic fields. An approximate expression of the GaEEN'S function is derived by using the fact that it has the periodicity of the lattice of flux lines in the center-ofmass coordinates. In comparison to the normal state GREEN'S function a correction term proportional to the absolute square of the order parameter arises. This is seen to act as a self-energy part depending strongly on the polar angle O of the "quasiparticle" momentum relative to the direction of the field. The corresponding density of states, as a function of the excitation energy, is found to vary from the gapless to the BCS type as the parameter O changes from u]2 to zero (or u). The averaged state density varies gradually from a uniform to a BCS-like state density as the external field decreases sufficiently far below the upper critical field. The results of the present theory for the averaged density of states agree fairly well with the results due to a conjecture by MAKI if the field is very close to the upper critical field. I. IntroductionSeveral attempts have been made to calculate the space average of the density of states, N(co), in a type-II superconductor in the high magnetic field region by means of a perturbation expansion in powers of the order parameter, A (r). For a pure type-II superconductor it was found first by DE GENNES et al. 1 that N(co) has a logarithmic singularity at zero excitation energy co (where co is measured relatively to the chemical potential). Later the density of states was calculated exactly by NEU-MANN z to order ]A 12 (the bar denotes the spatial average) for all mean free paths of the electrons. It turns out that for finite mean free paths, no matter how large, the singularity disappears. Then the shape of the curve of N(co) versus co becomes qualitatively similar to that of the dirty limit 3, in particular it shows no energy gap.Recently it was shown by MAKI 4 that for pure type-II superconductors the contribution to N(co) of the order ]AI ~ diverges even stronger than that of the order [A [2, namely, it goes like 1/co 2 as co tends to zero.

Exact solutions of the Hubbard model and the periodic Anderson model in the limit of infinite interaction strength are presented. Both models are studied on a D-dimensional decorated hypercubic lattice with periodic boundary conditions for any dimension D>2 and arbitrary size. The lattice is very similar to the perovskite lattice. In addition to the ground-state energy, a corresponding eigenstate is constructed. This ground state contains at least two particles per unit cell. For the Anderson model, the exact solution is restricted to a surface in the (E/,V) parameter space; however, the resulting relation ViEf) does not lead to unphysical parameters. PACS numbers: 7I.10.+X, 71.28.+d, 74.70.Vy Strongly interacting many-particle systems are a classical problem in solid-state physics. Numerous experiments indicate the breakdown of one-particle pictures; however, the theoretical description of truly interacting systems is far from being satisfactory. Highly correlated Fermi systems are frequently modeled by the familiar Hubbard and Anderson Hamilton operators [1], These models describe the interplay between properties of itinerant and strongly interacting electrons; however, they only contain the absolute minimum of "ingredients" in order to remain tractable. Unfortunately, these models are still very complicated and exact results [2] are rare. In the light of this situation, it is highly valuable to obtain additional exact results as constraints for approximation schemes.The model Hamiltonians and a particular £>-dimensional lattice are defined. For these systems, the groundstate energy and a corresponding eigenstate are calculated analytically in the limit of infinite interaction strength (U-+ oo) for any dimension D>2.In a first step, the model Hamiltonians are rewritten in terms of suitable operators. This operator transformation is surprisingly simple, and the eigenstate which is an exact ground state follows immediately. In order to discuss the nature of the ground state in the final part of this Letter, the oneparticle spectra of the models are briefly mentioned.The lattice. -The exact solution of the Hubbard and Anderson models is an unsolved problem; however, a particular lattice where a solution is obtained may be derived from a Z>-dimensional decorated cubic lattice: The cubic lattice vectors are denoted by /?, and the D basis vectors by e v . The electronic orbitals are located at the "decorated" sites r*/?+je w i.e., at the centers of the cubic bonds. The unit cell of this lattice %l(R) contains D sites. For the sake of brevity, the set of all 2D sites r =/? ± j e v surrounding a lattice point R is called JV(R). Figure 1 illustrates this lattice for D=2. The cubic lattice points are represented by open circles, and the particle sites by solid circles, respectively. For D -3 the sites JV(/?) form octahedra. The structure of such a lattice is similar to the ReC>3 structure. (It is possible to consider the number of unit cells in one of the three dimensions to be 1, a lattice realized in the Cu-O planes in...

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