In order to extend the density-matrix renormalization-group (DMRG) method to two-dimensional systems, we formulate two alternative methods to prepare the initial states. We Gnd that the number of states that is needed for accurate energy calculations grows exponentially with the linear system size. We also analyze how the states kept in the DMRG method manage to preserve both the intrablock and interblock Hamiltonians, which is the key to the high accuracy of the method. We also prove that the energy calculated on a finite cluster is always a variational upper bound.Exact diagonalization is often the only reliable technique for obtaining the ground-state properties of interacting many-body systems. Since the Hilbert space grows exponentially with the size of the system, current computing power limits the diagonalization to systems too small to infer the thermodynamic limit for most problems.

The phase diagram of the two-channel Kondo lattice model is examined with a Quantum Monte Carlo simulation in the limit of infinite dimensions. Commensurate (and incommensurate) antiferromagnetic and superconducting states are found. The antiferromagnetic transition is very weak and continuous; whereas the superconducting transition is discontinuous to an odd-frequency channel-singlet and spin-singlet pairing state.Comment: 5 pages, LaTeX and 4 PS figures (see also cond-mat/9609146 and cond-mat/9605109

The paramagnetic phase of the two-channel Kondo lattice model is examined with a quantum Monte Carlo simulation in the limit of infinite dimensions. We find non-Fermi-liquid behavior at low temperatures including a finite low-temperature single-particle scattering rate, no Fermi distribution discontinuity, and zero Drude weight. However, the low-energy density of electronic states is finite. We label our model system in this phase an "incoherent metal." We discuss the relevance of our results for concentrated heavy fermion metals with non-Fermi-liquid behavior. [S0031-9007(96) The Fermi liquid theory of Landau has provided a remarkably robust paradigm for describing the properties of interacting fermion systems such as liquid 3 He and alkali metals (e.g., sodium). The key notion of this theory is that the low lying excitations of the interacting system possess a 1:1 map to those of the noninteracting system and hence are called "quasiparticles." In the metallic context, one may think of the quasiparticles as propagating electronlike wave packets with renormalized magnetic moment and effective mass reflecting the "molecular field" of the surrounding medium. A sharp Fermi surface remains in the electron occupancy function n k which measures the number of electrons with a given momentum, and for energies v and temperatures T asymptotically close to the Fermi surface the excitations have a decay rate going as v 2 1 p 2 ͑k B T͒ 2 , which is much smaller than the quasiparticle energy, and generally translates into a T 2 contribution to the electrical resistivity r͑T ͒. This theory has proven useful in describing phase transitions within the Fermi liquid, such as superconductivity which is viewed as a pairing of Landau quasiparticles in conventional metals such as aluminum.The Fermi liquid paradigm appears now to be breaking down empirically in numerous materials, notably the quasi-two-dimensional cuprate superconductors [1] and a number of fully three-dimensional heavy Fermion alloys and compounds [2]. In these systems such anomalies as a conductivity with linear dependence on v, T and logarithmically divergent linear specific heat coefficients are often observed. If the quasiparticle paradigm indeed breaks down, this may require completely new concepts to explain the superconducting phases of these materials. While the Luttinger liquid theory provides an elegant way to achieve non-Fermi-liquid theory in one dimension (with, e.g., no jump discontinuity in n k , and separation or unbinding of spin and charge quantum numbers), this results from the special point character of the Fermi surface. Whether the essential spin-charge separation may "bootstrap" into higher dimensions remains unclear [3].Among the remaining theories to explain experiment are those based upon proximity to a zero-temperature quantum critical point [4], those based upon disorder induced distributions of Kondo scales in local moment systems [5], and those which hope to explain the physics from impurity to lattice crossover effects in the multichanne...

PACS. 75.10-b -General theory and models of magnetic ordering. PACS. 71.27 + a -Strongly correlated electron systems.

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