The problem of an electron gas interacting via exchanging transverse gauge bosons is studied using the renormalization group method. The long wavelength behavior of the gauge field is shown to be in the Gaussian universality class with a dynamical exponent z = 3 in dimensions D ≥ 2. This implies that the gauge coupling constant is exactly marginal. Scattering of the electrons by the gauge mode leads to non-Fermi liquid behavior in D ≤ 3. The asymptotic electron and gauge Green's functions, interaction vertex, specific heat and resistivity are presented.

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The two-impurity Kondo model with particle-hole symmetry is known to have a critical point at comparable RKKY interaction and Kondo temperature. Using bosonization and controlled low energy projection, we identify the critical point and map it to a solvable resonant level model. The physics of the critical point is shown to be the same as the two-channel Kondo model. An effective Hamiltonian is derived from which the solutions for the critical point and surrounding Fermi-liquid phase follow immediately.The universality of the critical point is strongly supported by the overall excellent agreement with the numerical renormalization group and conformal field theory results. PACS numbers: 75.20.Hr, 75.30.MbThe essence of the two-impurity Kondo model (TIKM) is the competition between Kondo effect and RKKY interaction [1 -4]. This competition is believed to be the core of many interesting properties of strongly correlated systems. Extensive numerical renormalization group (NRG) study on TIKM [5] revealed that the low energy behavior is of local Fermi-liquid (FL) type for most regions of the parameter space, except for a critical value of the RKKY interaction in the presence of particle-hole symmetry. The existence of the critical point was later put on firm ground by proving analytically the existence of a discontinuous point in the electron scattering phase shifts [6]. Although real systems are unlikely to fall right on the critical point, its presence, however, stipulates a new small energy scale,

The non-Fermi-liquid fixed point of the overscreened Kondo problem is studied in the limit of a large number of conduction electron channels, k^> 1, using perturbation theory in \/k. By expanding the beta function and self-energy to sub-leading-order in \/k, we examine the scaling, thermodynamics, and dynamic response functions in detail. Our results compliment and extend previous work based on conformal field theory. We present the dynamical spin susceptibility for the first time and show that the impurity spin is marginally quenched, with an inelastic linewidth of order T.

We study the phase diagram of the Ising-Kondo lattice with transverse magnetic field as a possible model for the weak-moment heavy-fermion compound URu 2 Si 2 , in terms of two low-lying f singlets in which the uranium moment is coupled by on-site exchange to the conduction electron spins. In the mean-field approximation for an extended range of parameters, we show that the conduction electron magnetization responds logarithmically to f -moment formation, that the ordered moment in the antiferromagnetic state is anomalously small, and that the Néel temperature is of the order observed. The model gives a qualitatively correct temperature-dependence, but not magnitude, of the specific heat. The majority of the specific heat jump at the Néel temperature arises from the formation of a spin gap in the conduction electron spectrum. We also discuss the single-impurity version of the model and speculate on ways to increase the specific heat coefficient. In the limits of small bandwidth and of small Ising-Kondo coupling, we find that the model corresponds to anisotropic Heisenberg and Hubbard models respectively. PACS numbers: 71.10. Fd, 71.27.+a, 71.70.Ch, 75.30.Mb Γ t1 1 higher singlets doublets and t2 J J J -+ z Γ FIG. 5. Spectrum of the crystal-field Hamiltonian, showing states related to the low-lying singlets by application of the operator J.

A detailed and comprehensive study of the one-impurity multichannel Kondo model is presented. In the limit of a large number of conduction electron channels k ≫ 1, the low energy fixed point is accessible to a renormalization group improved perturbative expansion in 1/k. This straightforward approach enables us to examine the scaling, thermodynamics and dynamical response functions in great detail and make clear the following features: i) the criticality of the fixed point; ii) the universal non-integer degeneracy; iii) that the compensating spin cloud has the spatial extent of the order of one lattice spacing.

An asymptotically exact solution is presented for the two-impurity Kondo model for a finite region of the parameter space surrounding the critical point. This region is located in the most interesting intermediate regime where RKKY interaction is comparable to the Kondo temperature. After several exact simplifications involving reduction to one dimension and abelian bosonization, the critical point is explicitly identified, making clear its physical origin. By using controlled low energy projection, an effective Hamiltonian is mapped out for the finite region in the phase diagram around the critical point. The completeness of the effective Hamiltonian is rigorously proved from general symmetry considerations. The effective Hamiltonian is solved exactly not only at the critical point but also for the surrounding Fermi-liquid phase. Analytic crossover functions from the critical to Fermi-liquid behavior are derived for the specific heat and staggered susceptibility. It is shown that applying a uniform magnetic field has negligible effect on the critical behavior. A detailed comparison is made with the numerical renormalization group * Current address:

Numerical studies, from variational calculation to exact diagonalization, all indicate that the quasiparticle generated by introducing one hole into a two-dimensional quantum antiferromagnet has the same nature as a string state in the t − Jz model. Based on this observation, we attempt to visualize the quasiparticle formation and subsequent coherent propagation at low energy by studying the generalized t − Jz − J ⊥ model in which we first diagonalize the t − Jz model and then perform a degenerate perturbation in J ⊥ . We construct the quasiparticle state and derive an effective Hamiltonian describing the coherent propagation of the quasiparticle and its interaction with the spin wave excitations in the presence of the Néel order. We expect that qualitative properties of the quasiparticle remain intact when analytically continuing J ⊥ from the anisotropic J ⊥ < Jz to the isotropic J ⊥ = Jz limit, despite the fact that the spin wave excitations change from gapful to gapless. Extrapolating to J ⊥ = Jz, our quasiparticle dispersion and spectral weight compare well with the exact numerical results for small clusters.