Impurity Quantum Phase Transitions

We review recent work on continuous quantum phase transitions in impurity models, both with fermionic and bosonic baths - these transitions are interesting realizations of boundary critical phenomena at zero temperature. The models with fermion bath are generalizations of the standard Kondo model, with the common feature that Kondo screening of the localized spin can be suppressed due to competing processes. The models with boson bath are related to the spin-boson model of dissipative two-level systems, where the interplay between tunneling and friction results in multiple phases. The competition inherent to all models can generate unstable fixed points associated with quantum phase transitions, where the impurity properties undergo qualitative changes. Interestingly, certain impurity transitions feature both lower-critical and upper-critical "dimensions" and allow for epsilon-type expansions. We present results for a number of observables, obtained by both analytical and numerical renormalization group techniques, and make connections to experiments.Comment: 22 pages, 11 figs, review article to be published in Phil. Ma

Enhancement of Spin Susceptibility near Charge-Ordering Transition in a Two-Dimensional Extended Hubbard Model

Based on the non-skeleton diagrammatic expansion satisfying the compressibility and spin-susceptibility sum rules, we investigate static charge and spin responses in a two-dimensional extended Hubbard model with the nearest-neighbor Coulomb repulsion in the vicinity of its charge-ordering transition point. In this expansion, we can calculate approximate charge and spin response functions by systematic inclusion of vertex corrections, from which we obtain the uniform susceptibility equal to the so-called q-limit of the response function and the second-order transition point as a divergent point in the same response function at some finite wave-number vector. It is shown that the reentrant charge-ordering transition, which has already been observed in the random-phase approximation (RPA), remains to take place even though the vertex corrections are included beyond the RPA. As a prominent effect of the vertex corrections, we find that the uniform spin susceptibility is enhanced due to charge fluctuations developing toward the charge-ordering transition. We give a qualitative comparison of this enhanced spin susceptibility with the experimental results on the quasi-two-dimensional organic conductors, together with its explanation in the Landau's Fermi-liquid theory.Comment: 24 pages, 8 figure