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Universality and Convergence of Energy Scales at Quantum Critical Points in Local and Lattice Models

Alex C. Hewson, Daniel J. G. Crow, Yunori Nishikawa

Published Jul 22, 2015• 1 citation
Publisher
DOI
10.1142/9789814704090_0004

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We find the emergence of strong correlations and universality on the approach to the quantum critical points of a two-impurity Anderson model. The two impurities are coupled by an interimpurity exchange interaction J and direct interaction U{12} and are hybridized with separate conduction channels. The low energy behavior is described in terms of renormalized parameters. We show that on the approach to the transitions to a local singlet and a local charged ordered state, the quasiparticle weight factor z→0, and the renormalized parameters can be expressed in terms of a single energy scale T{*}. The values of the renormalized interaction parameters in terms of T{*} can be predicted from the condition of continuity of the spin and charge susceptibilities, and correspond to strong correlation. These predictions are confirmed by the numerical renormalization group calculations, including the case when the on site interaction U=0.
The pseudogap Anderson impurity model provides a classic example of an essentially local quantum phase transition. Here we study its single-particle dynamics in the vicinity of the symmetric quantum critical point (QCP) separating generalized Fermi-liquid and local-moment phases, via the local-moment approach. Both phases are shown to be characterized by a low-energy scale that vanishes at the QCP; and the universal scaling spectra, on all energy scales, are obtained analytically. The spectrum precisely at the QCP is also obtained; its form showing clearly the non–Fermi-liquid, interacting nature of the fixed point.
The Enigma of the Pseudogap Phase of the Cuprate Superconductors (Debanjan Chowdhury and Subir Sachdev) Resonant Spin Excitations in Unconventional Heavy Fermion Superconductors and Kondo Lattice Comppounds (Peter Thalmeier and Alireza Akbari) Quantum Critical Heavy Fermion Metal Ybrh2si2 (Gertrud Zwicknagl) Universality and Convergence of Energy Scales at Quantum Critical Points in Local and Lattice Models (A C Hewson, D J G Crow and Y Nishikawa) Unparticles in Strongly Correlated Electron Matter (Philip W Phillips) Fidelity Approach to Quantum Phase Transitions in Quantum Ising Model (Bogdan Damski) Dynamics of Quantum Phase Transitions: Quantum Kibble-Zurek Mechanism (Jacek Dziarmaga) Theory of Temporal Fluctuations in Isolated Quantum Systems (L Campos Venuti)