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

摘要

A common feature of magnetic impurity systems with strongly correlated electrons is the emergence of a unique low energy scale, the Kondo temperature Tk, such that the low energy thermodyamics and the response functions are universal functions of the temperature T and frequency ω in terms of Tk. We show that this type of universality occurs on the approach to the critical points in a two-impurity model with the emergence of a single energy scale T*, such that T* → 0 at the critical points. We also find this convergence of energy scales in infinite dimensional lattice models, such as the Hubbard and Hubbard-Holstein models on the approach to the metal to insulator transitions. This form of universality is consistent with the ω/T scaling as T* → 0 as observed in dynamic response functions in some non-Fermi-liquid heavy fermion systems near the quantum critical point.