Quantum Critical Behavior of Correlated Electrons: Resonant States

Abstract

Coulomb repulsion drives correlated electrons toward a critical point where bound electron-hole pairs condense. However, before the critical point is reached quantum fluctuations dominate the critical region and can lead to formation of resonant pair states. We use a two-particle parquet approach to describe quantum criticality. We show with a simplified version of the parquet equations that due to a two-particle self-consistence of the nonlinear parquet equations, a new phase with anomalous vertex functions may arise. The new solution describes a phase with resonant pair states where the effective interaction between the quasiparticles becomes complex. Although the two-particle vertex functions display symmetry breaking with order parameters, the low-energy one-particle spectrum of the phase with resonant states remains Fermi-liquid like.