Collective excitations and stability of a non-Fermi liquid state near a quantum-critical point of a metal

Abstract

We examine the spectral properties of collective excitations with finite angular momentum $l$ for a system of interacting fermions near a Pomeranchuk quantum critical point, both in the Fermi liquid and non-Fermi liquid regimes. Previous studies found that deep in the Fermi liquid regime, the spectral functions for even and odd $l$ behave differently - the latter is suppressed compared to the former because of kinematic constraints on scattering processes. The main focus of our paper is to understand how the spectral functions for even and odd $l$ evolve as the system enters the non-Fermi liquid regime. We obtain the full scaling function for the electron polarization bubble at arbitrary $l$, which interpolates between the Fermi liquid and non-Fermi liquid regimes. We show that collective excitations for all $l$ remain stable and causal throughout the crossover and right at the quantum critical point.

arXiv comment12 pages, 5 figures

References in corpus (31)

• Quantum Theory of a Nematic Fermi Fluid
• Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order
• On the low energy properies of fermions with singular interactions
• Superconductivity in the repulsive Hubbard model: an asymptotically exact weak-coupling solution
• Pseudogap state from quantum criticality
• Soft Fermi Surfaces and Breakdown of Fermi Liquid Behavior
• Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point
• Gauge-invariant response functions of fermions coupled to a gauge field
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Recent Developments in Non-Fermi Liquid Theory
• Fermi surface fluctuations and single electron excitations near Pomeranchuk instability in two dimensions
• Transport near the Ising-nematic quantum critical point of metals in two dimensions
• Large $N$ theory of critical Fermi surfaces
• Non-Fermi liquid behavior of large N_B quantum critical metals
• Fermi liquid near Pomeranchuk quantum criticality
• Large $N$ theory of critical Fermi surfaces II: conductivity
• Optical response of correlated electron systems
• The Hierarchy of Excitation Lifetimes in Two-Dimensional Fermi Gases
• Gifts from anomalies: Exact results for Landau phase transitions in metals
• Zero temperature optical conductivity of ultra-clean Fermi liquids and superconductors
• Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter
• Collective modes near a Pomeranchuk instability
• Free energy and specific heat near a quantum critical point of a metal
• Zero sound and plasmon modes for non-Fermi liquids
• Dynamical susceptibility of a near-critical non-conserved order parameter and B2g Raman response in Fe-based superconductors
• Optical conductivity of a metal near an Ising-nematic quantum critical point
• Fermi Surface Geometry and Optical Conductivity of a 2D Electron Gas near an Ising-Nematic Quantum Critical Point
• Fluctuation Spectrum of Critical Fermi Surfaces
• Interplay of superconductivity and localization near a 2D ferromagnetic quantum critical point
• Fermi Liquid near a q=0 Charge Quantum Critical Point
• Quantum criticality and optical conductivity in a two-valley system