[Paper Review] Fermi and Non-Fermi Liquid Behavior of Local Moment Systems within a Conserving Slave Boson Theory

Johann Kroha, Peter Woelfle|arXiv (Cornell University)|Apr 6, 1998

Physics of Superconductivity and Magnetism3 citations

TL;DR

This paper develops a conserving T-matrix approximation (CTMA) within a slave boson framework to describe both Fermi and non-Fermi liquid behavior in local moment systems with strong correlations. By preserving local gauge symmetry and capturing coherent spin-flip and charge fluctuation processes, the method correctly reproduces the infrared threshold exponents for both regimes in the SU(N)×SU(M) Anderson impurity model, resolving a key limitation of prior auxiliary boson theories.

ABSTRACT

The question of Fermi liquid vs. non-Fermi liquid behavior induced by strong correlations is one of the prominent problems in metallic local moment systems. As standard models for such systems, the SU(N) x SU(M) Anderson impurity models exhibit both Fermi liquid and non-Fermi liquid behavior, depending on their symmetry. Using an auxiliary boson method, we present a generally applicable scheme to select the relevant contributions in the low frequency regime, while preserving the local gauge symmetry of the model. It amounts to a conserving T-matrix approximation (CTMA) including coherent spin flip as well as charge fluctuation processes, which are found to dominate in the Kondo and in the mixed valence regime, respectively. The infrared threshold exponents of the auxiliary particle spectral functions are indicators for the presence of Fermi or non-Fermi liquid behavior in any given model with strong on-site repulsion. We show that, in contrast to earlier auxiliary boson theories, the CTMA recovers the correct exponents in both cases, indicating that it correctly describes both the Fermi and the non-Fermi regimes of the Anderson model.

Motivation & Objective

• To resolve the long-standing challenge of describing both Fermi and non-Fermi liquid behavior in strongly correlated local moment systems within a unified theoretical framework.
• To develop a conserving approximation scheme that preserves local gauge symmetry in the slave boson formalism, which is essential for correct low-energy physics.
• To identify and correctly describe the dominant physical processes—coherent spin flips and charge fluctuations—in the Kondo and mixed valence regimes, respectively.
• To determine whether the infrared threshold exponents of auxiliary particle spectral functions can serve as reliable indicators of Fermi versus non-Fermi liquid behavior.
• To overcome the failure of earlier auxiliary boson theories in correctly capturing the critical exponents in both regimes.

Proposed method

• The authors employ a slave boson representation to decouple the local Hilbert space, preserving the local U(1) gauge symmetry of the Anderson impurity model.
• They derive a conserving T-matrix approximation (CTMA) that includes both coherent spin-flip and charge fluctuation processes, ensuring conservation laws are respected.
• The method systematically selects relevant low-frequency contributions in the self-energy, focusing on the infrared regime where Fermi/non-Fermi liquid crossover occurs.
• The infrared threshold exponents of the auxiliary particle spectral functions are computed as key indicators of the low-energy fixed-point behavior.
• The approach is applied to the SU(N)×SU(M) Anderson model, allowing a unified treatment of Kondo and mixed valence regimes.
• The formalism is validated by comparing the resulting exponents with known exact results for both Fermi and non-Fermi liquid fixed points.

Experimental results

Research questions

• RQ1 Can a single, conserving slave boson approach describe both Fermi and non-Fermi liquid behavior in local moment systems?
• RQ2 Do the infrared threshold exponents of auxiliary particle spectral functions correctly signal the presence of Fermi or non-Fermi liquid behavior?
• RQ3 Does the inclusion of both coherent spin-flip and charge fluctuation processes in the T-matrix approximation lead to correct low-energy fixed-point exponents?
• RQ4 How does the proposed CTMA method improve upon earlier auxiliary boson theories that failed to reproduce the correct exponents?
• RQ5 Is it possible to preserve local gauge symmetry in a conserving approximation while capturing the essential physics of strong correlations?

Key findings

• The conserving T-matrix approximation (CTMA) successfully reproduces the correct infrared threshold exponents for both Fermi and non-Fermi liquid fixed points in the SU(N)×SU(M) Anderson impurity model.
• The method correctly identifies coherent spin-flip processes as dominant in the Kondo regime and charge fluctuations in the mixed valence regime.
• Unlike earlier auxiliary boson theories, the CTMA preserves local gauge symmetry and avoids unphysical results in the low-energy limit.
• The infrared exponents of the auxiliary particle spectral functions serve as reliable indicators of the underlying Fermi or non-Fermi liquid character.
• The CTMA provides a unified framework that correctly describes both regimes within a single, conserving formalism.
• The approach confirms the validity of the slave boson method when extended to include conserving approximations with proper low-frequency selection.