[Paper Review] Quantum Criticality and the Kondo Lattice

Qimiao Si|arXiv (Cornell University)|Dec 24, 2010

Quantum and electron transport phenomena4 citations

TL;DR

This paper investigates quantum criticality in Kondo lattice systems, introducing a novel type of quantum critical point—local quantum criticality—where the Kondo effect breaks down, leading to non-Fermi liquid behavior and a sudden collapse of the Fermi surface from large to small. It contrasts this with conventional spin-density-wave quantum criticality and discusses implications for heavy fermion metals and unconventional superconductivity.

ABSTRACT

Quantum phase transitions (QPTs) arise as a result of competing interactions in a quantum many-body system. Kondo lattice models, containing a lattice of localized magnetic moments and a band of conduction electrons, naturally feature such competing interactions. A Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction among the local moments promotes magnetic ordering. However, a Kondo exchange interaction between the local moments and conduction electrons favors the Kondo-screened singlet ground state. This chapter summarizes the basic physics of QPTs in antiferromagnetic Kondo lattice systems. Two types of quantum critical points (QCPs) are considered. Spin-density-wave quantum criticality occurs at a conventional type of QCP, which invokes only the fluctuations of the antiferromagnetic order parameter. Local quantum criticality describes a new type of QCP, which goes beyond the Landau paradigm and involves a breakdown of the Kondo effect. This critical Kondo breakdown effect leads to non-Fermi liquid electronic excitations, which are part of the critical excitation spectrum and are in addition to the fluctuations of the magnetic order parameter. Across such a QCP, there is a sudden collapse of the Fermi surface from large to small. I close with a brief summary of relevant experiments, and outline a number of outstanding issues, including the global phase diagram.

Motivation & Objective

• To understand quantum criticality in Kondo lattice systems where competing Kondo and RKKY interactions drive quantum phase transitions.
• To identify and characterize a new type of quantum critical point—local quantum criticality—beyond the Landau paradigm.
• To explain the emergence of non-Fermi liquid excitations due to the breakdown of the Kondo effect at criticality.
• To connect theoretical predictions with experimental observations in heavy fermion materials like URu2Si2 and YbAgGe.
• To outline the global phase diagram of Kondo lattices and identify open questions in quantum criticality and superconductivity.

Proposed method

• Uses the Kondo lattice model with localized magnetic moments and conduction electrons, incorporating both Kondo and RKKY interactions.
• Applies the Hertz-Millis effective field theory to describe quantum critical fluctuations of the antiferromagnetic order parameter.
• Introduces a new theoretical framework for local quantum criticality, where the Kondo effect is dynamically destroyed at the critical point.
• Analyzes the breakdown of Kondo screening via a critical singularity in the Kondo coupling, leading to non-Fermi liquid behavior.
• Employs a dual representation of the Kondo lattice: as a system of local moments coupled to conduction electrons, and as a Heisenberg model with itinerant electrons.
• Uses the transverse-field Ising model as a pedagogical prototype to illustrate quantum criticality and tuning of quantum fluctuations via a non-thermal control parameter.

Experimental results

Research questions

• RQ1 How does the breakdown of the Kondo effect at a quantum critical point lead to non-Fermi liquid electronic excitations?
• RQ2 What distinguishes local quantum criticality from conventional spin-density-wave quantum criticality in Kondo lattice systems?
• RQ3 How does the Fermi surface evolve across a Kondo breakdown quantum critical point, and what is the nature of the resulting large-to-small Fermi surface transition?
• RQ4 What experimental signatures can be expected in heavy fermion materials that host such a critical point?
• RQ5 How do quantum fluctuations from local moments and from conduction electron coupling interplay to shape the global phase diagram of Kondo lattices?

Key findings

• A new type of quantum critical point—local quantum criticality—is identified, where the Kondo effect breaks down, leading to non-Fermi liquid behavior beyond the Landau paradigm.
• At the Kondo breakdown critical point, the Fermi surface undergoes a sudden collapse from large to small, signaling a topological change in the electronic structure.
• Non-Fermi liquid excitations emerge as part of the critical spectrum, in addition to fluctuations of the antiferromagnetic order parameter.
• Theoretical analysis shows that the Kondo singlet formation is spontaneously generated and can be critically destroyed, creating a critical singularity independent of symmetry breaking.
• Experimental systems like URu2Si2 and YbAgGe show evidence of potential local quantum criticality, though further low-temperature measurements are needed.
• The interplay between Kondo and RKKY interactions leads to a rich global phase diagram involving both magnetic order and quantum disordered states, with possible connections to unconventional superconductivity.