Fermi-liquid instabilities at magnetic quantum phase transitions

Abstract

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

62 pages, 29 figs, review article for Rev. Mod. Phys; (v2) discussion extended, refs added; (v3) shortened; final version as published

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Cited by in corpus (64)

• The numerical renormalization group method for quantum impurity systems
• Quantum Criticality in Heavy Fermion Metals
• Electric Field Control of the LaAlO${}_3$/SrTiO${}_3$ Interface Ground State
• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• A Non-Fermi Liquid from a Charged Black Hole; A Critical Fermi Ball
• Quantum phase transition in a single-molecule quantum dot
• Critical fermi surfaces and non-fermi liquid metals
• Iron pnictides as a new setting for quantum criticality
• Superfluid-Mott Insulator Transition of Light in the Jaynes-Cummings Lattice
• The quantum critical point in CeRhIn_5: a resistivity study
• Fluctuating spin density waves in metals
• Infinite-randomness quantum critical points induced by dissipation
• Divergence of the Magnetic Grüneisen Ratio at the Field-Induced Quantum Critical Point in YbRh${}_2$Si${}_2$
• T=0 heavy fermion quantum critical point as an orbital selective Mott transition
• Unconventional metamagnetic electron states in orbital band systems
• Layered Kondo lattice model for quantum critical beta-YbAlB4
• Determining the crystal-field ground state in rare earth Heavy Fermion materials using soft-x-ray absorption spectroscopy
• From itinerant to local-moment antiferromagnetism in Kondo lattices: Adiabatic continuity vs. quantum phase transitions
• Fluctuating Stripes in Strongly Correlated Electron Systems and the Nematic-Smectic Quantum Phase Transition
• Evolution of critical scaling behavior near a ferromagnetic quantum phase transition
• Nonanalytic paramagnetic response of itinerant fermions away and near a ferromagnetic quantum phase transition
• Selective Mott transition and heavy fermions
• Evidence of quantum criticality in the phase diagram of K${}_x$Sr${}_{1-x}$Fe${}_2$As${}_2$ from measurements of transport and thermoelectricity
• Multi-scale fluctuations near a Kondo Breakdown Quantum Critical Point
• Quantum Critical Paraelectrics and the Casimir Effect in Time
• Non-analytic spin susceptibility of a nested Fermi liquid: the case of Fe-based pnictides
• Universal Behavior of Two-Dimensional 3He at Low Temperatures
• YbRh2Si2: Quantum tricritical behavior in itinerant electron systems
• Renormalization group for phases with broken discrete symmetry near quantum critical points
• Signature of quantum criticality in photoemission spectroscopy at elevated temperature
• Zero-Temperature Magnetic Transition in an Easy-Axis Kondo Lattice Model
• A novel non-Fermi-liquid state in the iron-pnictide FeCrAs
• Violation of critical universality at the antiferromagnetic phase transition of YbRh2Si2
• Quantum Criticality out of Equilibrium: Steady State in a Magnetic Single-Electron Transistor
• Andreev reflection and order parameter symmetry in heavy-fermion superconductors: the case of CeCoIn${}_5$
• Spin-spin correlations of the spin-ladder compound (C${}_5$H${}_{12}$N)${}_2$CuBr${}_4$ measured by magnetostriction and comparison to Quantum Monte Carlo results
• Kondo volume collapse, Kondo breakdown, and Fermi surface transitions in heavy-fermion metals
• Scaling and Enhanced Symmetry at the Quantum Critical Point of the Sub-Ohmic Bose-Fermi Kondo Model
• Heavy-fermion metals with hybridization nodes: Unconventional Fermi liquids and competing phases
• Finite Size Scaling of Classical Long-Ranged Ising Chains and the Criticality of Dissipative Quantum Impurity Models
• Quantum phase transitions and dimensional reduction in antiferromagnets with inter-layer frustration
• Reduced dimensionality in layered quantum dimer magnets: Frustration vs. inhomogeneous condensates
• Evolution of Quantum Criticality in CeNi_{9-x}Cu_xGe_4
• Grüneisen ratio at the Kondo breakdown quantum critical point
• Strongly correlated Fermi-systems: non-Fermi liquid behavior, quasiparticle effective mass and their interplay
• Non-perturbative microscopic theory of superconducting fluctuations near a quantum critical point
• Renormalized phi^6 model for quantum phase transitions in systems of itinerant fermions
• Signatures of non-monotonic d-wave gap in electron-doped cuprates
• Distribution of conductance for Anderson Insulators: A theory with a single parameter
• Apparent Violation of the Wiedemann-Franz law near a magnetic field tuned metal-antiferromagnetic quantum critical point
• Dynamical correlations in the spin-half two-channel Kondo model
• Scaling and commensurate-incommensurate crossover for the d=2, z=2 quantum critical point of itinerant antiferromagnets
• Dimensional crossover in quantum critical metallic magnets
• Energy scales and magnetoresistance at a quantum critical point
• Interaction effects in 2D electron gas in a random magnetic field: Implications for composite fermions and quantum critical point
• Quantum Phase Transition in the Itinerant Antiferromagnet (V0.9Ti0.1)2O3
• He3 bi-layers as a simple example of de-confinement
• Quantum critical point in high-temperature superconductors
• Heavy Fermions: electrons at the edge of magnetism
• Lattice models for non-Fermi liquid metals
• Evidence for the existence of Kondo coupled resonant modes in heavy fermions
• Resistivity of Mn${}_{1-x}$Fe${}_x$Si single crystals: Evidence for quantum critical behavior
• Computing quantum phase transitions