1 Introduction
I Magnetic frustration, quenched disorder, and their interplay
2 Elements of frustrated magnetism
2.1 Heisenberg magnetism in Mott insulators
2.2 Frustration and classical ground-state degeneracies
2.3 Order by disorder
2.3.1 Thermal order by disorder
2.3.2 Quantum order by disorder
2.3.3 Conceptual differences and possible competition between thermal and quantum order by disorder
2.3.4 Pseudo-Goldstone modes and experimental realizations
2.4 Classical spin liquids
2.5 Quantum spin liquids
3 Quenched disorder in magnetic systems
3.1 Types of disorder and their consequences
3.2 Random-field disorder: Stability of long-range order and the Imry-Ma argument
3.3 Random-mass disorder: Rounding of first-order phase transitions and the Harris criterion
3.4 Spin glasses: Basic concepts and experimental signatures
3.4.1 The spin glass transition
4 Spiral spin liquids
4.1 J1-J2 Heisenberg model on the honeycomb lattice
4.1.1 Teaser: Enhanced ground-state degeneracy at J2/J1 = 1/2
4.2 Classical ground states and the spiral contour
4.3 Influence of thermal fluctuations
4.3.1 Low temperatures: Thermal order by disorder and nematic order
4.3.2 Intermediate temperatures: Spin liquid regimes
4.4 Linear spin-wave theory and quantum order by disorder
5 Disorder effects in spiral spin liquids
5.1 Disordered J1-J2 Heisenberg model on the honeycomb lattice
5.2 Isolated impurities
5.2.1 Linear response theory: Spin textures and energy corrections
5.2.2 Order by quenched disorder
5.2.3 Friedel-like oscillations
5.2.4 In-plane textures and their impact on long-range order
5.3 Numerics on clean finite systems
5.4 Nonvanishing concentration of impurities
5.4.1 Bond defects of the same type and orientation
5.4.2 Bond defects of random orientation: Emergent glassiness from competing order-by-quenched-disorder mechanisms
5.4.3 Randomly distributed vacancies
5.5 Effects or thermal fluctuations and additional couplings
5.5.1 J1-J2 honeycomb model
5.5.2 Spiral spin liquids in three dimensions
5.6 Connections to experiments
5.7 Summary and outlook
II Quantum phase transitions in local-moment metals
6 Single-impurity and lattice Kondo effects: Experimemtal signatures, theory basics, and Kondo breakdown
6.1 Dilute magnetic impurities in metals and the Kondo effect
6.1.1 The Anderson impurity model and local moment formation
6.1.2 From the Anderson to the Kondo model
6.1.3 Kondo temperature and the onset of screening
6.1.4 Breakdown of the Kondo effect in quantum impurity models
6.2 Heavy-fermion metals and Kondo lattices
6.2.1 Anderson and Kondo lattice models
6.2.2 Heavy Fermi liquid
6.2.3 RKKY interaction
6.2.4 Doniach picture and quantum criticality in heavy-fermion systems
6.2.5 Breakdown of screening in Kondo lattices
7 Kondo-breakdown transitions and phase-separation tendencies in valence-fluctuating heavy-fermion metals
7.1 Anderson-Heisenberg lattice model and relevant limits
7.2 Parton mean-field theory
7.2.1 Mean-field equations
7.2.2 Implementation: Lattice, numerics, and temperature regime
7.3 Mean-field phases and phase diagrams
7.3.1 Mean-field phases
7.3.2 Phase diagram and Kondo breakdown at a fixed chemical potential
7.3.3 Phase diagram and Kondo breakdown at a fixed filling
7.4 Discussion: Fluctuation effects, frustrated phase separation, and inhomogeneous states
7.5 Summary and outlook
III Modifying magnetic order by symmetry reduction
8 Classification of nonrelativistic collinear magnetic states
8.1 Spin-space and spin point groups
8.1.1 Four classes of collinear magnetism
8.2 Application to collinear magnets in metallic systems
8.3 Application to collinear magnets in insulating systems
8.3.1 Linear spin-wave theory for a collinear Heisenberg magnet
8.3.2 Symmetries of the linear spin-wave spectrum
9 Fluctuation-induced ferrimagnetism
9.1 Ferrimagnetism from thermal fluctuations in a toy model
9.1.1 The toy model, its symmetries, and its ground state
9.1.2 Ground-state antiferromagnetism
9.1.3 Spin-wave spectrum
9.1.4 Uniform magnetization at T>0
9.1.5 Discussion: Nonmonotonic magnetization curves and the influence of magnetic anisotropies
9.2 Ferrimagnetism in a layered and distorted Shastry-Sutherland model
9.2.1 Background: The Shastry-Sutherland model
9.2.2 The layered and distorted Shastry-Sutherland model
9.2.3 Spin-wave theory: Magnon spectrum and ferrimagnetism
9.2.4 Application to SrCu(BO3)2 under pressure
9.3 Summary and outlook
10 From SU(2) to SU(N) altermagnetism
10.1 Prelude: Elements of the theory of su(N) algebras, their representations, and applications to magnetism
10.1.1 The {M,0} irreps of SU(N): Schwinger bosons and the Holstein-Primakoff transformation
10.2 Heisenberg models for SU(N) altermagnetism
10.2.1 Symmetries and good quantum numbers
10.2.2 SU(2) Heisenberg model on the checkerboard lattice
10.2.3 SU(3) Heisenberg model on the hexatriangular lattice
10.2.4 SU(4) Heisenberg model on the cross-cubic lattice
10.3 Spin-wave and flavor-wave theories: Magnon spectra and their symmetries
10.3.1 SU(2) altermagnet
10.3.2 SU(3) altermagnet
10.4 Magnon chirality
10.4.1 SU(2) altermagnet
10.4.2 SU(3) altermagnet
10.5 Electronic band structure: Spin- and flavor-split bands
10.5.1 SU(2) checkerboard Kondo lattice model
10.5.2 SU(3) hexatriangular Kondo lattice model
10.6 Summary and outlook
Appendices
A Ground-state degeneracy at J2/J1 = 1/2 (Chapter 4)
B Iterative minimization algorithm (Chapter 5)
C Details on derivations from Chapter 5
C.1 Derivation of Eq. (5.10)
C.2 Derivation of Eq. (5.16)
C.3 Asymptotic behavior of Friedel-like oscillations for a circular spiral contour
D In-plane component of impurity-induced textures: A case study (Chapter 5)
D.1 Implementation
D.2 Nearest-neighbor bond defect
D.3 Next-nearest-neighbor bond defect
D.4 Vacancy
D.4.1 Changes in textures with increasing J2/J1
E Different parton mean-field theories (Chapter 7)
E.1 Fermionic SU(N) and Sp(2N) theories
E.1.1 SU(N) large-N limit
E.1.2 Sp(2N) large-N limit
E.2 Compressibility of different homogeneous spin-liquid states
Bibliography