Frustration and quantum criticality

Abstract

This review article is devoted to the interplay between frustrated magnetism and quantum critical phenomena, covering both theoretical concepts and ideas as well as recent experimental developments in correlated-electron materials. The first part deals with local-moment magnetism in Mott insulators and the second part with frustration in metallic systems. In both cases, frustration can either induce exotic phases accompanied by exotic quantum critical points or lead to conventional ordering with unconventional crossover phenomena. In addition, the competition of multiple phases inherent to frustrated systems can lead to multi-criticality.

25 pages, 8 figs; review prepared for Rep. Prog. Phys.; (v2) final version as published

References in corpus (66)

• Spontaneous Skyrmion Ground States in Magnetic Metals
• Fermi-liquid instabilities at magnetic quantum phase transitions
• "Deconfined" quantum critical points
• Quantum Criticality in Heavy Fermion Metals
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Bose-Einstein Condensation in Magnetic Insulators
• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• Spin-Liquid State in the S = 1/2 Hyperkagome Antiferromagnet Na4Ir3O8
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Fractionalized Fermi liquids
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Condensate induced transitions between topologically ordered phases
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Unusual ordered phases of highly frustrated magnets: a review
• Fluctuation-induced first-order phase transition in Dzyaloshinskii-Moriya helimagnets
• Dimensional reduction at a quantum critical point
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Critical fermi surfaces and non-fermi liquid metals
• Possible proximity of the Mott insulating Iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field
• Theory of a continuous Mott transition in two dimensions
• Mott Transition, Antiferromagnetism, and d-wave Superconductivity in Two-Dimensional Organic Conductors
• Frustration and the Kondo effect in heavy fermion materials
• Magnetization processes of zigzag states on the honeycomb lattice: Identifying spin models for $\alpha$-RuCl${}_3$ and Na${}_2$IrO${}_3$
• Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice
• Honeycomb-lattice Heisenberg-Kitaev model in a magnetic field: Spin canting, metamagnetism, and vortex crystals
• Unusual liquid state of hard-core bosons on the pyrochlore lattice
• Quantum order by disorder and accidental soft mode Er2Ti2O7
• Kondo Breakdown as a Selective Mott Transition in the Anderson Lattice
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Orbital-selective Mott transitions: Heavy fermions and beyond
• Mott transition in Kagomé lattice Hubbard model
• Finite temperature Mott transition in Hubbard model on anisotropic triangular lattice
• A Spin-Orbital Singlet and Quantum Critical Point on the Diamond Lattice: FeSc2S4
• Characteristic signatures of quantum criticality driven by geometrical frustration
• Entropy evolution in the magnetic phases of partially frustrated CePdAl
• Unified theory of spiral magnetism in the harmonic-honeycomb iridates α, β, γ Li2IrO3
• Importance of Spin-Orbit Coupling in Organic BEDT-TTF and BEDT-TSF Salts
• Transport anomalies in a simplified model for a heavy electron quantum critical point
• β-YbAlB4: a critical nodal metal
• Quantum criticality of the kagome antiferromagnet with Dzyaloshinskii-Moriya interactions
• Quantum critical properties of a metallic spin density wave transition
• Grüneisen parameter studies on heavy fermion quantum criticality
• From itinerant to local-moment antiferromagnetism in Kondo lattices: Adiabatic continuity vs. quantum phase transitions
• Quantum and thermal transitions out of the supersolid phase of a 2D quantum antiferromagnet
• Breakdown of Luttinger's theorem in two-orbital Mott insulators
• Quantum phase transitions out of the heavy Fermi liquid
• Fractionalized Fermi liquids and exotic superconductivity in the Kitaev-Kondo lattice
• Higgs criticality in a two-dimensional metal
• Chiral RKKY interaction in Pr2Ir2O7
• Antiferromagnetism in metals: from the cuprate superconductors to the heavy fermion materials
• Spin liquid and quantum phase transition without symmetry breaking in a frustrated three-dimensional Ising model
• Global Phase Diagram of the Kondo Lattice: From Heavy Fermion Metals to Kondo Insulators
• Reduced dimensionality in layered quantum dimer magnets: Frustration vs. inhomogeneous condensates
• Multidimensional entropy landscape of quantum criticality
• Frustration and Entanglement in Compass and Spin-Orbital Models
• On confined fractional charges: a simple model
• Dimensional crossover in quantum critical metallic magnets
• Pressure-induced magnetic transition exceeding 30 K in the Yb-based heavy fermion superconductor $\beta$-YbAlB${}_4$

Cited by in corpus (69)

• Spin-orbit-entangled electronic phases in 4$d$ and 5$d$ transition-metal compounds
• Topological excitations in the ferromagnetic Kitaev-Heisenberg model
• Dynamical structure factor of the triangular antiferromagnet: the Schwinger boson theory beyond the mean field approach
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• Fractionalized fermionic quantum criticality in spin-orbital Mott insulators
• Quantum Ising model on the frustrated square lattice
• Emergent Anisotropic Non-Fermi Liquid at a Topological Phase Transition in Three Dimensions
• Quantum dynamics of topological strings in a frustrated Ising antiferromagnet
• Bilayer Kitaev models: Phase diagrams and novel phases
• Triangular Kondo lattice in $\mathrm{Yb}{\mathrm{V}}_6\mathrm{S}{\mathrm{n}}_6$ and its quantum critical behaviors in magnetic field
• Highly frustrated magnetism in relativistic ${\mathbf{d}}^4$ Mott insulators: Bosonic analog of Kitaev honeycomb model
• Emergence of mesoscale quantum phase transitions in a ferromagnet
• Simulations of Frustrated Ising Hamiltonians with Quantum Approximate Optimization
• Dual Orbital Degeneracy Lifting in a Strongly Correlated Electron System
• Emergent magnetic state in (111)-oriented quasi-two-dimensional spinel oxides
• Spin vestigial orders in extended Heisenberg-Kitaev models near hidden SU(2) points: Application to Na${}_2$Co${}_2$TeO${}_6$
• Theory of partial quantum disorder in the stuffed honeycomb Heisenberg antiferromagnet
• Modern Physics of the Condensed State: Strong Correlations and Quantum Topology
• Unconventional magnetism and electronic state in frustrated layered system PdCrO${}_2$
• Long-range magnetic order in the anisotropic triangular lattice system CeCd3As3
• Local magnetism, magnetic order and spin freezing in the 'nonmetallic metal' FeCrAs
• Dynamical scaling as a signature of multiple phase competition in Yb${}_2$Ti${}_2$O${}_7$
• Frustrations in the Ising chain with the third-neighbor interactions
• Field-angle-resolved landscape of non-Fermi-liquid behavior in the quasi-kagome Kondo Lattice CeRhSn
• Thermoelectric signature of quantum critical phase in a doped spin liquid candidate
• Crystallographic and magnetic structure of UNi${}_4$${}^{11}$B
• Quantum tricriticality of incommensurate phase induced by quantum domain walls in frustrated Ising magnetism
• Topological symplectic Kondo effect
• Peak in the critical current density in (Ca${}_x$Sr${}_{1-x}$)${}_3$Rh${}_4$Sn${}_{13}$ tuned towards the structural quantum critical point
• Twist-tuned quantum criticality in moiré bilayer graphene
• Critical properties of metallic and deconfined quantum phase transitions in Dirac systems
• Topological nature of Hubbard bands in strongly correlated systems
• Fluctuation-induced ferrimagnetism in sublattice-imbalanced antiferromagnets with application to SrCu${}_2$(BO${}_3$)${}_2$ under pressure
• Frustrated ferromagnetic transition in AB-stacked honeycomb bilayer
• Quantum bicritical point and phase separation in a frustrated Heisenberg ladder
• Rapid filling of the spin gap with temperature in the Schwinger-boson mean-field theory of the antiferromagnetic Heisenberg kagome model
• Gross-Neveu-XY quantum criticality in moiré Dirac materials
• Dressed Rabi oscillation in a crystalline organic radical
• Continuous transition between Ising magnetic order and a chiral spin liquid
• Neutron Depolarization due to Ferromagnetism and Spin Freezing in CePd${}_{1-x}$Rh${}_x$
• Atacamite Cu${}_2$Cl(OH)${}_3$ in High Magnetic Fields: Quantum Criticality and Dimensional Reduction of a Sawtooth-Chain Compound
• Quantum topological transitions and spinons in metallic ferro- and antiferromagnets
• Topological states in strongly correlated systems
• Topological phase transitions in strongly correlated systems: application to Co${}_3$Sn${}_2$S${}_2$
• Electronic States and Anomalous Hall Effect in Strongly Correlated Topological Systems
• Partial magnetic order in kagome spin ice
• Hubbard bands, Mott transition and deconfinement in strongly correlated systems
• Magnetic properties and field-induced phenomena in the Jeff = 1/2 distorted kagome antiferromagnet
• Two-band model and RVB-type states: application to Kondo lattices, pyrochlores and Mn-based systems
• Low-temperature magnetic behaviour on the triangular lattice in hexagonal Ba${}_3$Tb(BO${}_3$)${}_3$
• Magnetic Moiré Systems: a review
• Scaling theory of magnetism in frustrated Kondo lattices
• Divergence of the Grüneisen ratio at symmetry-enhanced first-order quantum phase transitions
• Mixed system $C{s}_{3}C{u}_{3}C{l}_{8-x}B{r}_{x}OH$ with weakly connected Cu-triangles
• Bilayer, hydrogenated and fluorinated graphene: QED vs SU(2) QCD theory
• Quantum Geometric Origin of Orbital Magnetization
• Spin nematic order and superconductivity in $J_1$-$J_2$ Kondo lattice model on square lattice
• Microscopic Origin of Reduced Magnetic Order in a Frustrated Metal
• Topology-driven deconfined quantum criticality in magnetic bilayers
• Stripe order in quasicrystals
• Rotational Grüneisen ratio: a probe for quantum criticality in anisotropic systems
• Hubbard Bands and Exotic States in Doped and Undoped Mott Systems: The Kotliar-Ruckenstein Representation
• Magnetic Field Dependence of the Spin Fluctuations in CeCu${}_{5.8}$Ag${}_{0.2}$
• Disorder, Low-Energy Excitations, and Topology in the Kitaev Spin Liquid
• Emergent spacetime supersymmetry at 2D fractionalized quantum criticality
• Excitation spectrum and low-temperature magnetism in disordered defect-fluorite Ho2Zr2O7
• Frustration and ordering in Ising chain in an external magnetic field with third-neighbor interactions
• Spin dynamics in natural multiferroic pyroxene NaFeSi${}_2$O${}_6$
• Magnetism, non-Fermi-liquid behavior and deconfinement in Kondo lattices