Topological approach to Luttinger's theorem and the Fermi surface of a Kondo lattice

Abstract

A non-perturbative proof of Luttinger's theorem, based on a topological argument, is given for Fermi liquids in arbitrary dimensions. Application to the Kondo lattice shows that even the completely localized spins do contribute to the Fermi sea volume as electrons, whenever the system can be described as a Fermi liquid.

4 pages in REVTEX (no figure), accepted for publication in Phys. Rev. Letters

References in corpus (1)

• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice

Cited by in corpus (249)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms
• How do Fermi liquids get heavy and die?
• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• Hall-effect evolution across a heavy-fermion quantum critical point
• Fractionalized Fermi liquids
• Generalized Symmetries in Condensed Matter
• Superfluid analogies of cosmological phenomena
• Critical fermi surfaces and non-fermi liquid metals
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• From high temperature supercondutivity to quantum spin liquid: progress in strong correlation physics
• Electron stars for holographic metallic criticality
• A Phenomenological Theory of the Anomalous Pseudogap Phase in Underdoped Cuprates
• Filling-Enforced Gaplessness in Band Structures of the 230 Space Groups
• Flat bands, strange metals, and the Kondo effect
• Topological Invariants of Metals and Related Physical Effects
• Quantum Criticality and Global Phase Diagram of Magnetic Heavy Fermions
• Frustration and quantum criticality
• Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
• Experimental electronic heat capacities of $\alpha -$ and $\delta -$Plutonium; heavy-fermion physics in an element
• Fractionalization, topological order, and quasiparticle statistics
• Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
• Topological order in the pseudogap metal
• Orbital-selective Mott transitions: Heavy fermions and beyond
• Extending Luttinger's theorem to Z(2) fractionalized phases of matter
• Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals
• A quantum dimer model for the pseudogap metal
• Stellar spectroscopy: Fermions and holographic Lifshitz criticality
• Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems
• Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
• Obstructions to Gapped Phases from Non-Invertible Symmetries
• Symmetric Mass Generation
• Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function
• Fermionic Lieb-Schultz-Mattis Theorems and Weak Symmetry-Protected Phases
• From spinon band topology to the symmetry quantum numbers of monopoles in Dirac spin liquids
• Holographic theory for continuous phase transitions -- the emergence and symmetry protection of gaplessness
• What is the fate of the heavy electron at a quantum critical point?
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Laser-induced magnetization curve
• Evolution of a Large Fermi Surface in the Kondo Lattice
• Parton theory of ARPES spectra in anti-ferromagnetic Mott insulators
• From itinerant to local-moment antiferromagnetism in Kondo lattices: Adiabatic continuity vs. quantum phase transitions
• Fermi surface topology of the two-dimensional Kondo lattice model: a dynamical cluster approximation approach
• Luttinger-volume violating Fermi liquid in the pseudogap phase of the cuprate superconductors
• The Pauli exclusion principle at strong coupling: Holographic matter and momentum space
• Luttinger theorem for the strongly correlated Fermi liquid of composite fermions
• Electric polarization as a nonquantized topological response and boundary Luttinger theorem
• The one dimensional Kondo lattice model at partial band filling
• Mott insulators with boundary zeros
• Breakdown of Luttinger's theorem in two-orbital Mott insulators
• Sum Rules and Ward Identities in the Kondo Lattice
• Chiral Kondo Lattice in Doped MoTe${}_2$/WSe${}_2$ Bilayers
• Elasticity tetrads, mixed axial-gravitational anomalies, and 3+1d quantum Hall effect
• Metallic Ferromagnetism in the Kondo Lattice
• Filling-enforced constraint on the quantized Hall conductivity on a periodic lattice
• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
• Holographically smeared Fermi surface: Quantum oscillations and Luttinger count in electron stars
• Cyclotron effective masses in layered metals
• Topological interpretation of Luttinger theorem
• Metal-chalcogen bond-length induced electronic phase transition from semiconductor to topological semimetal in ZrX${}_2$ (X = Se and Te)
• The novel metallic states of the cuprates: Fermi liquids with topological order, and strange metals
• Paired electron pockets in the hole-doped cuprates
• Emergent Charge Fluctuations at the Kondo Breakdown of Heavy Fermions
• Fractionalized Fermi liquids and exotic superconductivity in the Kitaev-Kondo lattice
• Higher-group symmetry in finite gauge theory and stabilizer codes
• Large-density field theory, viscosity, and "$2k_F$" singularities from string duals
• Higgs criticality in a two-dimensional metal
• Luttinger's theorem, superfluid vortices, and holography
• Triplet pairing mechanisms from Hund's-Kondo models: applications to UTe${}_2$ and CeRh${}_2$As${}_2$
• Fractional Quantum Hall Effect in Weyl Semimetals
• A solvable 3D Kondo lattice exhibiting odd-frequency pairing and order fractionalization
• Hall effect in heavy-fermion metals
• Emergent gauge fields and the high temperature superconductors
• Charge density waves in Weyl semimetals
• Coupled topological flat and wide bands: Quasiparticle formation and destruction
• Connecting the Many-Body Chern Number to Luttinger's Theorem through Středa's Formula
• Fermi Surface Properties, Metamgnetic Transition and Quantum Phase Transition of CeRu${}_2$Si${}_2$ and Its Alloys Probed by the dHvA Effect--Fermi Surface Studies on the Itinerant and Localized Dichotomy of $f$ Electron Nature
• Geometric phases and the magnetization process in quantum antiferromagnets
• Antiferromagnetism in metals: from the cuprate superconductors to the heavy fermion materials
• Luttinger's theorem in presence of Luttinger surfaces
• Rotation Symmetry-Protected Topological Phases of Fermions
• Are Heavy Fermion Strange Metals Planckian?
• Insulator, conductor and commensurability: a topological approach
• TQFT, Symmetry Breaking, and Finite Gauge Theory in 3+1D
• Exact Mapping of Periodic Anderson Model to Kondo Lattice Model
• Controlled bond expansion for DMRG ground state search at single-site costs
• Order Fractionalization in a Kitaev-Kondo model
• Quantum Many-Body Simulations of the 2D Fermi-Hubbard Model in Ultracold Optical Lattices
• Emergent anomalies and generalized Luttinger theorems in metals and semimetals
• Unquantized anomalies in topological semimetals
• The enigma of the pseudogap phase of the cuprate superconductors
• Theory of the first-order isostructural valence phase transitions in mixed valence compounds YbIn_{x}Ag_{1-x}Cu_{4}
• Lieb-Schultz-Mattis type constraints on Fractonic Matter
• Small Fermi surface in the one-dimensional Kondo lattice model
• Necessary and Sufficient Conditions for the Validity of Luttinger's Theorem
• Fermi-surface reconstruction without symmetry breaking
• Two dimensional spin liquids with ${\mathbb{Z}}_2$ topological order in an array of quantum wires
• Kondo breakdown in a spin-1/2 chain of adatoms on a Dirac semimetal
• Solvable Periodic Anderson Model with Infinite-Range Hatsugai-Kohmoto Interaction: Ground-states and beyond
• Theory of the fractional quantum Hall effect in Weyl semimetals
• Quantized axial charge of staggered fermions and the chiral anomaly
• Fractionalized Fermi Liquid in a Kondo-Heisenberg Model
• Confinement transition to density wave order in metallic doped spin liquids
• Large-N Approach to the Two-Channel Kondo Lattice
• The Mott transition as a topological phase transition
• Fractionalization on the Surface: Is Type-II Terminated $1T$-TaS${}_2$ Surface an Anomalously Realized Spin Liquid?
• Kondo Breakdown via Fractionalization in a Frustrated Kondo Lattice Model
• Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene
• Nonlinear Sigma Model Analysis of the AFM Phase Transition of the Kondo Lattice
• Doped Kondo chain, a heavy Luttinger liquid
• Pairing instability on a Luttinger surface: A non-Fermi liquid to superconductor transition and its Sachdev-Ye-Kitaev dual
• Solvable model for a charge-$4e$ superconductor
• Charge dynamics of the antiferromagnetically ordered Mott insulator
• Odd-frequency pair density wave in the Kitaev-Kondo lattice model
• Fermi Surface Symmetric Mass Generation
• Spin Liquids and Pseudogap Metals in $SU(4)$ Hubbard Model in Moiré Superlattice
• Spin chain on a metallic surface: Dissipation-induced order vs. Kondo entanglement
• Metal to Orthogonal Metal Transition
• Emergent Spinon Dispersion and Symmetry Breaking in Two-Channel Kondo Lattices
• Non-perturbative conserving approximations and Luttinger's sum rule
• Stripes and electronic quasiparticles in the pseudogap state of cuprate superconductors
• Small to large Fermi surface transition in a single band model, using randomly coupled ancillas
• Relaxation dynamics of the Kondo lattice model
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Soluble limit and criticality of fermions in Z2 gauge theories
• Edge zeros and boundary spinons in topological Mott insulators
• Exact solution of a two-species quantum dimer model for pseudogap metals
• Transitions from small to large Fermi momenta in a one-dimensional Kondo lattice model
• Temperature dependent Fermi arcs in the normal state of the underdoped cuprate superconductors
• Exact ground states and correlation functions of chain and ladder models of interacting hardcore bosons or spinless fermions
• Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
• Modern Physics of the Condensed State: Strong Correlations and Quantum Topology
• Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly
• Lieb Schultz Mattis-Type Theorems and Other Non-perturbative Results for Strongly Correlated Systems with Conserved Dipole Moments
• Luttinger sum rules and spin fractionalization in the SU(N) Kondo Lattice
• Detecting Quantum Anomalies in Open Systems
• Filling constraints on fermionic topological order in zero magnetic field
• Quantum phase transitions, frustration, and the Fermi surface in the Kondo lattice model
• Magnetic field induced quantum criticality and the Luttinger sum rule
• Fermi arcs and pseudogap in a lattice model of a doped orthogonal metal
• Low energy effective field theories of fermion liquids and mixed $U(1)\times {\mathbb{R}}^d$ anomaly
• Physics of Arbitrary Doped Kondo Lattices: from a Commensurate Insulator to a Heavy Luttinger Liquid and a Protected Helical Metal
• A Comment on Holographic Luttinger Theorem
• Quantum critical metals and loss of quasiparticles
• Variational cluster approach to superconductivity and magnetism in the Kondo lattice model
• Valence transition in the periodic Anderson model
• Equilibrium Surface Current and Role of U(1) Symmetry: sum rule and surface perturbations
• Observation of a Critical Charge Mode in a Strange Metal
• Zero sound and higher-form symmetries in compressible holographic phases
• Emergence of nodal Bogoliubov quasiparticles across the transition from the pseudogap metal to the d-wave superconductor
• Holographic unitary renormalization group for correlated electrons -- II: insights on fermionic criticality
• Holographic unitary renormalization group for correlated electrons -- I: a tensor network approach
• Average-exact mixed anomalies and compatible phases
• Breakdown of heavy quasiparticles in a honeycomb Kondo lattice: A quantum Monte Carlo study
• Two-channel Kondo Lattice Model on a ladder studied by the Density Matrix Renormalization Group Method
• Topological nature of Hubbard bands in strongly correlated systems
• Matrix Product Study of Spin Fractionalization in the 1D Kondo Insulator
• Generalization of Luttinger's Theorem for Strongly Correlated Electron Systems
• Holographic models of non-Fermi liquid metals revisited: an effective field theory approach
• Solvable Theory of a Strange Metal at the Breakdown of a Heavy Fermi Liquid
• Luttinger theorem and imbalanced Fermi systems
• Filling-enforced Kondo semimetals in two-dimensional non-symmorphic crystals
• Ferromagnets, a New Anomaly, Instantons, and (noninvertible) Continuous Translations
• Quantum oscillations in the hole-doped cuprates and the confinement of spinons
• Altermagnetism in Heavy Fermion Systems: Mean-Field study on Kondo Lattice
• Polaronic correlations from optimized ancilla wave functions for the Fermi-Hubbard model
• Surface Luttinger arcs in Weyl semimetals
• Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid
• Gapless Fermionic Systems as Phase-space Topological Insulators: Non-perturbative Results from Anomalies
• Two-orbital physics of high spin fermionic alkaline earth atoms confined in a one-dimensional chain
• Dynamic mass generation and topological order in overscreened Kondo lattices
• Topic Review: Hatsugai-Kohmoto models: Exactly solvable playground for Mottness and Non-Fermi Liquid
• Origin of Topological Order in a Cooper Pair Insulator
• A Proof of Luttinger Theorem
• Heavy electrons from Hund's rule and short-range Antiferromagnetism
• Crossover from Fermi Arc to Full Fermi Surface
• Nonlocal Kondo effect and two-fluid picture revealed in an exactly solvable model
• LSM and CPT
• Spontaneous layer selective Mott phase in the bilayer Hubbard model
• Quantum spin liquid from electron-phonon coupling
• Fractionalizing glide reflections in two-dimensional Z2 topologically ordered phases
• The strong coupling Kondo lattice model as a Fermi gas
• Anomalous Continuous Translations
• Non-perturbative approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets
• Electron doping of the iron-arsenide superconductor CeFeAsO controlled by hydrostatic pressure
• Critical phase induced by Berry phase and dissipation in a spin chain
• Ground-state phase diagram of the $S=1$ one-dimensional Kondo lattice model with a uniaxial anisotropy under transverse fields
• Quasiparticle Band Structure and Spin Excitation Spectrum of the Kondo Lattice
• Violation of Luttinger's theorem in the simplest doped Mott insulator: Falicov-Kimball model in strong correlation limit
• Topological states in strongly correlated systems
• Vortex structure in a $d$-wave superconductor obtained by a confinement transition from the pseudogap metal
• Transport in Magnetically Doped One-Dimensional Wires: Can the Helical Protection Emerge without the Global Helicity?
• Magnon Bose-Einstein Condensation and Superconductivity in a Frustrated Kondo Lattice
• Fractionalized Fermi liquids and the cuprate phase diagram
• Fractional Fermi liquid in a generalized $t-J$ model
• Static Magnetic Response of Non-Fermi Liquid Density
• The Future of the Correlated Electron Problem
• Topological 'Luttinger' invariants protected by non-symmorphic symmetry in semimetals
• Interpreting Angle Dependent Magnetoresistance in Layered Materials: Application to Cuprates
• Monte Carlo Study of Strongly-Interacting Degenerate Fermions: a Model for Voltage-Biased Bilayer Graphene
• Soliton Stars as Holographic Confined Fermi Liquids
• Fermi surface enlargement on the Kondo lattice
• de Haas-van Alphen oscillations for non-relativistic fermions coupled to an emergent U(1) gauge field
• Continuous Wigner-Mott transition at $\nu =1/5$
• Universal contributions to charge fluctuations in spin chains at finite temperature
• SU($\mathbf{N}$) Kondo-Heisenberg chain: Phase diagram, Ising criticality, and the coexistence of heavy quasiparticles and valence bond solid order
• Two-band model and RVB-type states: application to Kondo lattices, pyrochlores and Mn-based systems
• Geometric orthogonal metals: Hidden antiferromagnetism and pseudogap from fluctuating stripes
• A Mean-Field Study of Quantum Oscillations in Two-Dimensional Kondo Insulators
• T-matrix formulation of real-space dynamical mean-field theory and the Friedel sum rule for correlated lattice fermions
• Spontaneous interlayer coherence in bilayer Kondo systems
• Theory of dual fermion superconductivity in hole-doped cuprates
• Fermi Surface Volume of Interacting Systems
• Polarized solutions and Fermi surfaces in holographic Bose-Fermi systems
• Ground-State Degeneracy of Correlated Insulators with Edges
• Algebraic Hastatic Order in One-Dimensional Two-Channel Kondo Lattice
• Numerical identification and gapped boundaries of abelian fermionic topological order
• Universal entanglement signatures of quantum liquids as a guide to fermionic criticality
• Evidence for freezing of charge degrees of freedom across a critical point in CeCoIn${}_5$
• Universality classes of order parameters composed of many body bound states
• Signatures of correlated magnetic phases in the local two-particle density matrix
• Ordering the topological order in the fractional quantum Hall effect
• Status of the Fermi surface in mixed composite boson - composite fermion quantum Hall states
• Fractionalized Superconductivity Mediated by Majorana Fermions in the Kitaev-Kondo Lattice
• On the ground-state properties of antiferromagnetic half-integer spin chains with long-range interactions
• Solvable lattice models for metals with Z2 topological order
• Functional renormalization group for extremely correlated electrons
• Absence of localization in Weyl semimetals
• Visualizing spinon Fermi surfaces with time-dependent spectroscopy
• Anomalous Hall effect and quantum criticality in geometrically frustrated heavy fermion metals
• Direct measurement of a remnant Fermi surface in SmB6
• Thermopower across Fermi-volume-changing quantum phase transitions without translational symmetry breaking
• Impurity-induced Mott ring states and Mott zeros ring states in the Hubbard operator formalism
• Topological Phase Transitions of Interacting Fermions in the Presence of a Commensurate Magnetic Flux
• Kondo frustration via charge fluctuations: a route to Mott localisation
• The Luttinger Count is the Homotopy not the Physical Charge: Generalized Anomalies Characterize Non-Fermi Liquids
• Weakly damped bosons and precursor gap in the vicinity of an antiferromagnetic metallic transition
• Spin nematic order and superconductivity in $J_1$-$J_2$ Kondo lattice model on square lattice
• Role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal
• Yamaji effect in models of underdoped cuprates
• Non-Fermi Liquid Behavior of the $t$-$J$ Model in the Strange Metal Phase: $U(1)$ Gauge Theory Consistent with Local Constraints
• On non-canonical degrees of freedom
• Integrable Model of a Superconductor with non-Fermi liquid and Mott Phases
• Landau Quasiparticles in Weak Power-Law Liquids
• Phases and phase transitions of an $S=3/2$ chain on metallic and semi-metallic surfaces
• Holographic entanglement renormalisation for fermionic quantum matter
• Polarization-based indices in quantum many-body systems: validity and extension beyond one dimension
• Selective Kondo screening and strange metallicity by sliding Dirac semimetals