Fractionalized Fermi liquids and the cuprate phase diagram
arXiv:2508.20164 · doi:10.1088/1361-6633/ae530d
Abstract
We review a theoretical framework for the cuprate superconductors, rooted in a fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. The FL* theory predicted hole pockets each of fractional area at hole doping , in contrast to the area in spin density wave theory. Magnetotransport measurements, including observation of the Yamaji angle, show clear evidence of hole pocket quasiparticles which can tunnel coherently between square lattice layers, and are consistent with the FL* description. The FL* phase of a single-band model is described using a layer construction with a pair of ancilla qubits on each site: the Ancilla Layer Model (ALM). Fluctuations are described by the SU(2) gauge theory of a background spin liquid with critical Dirac spinons. A Monte Carlo study of the thermal SU(2) gauge theory transforms the hole pockets into Fermi arcs in photoemission. One route to confinement of FL* upon lowering temperature yields a -wave superconductor via a Kosterlitz-Thouless transition of vortices, with nodal Bogoliubov quasiparticles featuring anisotropic velocities and vortices surrounded by charge order halos. Increasing doping from the FL* phase in the ALM drives a transition to a conventional Fermi liquid (FL) at large doping, passing through an intermediate strange metal regime. We formulate a theory of the FL*-FL metal-metal transition without a symmetry-breaking order parameter, using a critical quantum `charge' liquid of mobile electrons in the presence of disorder, developed via an extension of the Sachdev-Ye-Kitaev model to two spatial dimensions. At low temperatures, and across optimal and over doping, we address the regimes of extended non-Fermi liquid behavior by Griffiths effects near quantum phase transitions in disordered metals.
arXiv comment101 pages, 43 figures. Review article based on lectures by SS at Boulder, Trieste, Hong Kong, with links to lecture videos. Comments welcome. v3. Introduced terminology of Ancilla Layer Model (ALM). v4. Added additional QMC results on variable exponents in Griffiths phase; v7. Updated results on quantum oscillations
References in corpus (239)
- A bound on chaos
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Comments on the Sachdev-Ye-Kitaev model
- A Common Thread: the pairing interaction for the unconventional superconductors
- "Deconfined" quantum critical points
- Theory of Intertwined Orders in High Temperature Superconductors
- Destruction of the Fermi Surface in Underdoped High Tc Superconductors
- Locally critical quantum phase transitions in strongly correlated metals
- Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
- A Four-Unit-Cell Periodic Pattern of Quasiparticle States Surrounding Vortex Cores in Bi2Sr2CaCu2O8+d
- Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
- Weak magnetism and non-Fermi liquids near heavy-fermion critical points
- Black Holes and Random Matrices
- Theory of Underdoped Cuprates
- Strange metal in magic-angle graphene with near Planckian dissipation
- The Physics Behind High-Temperature Superconducting Cuprates: The "Plain Vanilla" Version Of RVB
- The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
- Bekenstein-Hawking Entropy and Strange Metals
- Fractionalized Fermi liquids
- Intense paramagnon excitations in a large family of high-temperature superconductors
- Superconductivity in rhombohedral trilayer graphene
- Doping dependence of an n-type cuprate superconductor investigated by ARPES
- Fermionic Localization of the Schwarzian Theory
- Topological approach to Luttinger's theorem and the Fermi surface of a Kondo lattice
- A Phenomenological Theory of The Pseudogap State
- Deconfined quantum critical points: symmetries and dualities
- From a single-band metal to a high-temperature superconductor via two thermal phase transitions (Supporting Material)
- From a single-band metal to a high-temperature superconductor via two thermal phase transitions
- Connection between charge-density-wave order and charge transport in the cuprate superconductors
- Cluster Dynamical Mean Field Theory of the Mott Transition
- Universal -linear resistivity and Planckian limit in overdoped cuprates
- A strongly correlated metal built from Sachdev-Ye-Kitaev models
- Infinite-randomness quantum Ising critical fixed points
- Simultaneous Transitions in Cuprate Momentum-Space Topology and Electronic Symmetry Breaking
- Non-Fermi liquid regime of a doped Mott insulator
- Fractional excitations in the square-lattice quantum antiferromagnet
- Quantum Fluctuations of a Nearly Critical Heisenberg Spin Glass
- Fermi Surface and Quasiparticle Excitations of overdoped Tl2Ba2CuO6+d by ARPES
- Competing orders, non-linear sigma models, and topological terms in quantum magnets
- Topological order, emergent gauge fields, and Fermi surface reconstruction
- Weak Pseudogap Behavior in the Underdoped Cuprate Superconductors
- Gauge-invariant response functions of fermions coupled to a gauge field
- Phase Fluctuations and Spectral Properties of Underdoped Cuprates
- Non-Fermi Liquid Behavior in U and Ce Alloys: Criticality, Disorder, Dissipation, and Griffiths-McCoy singularities
- Fermi arcs and the hidden zeros of the Green's function in the pseudogap state
- Power-law out of time order correlation functions in the SYK model
- Momentum space anisotropy and pseudogaps: a comparative cluster dynamical mean field analysis of the doping-driven metal-insulator transition in the two dimensional Hubbard model
- Low-Energy Quasiparticles in Cuprate Superconductors: A Quantitative Analysis
- More on Supersymmetric and 2d Analogs of the SYK Model
- Emergent Symmetry at the Néel to Valence-Bond-Solid Transition
- Coherence scale of the Kondo lattice
- Anomalous High-Energy Spin Excitations in La2CuO4
- String patterns in the doped Hubbard model
- Notes on the complex Sachdev-Ye-Kitaev model
- Theta-terms in nonlinear sigma-models
- Planckian Dissipation in Metals
- Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
- Non Fermi Liquid Behaviour near a spin-glass transition
- Fermi Surface and Pseudogap Evolution in a Cuprate Superconductor
- Landau theory of quantum spin glasses of rotors and Ising spins
- Pseudogap opening and formation of Fermi arcs as an orbital-selective Mott transition in momentum space
- Microscopic theory of weak pseudogap behavior in the underdoped cuprate superconductors I: General theory and quasiparticle properties
- Local fluctuations in quantum critical metals
- Kondo Breakdown and Hybridization Fluctuations in the Kondo-Heisenberg Lattice
- Many-body spin Berry phases emerging from the -flux state: antiferromagnetic/valence-bond-solid competition
- Heavy-fermion and spin-liquid behavior in a Kondo lattice with magnetic frustration
- On the Reconstructed Fermi Surface in the Underdoped Cuprates
- Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
- Spectroscopic Fingerprint of Phase-Incoherent Superconductivity in the Cuprate Pseudogap State
- Critical local moment fluctuations in the Bose-Fermi Kondo model
- Angular fluctuations of a multi-component order describe the pseudogap regime of the cuprate superconductors
- Algebraic charge liquids
- Universal theory of strange metals from spatially random interactions
- Transport near the Ising-nematic quantum critical point of metals in two dimensions
- Cooper pairing of incoherent electrons: an electron-phonon version of the Sachdev-Ye-Kitaev model
- Translationally invariant non-Fermi liquid metals with critical Fermi-surfaces: Solvable models
- The Strange Metal State of the Electron-Doped Cuprates
- Finite doping signatures of the Mott transition in the two-dimensional Hubbard model
- Momentum-sector-selective metal-insulator transition in the eight-site dynamical mean-field approximation to the Hubbard model in two dimensions
- Quantum Griffiths effects in itinerant Heisenberg magnets
- Large theory of critical Fermi surfaces
- Quantum Oscillations in Hole-Doped Cuprates
- Linear-in temperature resistivity from an isotropic Planckian scattering rate
- Topological order in the pseudogap metal
- Pseudogap and Fermi surface topology in the two-dimensional Hubbard model
- Where is the quantum critical point in the cuprate superconductors?
- Magnetotransport in a model of a disordered strange metal
- Effects of dissipation on a quantum critical point with disorder
- High Temperature Superconductivity in a Lightly Doped Quantum Spin Liquid
- Protected nodal electron pocket from multiple-Q ordering in underdoped high temperature superconductors
- Mott physics and first-order transition between two metals in the normal state phase diagram of the two-dimensional Hubbard model
- Parton theory of magnetic polarons: Mesonic resonances and signatures in dynamics
- Fluctuating spin density waves in metals
- Infinite-randomness quantum critical points induced by dissipation
- Extending Luttinger's theorem to Z(2) fractionalized phases of matter
- High-spin polaron in lightly doped CuO planes
- Solvable Strong-coupling Quantum Dot Model with a Non-Fermi-liquid Pairing Transition
- Effective theory of Fermi pockets in fluctuating antiferromagnets
- Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals
- SU(2) gauge theory of the Hubbard model and application to the honeycomb lattice
- Gauge theory for the cuprates near optimal doping
- Gapless spin liquid and valence-bond solid in the Heisenberg model on the square lattice: insights from singlet and triplet excitations
- A quantum dimer model for the pseudogap metal
- Spectral signatures of fractionalization in the frustrated Heisenberg model on the square lattice
- DC resistivity at the onset of spin density wave order in two-dimensional metals
- Phase Diagram of BiSrCaCuO Revisited
- Kondo Destruction and Quantum Criticality in Kondo Lattice Systems
- Depletion of the Bose-Einstein condensate in Bose-Fermi mixtures
- Large theory of critical Fermi surfaces II: conductivity
- T=0 heavy fermion quantum critical point as an orbital selective Mott transition
- Quantum Monte Carlo Simulations of the 2D Su-Schrieffer-Heeger Model
- From spinon band topology to the symmetry quantum numbers of monopoles in Dirac spin liquids
- Optical response of correlated electron systems
- On quantum Griffiths effects in metallic systems
- High Frequency Behavior of the Infrared Conductivity of Cuprates
- Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering
- Hole dynamics in an antiferromagnet across a deconfined quantum critical point
- Fermi surface transformation at the pseudogap critical point of a cuprate superconductor
- Extremely Correlated Fermi Liquids
- Phase Fluctuations in Strongly Coupled -Wave Superconductors
- Observation of small Fermi pockets protected by clean CuO2 sheets of a high-Tc superconductor
- Luttinger-volume violating Fermi liquid in the pseudogap phase of the cuprate superconductors
- Reconciling scaling of the optical conductivity of cuprate superconductors with Planckian resistivity and specific heat
- Valence-bond solid to antiferromagnet transition in the two-dimensional Su-Schrieffer-Heeger model by Langevin dynamics
- Sum Rules and Ward Identities in the Kondo Lattice
- Fermion condensation and super pivotal categories
- Quantum Transition between an Antiferromagnetic Mott Insulator and Superconductor in Two Dimensions
- Phase Diagram of the Su-Schrieffer-Heeger-Hubbard model on a square lattice
- Antiferromagnetism induced by electron-phonon-coupling
- Characterization of quantum spin liquids and their spinon band structures via functional renormalization
- A critical strange metal from fluctuating gauge fields in a solvable random model
- Shot noise in a strange metal
- Multi-scale fluctuations near a Kondo Breakdown Quantum Critical Point
- Scattering mechanisms and electrical transport near an Ising nematic quantum critical point
- Quasiparticles in the Pseudogap Phase of Underdoped Cuprate
- The Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
- Phases and phase transitions in disordered quantum systems
- Evolution of the Fermi surface in phase fluctuating d-wave superconductors
- Loop current fluctuations and quantum critical transport
- Quantum Phase Transition in the Yukawa-SYK Model
- Quantum phase transition from an antiferromagnet to a spin liquid in a metal
- Intertwining topological order and broken symmetry in a theory of fluctuating spin density waves
- Quantum Monte Carlo Simulation of Frustrated Kondo Lattice Models
- Infinite randomness fixed point of the superconductor-metal quantum phase transition
- Fermi surface reconstruction in hole-doped t-J models without long-range antiferromagnetic order
- Seebeck coefficient in a cuprate superconductor: particle-hole asymmetry in the strange metal phase and Fermi surface transformation in the pseudogap phase
- Anisotropic damping of the spin fluctuations in doped La2-xSrxCuO4 studied by resonant inelastic x-ray scattering
- Higgs criticality in a two-dimensional metal
- New mean field theory of the tt't''J model applied to the high-Tc superconductors
- A new class of SYK-like models with maximal chaos
- Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids
- Pair Phase Fluctuations and the Pseudogap
- Fractionalized Fermi liquid with bosonic chargons as a candidate for the pseudogap metal
- The underdoped cuprates as fractionalized Fermi liquids: transition to superconductivity
- Monopole Quantum Numbers in the Staggered Flux Spin Liquid
- A model of -wave superconductivity, antiferromagnetism, and charge order on the square lattice
- Wess-Zumino-Witten Terms in Graphene Landau Levels
- A solvable 3D Kondo lattice exhibiting odd-frequency pairing and order fractionalization
- Robustness of Antiferromagnetism in the Su-Schrieffer-Heeger-Hubbard model
- Projected wave functions for fractionalized phases of quantum spin systems
- Dissipation-Induced Order: The Quantum Spin Chain Coupled to an Ohmic Bath
- Competing nodal d-wave superconductivity and antiferromagnetism
- Comprehensive mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model
- Antiferromagnetism in metals: from the cuprate superconductors to the heavy fermion materials
- Fluctuating orders and quenched randomness in the cuprates
- SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model
- Strange metal and superconductor in the two-dimensional Yukawa-Sachdev-Ye-Kitaev model
- Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
- Thermopower across the phase diagram of the cuprate LaNdSrCuO : signatures of the pseudogap and charge-density-wave phases
- Localization of overdamped bosonic modes and transport in strange metals
- Unveiling phase diagram of the lightly doped high-Tc cuprate superconductors with disorder removed
- Phase diagram of the spin-1/2 Yukawa-SYK model: Non-Fermi liquid, insulator, and superconductor
- The enigma of the pseudogap phase of the cuprate superconductors
- Superconducting valence bond fluid in lightly doped 8-leg - cylinders
- Charge-Density-Wave and Superconductor Competition in Stripe Phases of High Temperature Superconductors
- Kondo breakdown in a spin-1/2 chain of adatoms on a Dirac semimetal
- Fermi-surface reconstruction without symmetry breaking
- Pairing of holes by confining strings in antiferromagnets
- Optical conductivity of a two-dimensional metal near a quantum-critical point: the status of the "extended Drude formula"
- Fermi arcs and pseudogap phase in a minimal microscopic model of -wave superconductivity
- Theory of shot noise in strange metals
- Phase diagram and dynamics of the SU() symmetric Kondo lattice model
- Tunable non-Fermi liquid phase from coupling to two-level systems
- Deconfined metallic quantum criticality: A gauge-theoretic approach
- Bogoliubov Quasiparticle on the Gossamer Fermi Surface in Electron-Doped Cuprates
- Electronic spectra with paramagnon fractionalization in the single band Hubbard model
- A computational approach to a doped antiferromagnet: correlations between two spin-polarons in the lightly doped CuO plane
- Thermalization of non-Fermi-liquid electron-phonon systems: Hydrodynamic relaxation of the Yukawa-Sachdev-Ye-Kitaev model
- Pseudogap and Fermi-arc Evolution in the Phase-fluctuation Scenario
- T-linear resistivity, optical conductivity and Planckian transport for a holographic local quantum critical metal in a periodic potential
- Spin chain on a metallic surface: Dissipation-induced order vs. Kondo entanglement
- Small to large Fermi surface transition in a single band model, using randomly coupled ancillas
- Phase fluctuations in two-dimensional superconductors and pseudogap phenomenon
- Quantum Interference of Hydrodynamic Modes in a Dirty Marginal Fermi Liquid
- Cyclotron resonance and quantum oscillations of critical Fermi surfaces
- 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
- Solvable models of two-level systems coupled to itinerant electrons: Robust non-Fermi liquid and quantum critical pairing
- Pseudogap and (an)isotropic scattering in the fluctuating charge-density wave phase of cuprates
- Spin density wave, Fermi liquid, and fractionalized phases in a theory of antiferromagnetic metals using paramagnons and bosonic spinons
- Observation of emergent scaling of spin-charge correlations at the onset of the pseudogap
- Phases and Exotic Phase Transitions of a Two-Dimensional Su-Schrieffer-Heeger Model
- Tensor network study of the spin-1/2 square-lattice -- model: incommensurate spiral order, mixed valence-bond solids, and multicritical points
- Equivalence of single-particle and transport lifetimes from hybridization fluctuations
- Magneto-Thermoelectric Transport in Graphene Quantum Dot with Strong Correlations
- Resonating Valence Bond States in an Electron-Phonon System
- Strange metals and black holes: insights from the Sachdev-Ye-Kitaev model
- Monte Carlo study of thermal fluctuations and Fermi-arc formation in d-wave superconductors
- The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions
- Emergence of nodal Bogoliubov quasiparticles across the transition from the pseudogap metal to the d-wave superconductor
- Disordered quantum critical fixed points from holography
- Quantum statistical mechanics of the Sachdev-Ye-Kitaev model and charged black holes
- Deconfined quantum criticality of nodal -wave superconductivity, Néel order, and charge order on the square lattice at half-filling
- The correlation between the Nernst effect and fluctuation diamagnetism in strongly fluctuating superconductors
- Polaronic correlations from optimized ancilla wave functions for the Fermi-Hubbard model
- Strange metals and planckian transport in a gapless phase from spatially random interactions
- Quantum Oscillation as Diagnostics of Pseudogap State in Underdoped Cuprates
- Quantum oscillations in the hole-doped cuprates and the confinement of spinons
- Conductance and thermopower fluctuations in interacting quantum dots
- Robust d-wave superconductivity from the Su-Schrieffer-Heeger-Hubbard model: possible route to high-temperature superconductivity
- Intertwined Orders and the Physics of High Temperature Superconductors
- Observation of the Yamaji effect in a cuprate superconductor
- Extended strange metal regime from superconducting puddles
- Breakdown of order-fractionalization in the CPT model
- Quantum spin liquid from electron-phonon coupling
- Marginal Fermi liquid at magnetic quantum criticality from dimensional confinement
- Quantum Critical Phase and Lifshitz Transition in an Extended Periodic Anderson Model
- On the origin of the Fermi arc phenomena in the underdoped cuprates: signature of KT-type superconducting transition
- What do we learn from impurities and disorder in High Tc cuprates?
- Vortex structure in a -wave superconductor obtained by a confinement transition from the pseudogap metal
- Strange metal from spin fluctuations in a cuprate superconductor
- Strong non-linear response of strange metals
- Spin-charge bound states and emerging fermions in a quantum spin liquid
- Canted magnetism and fractionalization in metallic states of the Lieb lattice Hubbard model near quarter filling
- Fermionic spinon theory of the hourglass spin excitation spectrum of the cuprates
- Superlinear Hall angle and carrier mobility from non-Boltzmann magnetotransport in the spatially disordered Yukawa-Sachdev-Ye-Kitaev model on a square lattice
- Aspects of the normal state resistivity of cuprate superconductors Bi2201, Tl2201 and Hg1201
- Thermopower across Fermi-volume-changing quantum phase transitions without translational symmetry breaking
- Mott Criticality as the Confinement Transition of a Pseudogap-Mott Metal