From high temperature supercondutivity to quantum spin liquid: progress in strong correlation physics

Abstract

This review gives a rather general discussion of high temperature superconductors as an example of a strongly correlated material. The argument is made that in view of the many examples of unconventional superconductors discovered in the past twenty years, we should no longer be surprised that superconductivity emerges as a highly competitive ground state in systems where Coulomb repulsion plays a dominant role. The physics of the cuprates is discussed, emphasizing the unusual pseudogap phase in the underdoped region. It is argued that the resonating valence bond (RVB) picture, as formulated using gauge theory with fermionic and bosonic matter fields, gives an adequate physical understanding, even though many details are beyond the powers of current calculational tools. The recent discovery of quantum oscillations in a high magnetic field is discussed in this context. Meanwhile, the problem of the quantum spin liquid (a spin system with antiferromagnetic coupling which refuses to order even at zero temperature) is a somewhat simpler version of the high $T_c$ problem where significant progress has been made recently. It is understood that the existence of matter fields can lead to de-confinement of the U(1) gauge theory in 2+1 dimensions, and novel new particles (called fractionalized particles), such as fermionic spinons which carry spin $\frac{1}{2}$ and no charge, and gapless gauge bosons can emerge to create a new critical state at low energies. We even have a couple of real materials where such a scenario may be realized experimentally. The article ends with answers to questions such as: what limits $T_c$ if pairing is driven by an electronic energy scale? why is the high $T_c$ problem hard? why is there no consensus? and why is the high $T_c$ problem important?

Submitted as "Key Issue" essay for Report of Progress in Physics; v2: References are added and typos corrected

References in corpus (59)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Angle-resolved photoemission spectroscopy of the cuprate superconductors
• Spin Liquid State in an Organic Mott Insulator with Triangular Lattice
• Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor
• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• The Nernst effect in high-$T_c$ superconductors
• Non Fermi-Liquid States and Pairing of a general Model of Copper-Oxide Metals
• Theory of Underdoped Cuprates
• Vanishing of phase coherence in underdoped Bi_2Sr_2CaCu_2O_8+d
• Antiferromagnetic Order Induced by an Applied Magnetic Field in a High-Temperature Superconductor
• Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)_2 Cu_2 (CN)_3
• U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to k-(BEDT-TTF)_2 Cu_2 (CN)_3
• Order and quantum phase transitions in the cuprate superconductors
• Topological approach to Luttinger's theorem and the Fermi surface of a Kondo lattice
• Distinct Fermi-Momentum Dependent Energy Gaps in Deeply Underdoped Bi2212
• Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3
• Two Energy Scales and two Quasiparticle Dynamics in the Superconducting State of Underdoped Cuprates
• On the stability of U(1) spin liquids in two dimensions
• STM Studies of the Electronic Structure of Vortex Cores in Bi2Sr2CaCu2O8+d
• The Unusual Superconducting State of Underdoped Cuprates
• The Ground State of the Pseudogap in Cuprate Superconductors
• Fermi Surface and Quasiparticle Excitations of overdoped Tl2Ba2CuO6+d by ARPES
• Competition between Antiferromagnetism and Superconductivity in High $T_c$ Cuprates
• Thermal Conductivity across the Phase Diagram of Cuprates: Low-Energy Quasiparticles and Doping Dependence of the Superconducting Gap
• Mott Transition, Antiferromagnetism, and d-wave Superconductivity in Two-Dimensional Organic Conductors
• An SU(2) Formulation of the t-J model: Application to Underdoped Cuprates
• Superconductivity in the two-dimensional t-J model
• Polaron in t-J model
• Mixed-State Quasiparticle Spectrum for d-wave Superconductors
• Pseudogap and high-temperature superconductivity from weak to strong coupling. Towards quantitative theory
• Quasi-two-dimensional organic superconductors: a review
• High Tc Superconductors -- A Variational Theory of the Superconducting State
• Spin correlations in the algebraic spin liquid - implications for high Tc superconductors
• Theory of spin excitations in undoped and underdoped cuprates
• Dynamic Stripes and Resonance in the Superconducting and Normal Phases of YBa2Cu3O6.5 Ortho-II Superconductor
• Enhancement of long-range magnetic order by magnetic field in superconducting La2CuO(4+y)
• Staggered-vorticity correlations in a lightly doped t-J model: a variational approach
• The Structure of the Pairing Interaction in the 2D Hubbard Model
• Enhancement of Pairing Correlation by t' in the Two-Dimensional Extende d t-J Model
• Superconductivity and a Mott Transition in a Hubbard Model on an Anisotropic Triangular Lattice
• Extending Luttinger's theorem to Z(2) fractionalized phases of matter
• What the resonance peak cannot do
• Angle-resolved photoemission spectra in the cuprates from the d-density wave theory
• Antiferromagnetic Vortex Core of Tl_2Ba_2CuO_{6+x} Studied by Nuclear Magnetic Resonance
• Relativity Restored: Dirac Anisotropy in QED${}_3$
• d-Wave Pairing Correlation in the Two-Dimensional t-J Model
• Two-Hole Bound States from a Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet
• Antiferromagnetism and phase separation in the t-J model at low doping: a variational study
• Cuprates as doped U(1) spin liquids
• Onset of a boson mode at superconducting critical point of underdoped YBa2Cu3Oy
• New mean field theory of the tt't''J model applied to the high-Tc superconductors
• Destruction of Neel order and local spin spirals in insulating La_{2-x}Sr_xCuO_4
• Phase String Theory for Doped Antiferromagnets
• Oxygen-isotope effect on the in-plane penetration depth in underdoped Y_{1-x}Pr_xBa_2Cu_3O_{7-delta} as revealed by muon-spin rotation
• QED${}_3$ on a space-time lattice: compact versus noncompact formulation
• Effective electron-phonon coupling and polaronic transition in the presence of strong correlation
• Fractionalization in Spin Liquid Mott Insulators: Vison Wavefunctions and Gaps
• Testing for topological order in variational wavefunctions for Z(2) spin liquids

Cited by in corpus (129)

• Magnetic-field-induced charge-stripe order in the high temperature superconductor YBa2Cu3Oy
• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain
• Spin transport in a tunable Heisenberg model realized with ultracold atoms
• Unconventional Superconductivity
• $\mu$SR evidence for the U(1) quantum spin liquid ground state in the triangular antiferromagnet YbMgGaO${}_4$
• Quasiparticle mass enhancement approaching optimal doping in a high-Tc superconductor
• Evidence for unusual superconducting correlations coexisting with stripe order in La(1.875)Ba(0.125)CuO(4)
• Spiral order by disorder and lattice nematic order in a frustrated Heisenberg antiferromagnet on the honeycomb lattice
• The Chemistry of Quantum Spin Liquids
• Imaging spinon density modulations in a 2D quantum spin liquid
• Evidence of Spin Frustration in Vanadium Diselenide Monolayer Magnet
• Magnetic properties of BaCdVO(PO_4)_2: a strongly frustrated spin-1/2 square lattice close to the quantum critical regime
• Z2 spin liquid in S=1/2 Heisenberg model on Kagome lattice: A projective symmetry group study of Schwinger-fermion mean-field states
• A Phenomenological Theory of the Anomalous Pseudogap Phase in Underdoped Cuprates
• Fermi Surface Evolution in an Electron-Doped High-Tc Superconductor Revealed by Magnetic Quantum Oscillations
• Superconductivity close to the Mott state: From condensed-matter systems to superfluidity in optical lattices
• Scale-free antiferromagnetic fluctuations in the S=1/2 kagome antiferromagnet herbertsmithite
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• Fermi pockets and quantum oscillations of the Hall coefficient in high temperature superconductors
• Spinon Fermi surface spin liquid in a triangular lattice antiferromagnet NaYbSe${}_2$
• The Finite Temperature Pairing Gap of a Unitary Fermi Gas by Quantum Monte Carlo Calculations
• The Paired Electron Crystal: order from frustration in the quarter-filled band
• Normal-state nodal electronic structure in underdoped high-Tc copper oxides
• Extension of the spin-1/2 frustrated square lattice model: the case of layered vanadium phosphates
• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• High-spin polaron in lightly doped CuO${}_2$ planes
• Quantum electrodynamics of intense laser-matter interactions: A tool for quantum state engineering
• Molecular Quantum Magnetism in LiZn2Mo3O8
• Stripes, spin resonance and $d_{x^2-y^2}-$pairing symmetry in FeSe-based layered superconductors
• Observation of the phononic Lamb shift with a synthetic vacuum
• Paired chiral spin liquid with a Fermi surface in S=1 model on the triangular lattice
• Microscopic spinon-chargon theory of magnetic polarons in the t-J model
• A synthesis of the phenomenology of the underdoped cuprates
• 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
• Theory of Raman response in three-dimensional Kitaev spin liquids: application to $\beta -$ and $\gamma -$Li${}_2$IrO${}_3$ compounds
• Electronic structure near the 1/8-anomaly in La-based cuprates
• Experimental signatures of quantum and topological states in frustrated magnetism
• Toolbox for Abelian lattice gauge theories with synthetic matter
• Doping dependence of the chemical potential and surface electronic structure in YBa2Cu3O6+x and La2-xSrxCuO4 using hard x-ray photoemission spectroscopy
• Microscopic magnetic modeling for the $S$=1/2 alternating chain compounds Na${}_3$Cu${}_2$SbO${}_6$ and Na${}_2$Cu${}_2$TeO${}_6$
• Competing order, Fermi surface reconstruction, and quantum oscillations in underdoped high temperature superconductors
• Meson formation in mixed-dimensional t-J models
• Superconductivity in high-$T_c$ and related strongly correlated systems from variational perspective: Beyond mean field theory
• Frustrated square lattice with spatial anisotropy: crystal structure and magnetic properties of PbZnVO(PO4)2
• Spin-order driven Fermi surface revealed by quantum oscillations in an underdoped high Tc superconductor
• The Valence Bond Glass phase
• Fermi Surface of the Electron-doped Cuprate Superconductor Nd_{2-x}Ce_xCuO_{4} Probed by High-Field Magnetotransport
• Confinement and Mott transitions of dynamical charges in 1D lattice gauge theories
• Generic Spiral Spin Liquids
• Local study of the insulating quantum kagome antiferromagnets YCu3(OH)6OxCl3-x (x=0,1/3)
• Spin-Peierls transition in TiPO${}_4$
• Spin Susceptibility in Underdoped Cuprates: Insights from a Stripe-Ordered Crystal
• Many-body non-Hermitian skin effect under dynamic gauge coupling
• Conditions for magnetically induced singlet d-wave superconductivity on the square lattice
• Chiral Dynamics of Ultracold Atoms under a Tunable SU(2) Synthetic Gauge Field
• Quasi-two-dimensional $S=1/2$ magnetism of Cu[C${}_6$H${}_2$(COO)${}_4$][C${}_2$H${}_5$NH${}_3$]${}_2$
• Magnetic model for A2CuP2O7 (A = Na, Li) revisited: 1D versus 2D behavior
• On infrared pseudogap in cuprate and pnictide high-temperature superconductors
• Microscopic model of (CuCl)LaNb2O7: coupled spin dimers replace a frustrated square lattice
• Mott-driven BEC-BCS crossover in a doped spin liquid candidate, kappa-(BEDT-TTF)4Hg2.89Br8
• Quasiparticle self-consistent GW study of cuprates: electronic structure, model parameters, and the two-band theory for Tc
• Chemical potential oscillations from a single nodal pocket in the underdoped high-Tc superconductor YBa2Cu3O6+x
• Few-body systems capture many-body physics: tensor network approach
• General procedure for determining braiding and statistics of anyons using entanglement interferometry
• Topological spin ordering via Chern-Simons superconductivity
• Probing the connections between superconductivity, stripe order, and structure in La1.905Ba0.095Cu1-yZnyO4
• Angle dependent quasiparticle weights in correlated metals
• Magnetic monopole plasma phase in (2+1)d compact quantum electrodynamics with fermionic matter
• A Field Theory for Fermionic Ladder with Generic Intrachain Interactions
• Lifshitz quantum phase transitions and Fermi surface transformation with hole doping in high-$T_c$ superconductors
• Andreev and Single Particle Tunneling Spectroscopies in Underdoped Cuprates
• Mechanism of the insulator-to-metal transition and superconductivity in the spin liquid candidate NaYbSe${}_2$ under pressure
• Signatures of fractional statistics in nonlinear pump-probe spectroscopy
• CaCu2(SeO3)2Cl2: spin-1/2 Heisenberg chain compound with complex frustrated interchain couplings
• A computational approach to a doped antiferromagnet: correlations between two spin-polarons in the lightly doped CuO${}_2$ plane
• Simulating strongly interacting Hubbard chains with the Variational Hamiltonian Ansatz on a quantum computer
• Unconventional metallic conduction in two-dimensional Hubbard-Wigner lattices
• Aharonov-Bohm interference for a hole in a two-dimensional Ising antiferromagnet in a transverse magnetic field
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Featureless quantum paramagnet with frustrated criticality and competing spiral magnetism on spin-1 honeycomb lattice magnet
• Inhomogeneous Kondo-lattice in geometrically frustrated Pr${}_2$Ir${}_2$O${}_7$
• Signature of Quantum Entanglement in NH4CuPO4.H2O
• One-Dimensional Fermions with neither Luttinger-Liquid nor Fermi-Liquid Behavior
• Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state
• Superconductivity generated by coupling to a Cooperon in a 2-dimensional array of 4-leg Hubbard ladders
• Hall effect and symmetry breaking in non-magnetic metal with dynamic charge stripes
• Dynamic formation of quasicondensate and spontaneous vortices in a strongly interacting Fermi gas
• Critical-doping universality for cuprate superconductors: Oxygen nuclear-magnetic-resonance investigation of Ca(x)La(1-x)Ba(1.75-x)La(0.25+x)Cu(3)O(y)
• Phase-sensitive evidence for dx2-y2-pairing symmetry in the parent-structure high-Tc cuprate superconductor Sr1-xLaxCuO2
• Stretched exponential spin relaxation in organic superconductors
• Confinement in 1+1D ${\mathbb{Z}}_2$ Lattice Gauge Theories at Finite Temperature
• Hole pairing from attraction of opposite chirality spin vortices: Non-BCS superconductivity in Underdoped Cuprates
• Dynamical correlations in the spin-half two-channel Kondo model
• Real space inhomogeneities in high temperature superconductors: the perspective of two-component model
• Magnetic breakdown in ortho-II high-temperature cuprates
• The role of the lattice structure in determining the magnon-mediated interactions between charge carriers doped into a magnetically ordered background
• Projected d-wave superconducting state: a fermionic projected entangled pair state study
• Nanoscale phase separation and pseudogap in the hole-doped cuprates from fluctuating Cu-O-Cu bonds
• Spatially modulated susceptibility in thin film La${}_{2-x}$Ba${}_x$CuO${}_4$
• The Coming Decades of Quantum Simulation
• Lattice and orbital fluctuations in TiPO4
• Electronic and magnetic properties of the ionic Hubbard model on the striped triangular lattice at 3/4 filling
• Hydrodynamics of interacting spinons in the magnetized spin-$1/2$ chain with the uniform Dzyaloshinskii-Moriya interaction
• A simple model for in- and out-of-plane resistivities of hole doped cuprates
• The Isotope Effect in Superconductors
• Quantum Magnetic Properties in Perovskite with Anderson Localized Artificial Spin-1/2
• A case study of bilayered spin-$1/2$ square lattice compound [VO(HCOO)${}_2\cdot$(H${}_2$O)]
• Interleaved bond frustration in a triangular lattice antiferromagnet
• SU(2) approach to the pseudogap phase of high-temperature superconductors: electronic spectral functions
• Bottom-up configuration-interaction emulations of ultracold fermions in entangled optical plaquettes: building blocks of unconventional superconductivity
• Diagnosing electronic phases of matter using photonic correlation functions
• Pairing tendencies in the doped Kitaev-Heisenberg model
• Role of electronic nematicity in the interplay between s- and d-wave broken-symmetry states
• Rényi entropy of quantum anharmonic chain at non-zero temperature
• Magnetic Moiré Systems: a review
• Quantum Covariance Scalar Products and Efficient Estimation of Max-Ent Projections
• Many-body tunneling in a double-well potential
• A Unified Theory for the Cuprates, Iron-Based and Similar Superconducting Systems: Application for Spin and Charge Excitations in the Hole-Doped Cuprates
• $2{\mathbf{k}}_{\mathbf{F}}$ Density Wave Instability of Composite Fermi Liquid
• Computational scheme for the spin-1/2 square lattice Heisenberg antiferromagnet based on an octapartite description of the square lattice
• Even-odd effect in multilayer Kitaev honeycomb magnets
• Solving local constraint conditions in slave particle theory
• Comments on the d-wave pairing mechanism for cuprate high $T_c$ superconductors: Higher is different?
• Electron correlation effects and spin-liquid state in the Herbertsmithite Kagome lattice
• Surface Functional Renormalization Group for Layered Quantum Materials
• Non-Fermi Liquid Behavior of the $t$-$J$ Model in the Strange Metal Phase: $U(1)$ Gauge Theory Consistent with Local Constraints