Quantum phase transitions of antiferromagnets and the cuprate superconductors

Abstract

I begin with a proposed global phase diagram of the cuprate superconductors as a function of carrier concentration, magnetic field, and temperature, and highlight its connection to numerous recent experiments. The phase diagram is then used as a point of departure for a pedagogical review of various quantum phases and phase transitions of insulators, superconductors, and metals. The bond operator method is used to describe the transition of dimerized antiferromagnetic insulators between magnetically ordered states and spin-gap states. The Schwinger boson method is applied to frustrated square lattice antiferromagnets: phase diagrams containing collinear and spirally ordered magnetic states, Z_2 spin liquids, and valence bond solids are presented, and described by an effective gauge theory of spinons. Insights from these theories of insulators are then applied to a variety of symmetry breaking transitions in d-wave superconductors. The latter systems also contain fermionic quasiparticles with a massless Dirac spectrum, and their influence on the order parameter fluctuations and quantum criticality is carefully discussed. I conclude with an introduction to strong coupling problems associated with symmetry breaking transitions in two-dimensional metals, where the order parameter fluctuations couple to a gapless line of fermionic excitations along the Fermi surface.

49 pages, 19 figures; Lectures at the Les Houches School on "Modern theories of correlated electron systems", France, May 2009; and at the Mahabaleshwar Condensed Matter School, International Center for Theoretical Sciences, India, Dec 2009; (v2) expanded introductory discussion of cuprate phase diagram; (v2) corrected typos

References in corpus (41)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• "Deconfined" quantum critical points
• Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• An Intrinsic Bond-Centered Electronic Glass with Unidirectional Domains in Underdoped Cuprates
• Effects of Co substitution on thermodynamic and transport properties and anisotropic $H_{c2}$ in Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ single crystals
• Electronic liquid crystal state in the high-temperature superconductor YBCO(6.45)
• Electron pockets in the Fermi surface of hole-doped high-Tc superconductors
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Anomalous suppression of the orthorhombic distortion in superconducting Ba[Fe(1-x)Cox]2As2
• Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order
• Theory of interacting electrons on the honeycomb lattice
• Quantum Magnets under Pressure: Controlling Elementary Excitations in TlCuCl3
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Spin correlations in the electron-doped high-transition-temperature superconductor Nd{2-x}Ce{x}CuO{4+/-delta}
• Unconventional pairing in the iron arsenide superconductors
• Fermi Surface Evolution in an Electron-Doped High-Tc Superconductor Revealed by Magnetic Quantum Oscillations
• Tuning competing orders in La2-xSrxCuO4 cuprate superconductors by the application of an external magnetic field
• Renormalization group theory of nematic ordering in d-wave superconductors
• Magnetic-field-enhanced incommensurate magnetic order in the underdoped high-temperature superconductor YBa(2)Cu(3)O(6.45)
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Theory of the nodal nematic quantum phase transition in superconductors
• Condensed matter and AdS/CFT
• Competition between spin density wave order and superconductivity in the underdoped cuprates
• Fluctuating spin density waves in metals
• Instabilities near the onset of spin density wave order in metals
• Effective theory of Fermi pockets in fluctuating antiferromagnets
• Dynamics and transport of the Z_2 spin liquid: application to kappa-(ET)2Cu2(CN)3
• Magnetic Breakdown in the electron-doped cuprate superconductor Nd${}_{2-x}$Ce${}_x$CuO${}_4$: the reconstructed Fermi surface survives in the strongly overdoped regime
• Compensated electron and hole pockets in an underdoped high Tc superconductor
• Field-induced soft-mode quantum phase transition in La${}_{1.855}$Sr${}_{0.145}$CuO${}_4$
• Destruction of Neel order in the cuprates by electron-doping
• Paired electron pockets in the hole-doped cuprates
• The underdoped cuprates as fractionalized Fermi liquids: transition to superconductivity
• Nodal quasiparticles and the onset of spin density wave order in the cuprates
• Quantum criticality and the phase diagram of the cuprates
• Signatures of the nematic ordering transitions in the thermal conductivity of d-wave superconductors
• A Common Thread
• Spin-density-wave order in cuprates
• Magnetism and Superconductivity in CeRhIn5
• Quantum phase transitions in $d-wave$ superconductors

Cited by in corpus (14)

• Identifying Topological Order by Entanglement Entropy
• Magnetic Cluster Excitations
• Neutron scattering study of the magnetic phase diagram of underdoped YBa(2)Cu(3)O(6+x)
• Elastocaloric determination of the phase diagram of Sr${}_2$RuO${}_4$
• How many quantum phase transitions exist inside the superconducting dome of the iron pnictides?
• Unusual magnetic phases in the strong interaction limit of two-dimensional topological band insulators in transition metal oxides
• Fractionalized Fermi liquid with bosonic chargons as a candidate for the pseudogap metal
• Emergent gauge fields and the high temperature superconductors
• Evolution of the Superconductivity Dome in the two dimensional Hubbard Model
• Quantum phase transition in a two-dimensional Kondo-Heisenberg model: a Schwinger-boson large-N approach
• Three-body bound states in antiferromagnetic spin ladders
• Symmetry Transmutation and Anomaly Matching
• Fermionic spectral functions in backreacting p-wave superconductors at finite temperature
• Critical anomalous metals near superconductivity in models with random interactions