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

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• Magnetic properties of BaCdVO(PO_4)_2: a strongly frustrated spin-1/2 square lattice close to the quantum critical regime
• Fermi Surface Evolution in an Electron-Doped High-Tc Superconductor Revealed by Magnetic Quantum Oscillations
• 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
• Extension of the spin-1/2 frustrated square lattice model: the case of layered vanadium phosphates
• From itinerant to local-moment antiferromagnetism in Kondo lattices: Adiabatic continuity vs. quantum phase transitions
• Electronic structure near the 1/8-anomaly in La-based cuprates
• Competing order, Fermi surface reconstruction, and quantum oscillations in underdoped high temperature superconductors
• The Valence Bond Glass phase
• Conditions for magnetically induced singlet d-wave superconductivity on the square lattice
• Angle dependent quasiparticle weights in correlated metals
• Unconventional metallic conduction in two-dimensional Hubbard-Wigner lattices
• Dynamical correlations in the spin-half two-channel Kondo model
• SU(2) approach to the pseudogap phase of high-temperature superconductors: electronic spectral functions