Lectures on insulating and conducting quantum spin liquids

Abstract

Two of the iconic phases of the hole-doped cuprate materials are the intermediate temperature pseudogap metal and the lower temperature d-wave superconductor. Following the prescient suggestion of P.~W.~Anderson, there were numerous early theories of these phases as doped quantum spin liquids. However, these theories have had difficulties with two prominent observations: (i) angle-dependent magnetoresistance measurements (ADMR), including observation of the Yamaji effect, present convincing evidence of small hole pockets which can tunnel coherently between square lattice layers, and (ii) the velocities of the nodal Bogoliubov quasiparticles in the d-wave superconductor are highly anisotropic, with v_F >> v_\Delta. These lecture notes review how the fractionalized Fermi Liquid (FL*) state, which dopes quantum spin liquids with gauge-neutral electron-like quasiparticles, resolves both difficulties. Theories of quantum spin liquids employing fractionalization of the electron spin into bosonic and fermionic partons are reviewed. In the early theories, upon doping, the bosonic parton theory leads to a candidate holon metal theory of the pseudogap, while the fermionic parton theory leads to a d-wave superconductor. The construction of the FL* state is described using a quantum dimer model, followed by a more realistic description using the Ancilla Layer Model (ALM). Computations using the ALM resolve the difficulties in both the pseudogap metal and the d-wave superconductor.