Abstract
The Schwinger-boson theory of the frustrated square lattice antiferromagnet yields a stable, gapped $\mathbb{Z}_2$ spin liquid ground state with time-reversal symmetry, incommensurate spin correlations and long-range Ising-nematic order. We obtain an equivalent description of this state using fermionic spinons (the fermionic spinons can be considered to be bound states of the bosonic spinons and the visons). Upon doping, the $\mathbb{Z}_2$ spin liquid can lead to a fractionalized Fermi liquid (FL*) with small Fermi pockets of electron-like quasiparticles, while preserving the $\mathbb{Z}_2$ topological and Ising-nematic orders. We describe a Higgs transition out of this deconfined metallic state into a confining superconducting state which is usually of the Fulde-Ferrell-Larkin-Ovchinnikov type, with spatial modulation of the superconducting order.
Highlights
The spatially constant parts of the induced hopping amplitudes will just renormalize the bare hopping of the c fermions, but the terms at QCDW = QP DW = (0, π) correspond to a density wave with form factor PQCDW (k) = c1 cos(2kx) + c2 cos(2ky), which is of the s + d type
While several recent experiments23,24 have been consistent with a FL* model for the pseudogap metal at higher temperatures, the most recent Hall effect measurements25 indicate that the FL* model may well extend down to low temperatures just below optimal doping
In the light of this, it is useful to catalog the confinement instabilities of the simplest FL* state, the Z2-FL*. The excitations of this state invariably transform non-trivially under global symmetries of the model, and so the confinement transition is simultaneous with some pattern of symmetry breaking
Summary
The Z2 spin liquid is the simplest gapped quantum state with time-reversal symmetry and bulk anyon excitations. In most cases, for a set of symmetry operations O combining to identity, the phase factor picked up by the fermionic spinon σO is just the product of the phase σOe picked up by the bosonic spinon and the phase σOm picked up by the vison These have been referred to as the trivial fusion rules in Ref. 34. Once these fusion rules are known, the symmetry fractionalization quantum numbers for the can be calculated from those of e and m With this preamble, we outline the procedure to derive the fermionic spin liquid ansatz corresponding to the bosonic Z2 spin liquid obtained from the J1-J2-J3 antiferromagnetic Hamiltonian on the square lattice. We derive the non-trivial fusion rules, and use these to relate the bosonic and fermionic symmetry quantum numbers of time-reversal preserving mean-field spin liquids on the rectangular lattice. We find the specific set of quantum numbers for the fermionic spin liquid of our interest, and find an ansatz consistent with this particular pattern of symmetry fractionalization
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