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We develop a numerical technique based on the pseudofermion functional renormalization group (PFFRG) to calculate hopping and pairing amplitudes of emergent spinon quasiparticles in spin-1/2 quantum spin liquids. Within this approach, we first formulate a self-consistent Fock-like equation for these amplitudes where instead of the bare propagators and couplings we use the fully renormalized ones from PFFRG. We solve these equations using different ansätze for the hoppings and pairings which we take from a projective symmetry group (PSG) classification. From the overall size of these amplitudes we identify which of the PSGs are preferably realized in the system. We apply this approach to the antiferromagnetic J1-J2 Heisenberg model on the square lattice and to the antiferromagnetic nearest neighbor Heisenberg model on the kagome lattice. For the J1-J2 model, we find that in the regime of maximal frustration (J1~J2/2) the largest amplitudes are obtained for a U(1) pi-flux state with a Dirac cone spinon dispersion. In the case of the kagome model we identify a gapless Z2 pi-flux state where the bands show a Dirac-cone-like structure at finite energies but also feature a small circular Fermi surface at zero energy. We discuss our findings and benchmark them against variational Monte Carlo results.

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Johannes Reuther, FU Berlin
Seminar Room 0.03, ETP
Contact: Simon Trebst