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arXiv:2501.00096

Evidence for a $\mathbb{Z}_{2}$ Dirac spin liquid in the generalized Shastry-Sutherland model

Atanu Maity, Francesco Ferrari, Sylvain Capponi, Karlo Penc, Janik Potten, Müller, Tobias, Feuerpfeil, Andreas, Ronny Thomale, Jong Yeon Lee, Rhine Samajdar, Yasir Iqbal

Published Dec 30, 2024• 1 citation
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Abstract

We present a multimethod investigation of the recently reported quantum spin liquid (QSL) phase in the spin-1/2 Heisenberg antiferromagnet on the Shastry-Sutherland lattice. A comprehensive projective symmetry group classification of fermionic mean-field Ansätze on this lattice yields 46 U(1) and 80 $\mathbb{Z}_2$ states. Using density-matrix renormalization group (DMRG) and exact diagonalization, we find that the Shastry-Sutherland model and the square-lattice $J_1$-$J_2$ Heisenberg antiferromagnet share the same QSL phase. We therefore map our Ansätze to those on the square lattice and identify the counterpart of the square-lattice $\mathbb{Z}_2$ Dirac QSL (Z2Azz13) in the Shastry-Sutherland system. Using state-of-the-art variational Monte Carlo with Gutzwiller-projected wavefunctions improved by Lánczos steps, we demonstrate excellent agreement in energies and correlation functions between a gapless (Dirac) $\mathbb{Z}_2$ spin liquid, characterized by only a few variational parameters, and results from neural quantum states and DMRG. Within a unified variational family that continuously connects the spin liquid to the adjacent Néel and plaquette valence-bond-crystal states, we locate both phase boundaries in an unbiased way from order-parameter finite-size scaling and correlation-ratio crossings, and find that both order parameters vanish continuously. Finally, the recently developed Keldysh formulation of the pseudo-fermion functional renormalization group yields a dynamical spin structure factor with features consistent with Dirac cones, providing strong independent evidence for a Dirac QSL ground state. Our identification of a $d$-wave pairing $\mathbb{Z}_2$ Dirac QSL is consistent with recently observed signatures of QSL behavior in Pr$_2$Ga$_2$BeO$_7$ and makes predictions for future experiments.

DOI
10.48550/arxiv.2501.00096

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