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arXiv:2411.14114 · Physical review. B./Physical review. B

Dirac and chiral spin liquids on spin-1/2 square-lattice Heisenberg antiferromagnet

Hui-Ke Jin, Hong-Hao Tu, Ya-Hui Zhang

Published May 29, 2025• 1 citation
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Abstract

We revisit the challenging problem of identifying the quantum spin liquid candidate in the spin-1/2 $J_1$-$J_2$ Heisenberg antiferromagnet on the square lattice. By integrating the Gutzwiller-guided density matrix renormalization group method with analytical analyses, we present clear evidence that the ground state is a Z$_2$ Dirac spin liquid. This state can be efficiently described by a Gutzwiller-projected parton theory characterized by its projective symmetry group. To distinguish the difference between the projected Z$_2$ and U(1) parton state, we investigate the chiral spin liquid ground states as topological orders by incorporating a $J_χ$ term into the $J_1$-$J_2$ model and observe a transition from a Z$_2$ chiral spin liquid to a U(1)$_2$ chiral spin liquid as $J_χ$ increases.

DOI
10.1103/4yrt-nsth

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Evidence for a Z2\mathbb{Z}_{2}Z2​ Dirac spin liquid in the generalized Shastry-Sutherland model
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 Z2\mathbb{Z}_2Z2​ states. Using density-matrix renormalization group (DMRG) and exact diagonalization, we find that the Shastry-Sutherland model and the square-lattice J1J_1J1​-J2J_2J2​ 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 Z2\mathbb{Z}_2Z2​ 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) Z2\mathbb{Z}_2Z2​ 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 ddd-wave pairing Z2\mathbb{Z}_2Z2​ Dirac QSL is consistent with recently observed signatures of QSL behavior in Pr2_22​Ga2_22​BeO7_77​ and makes predictions for future experiments.
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