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arXiv:2605.24409

Spiral and Mixed Plaquette-Dimer Phases in the $S=1$ and $3/2$ Shastry-Sutherland Heisenberg Model

Han-Qing Wu, Muwei Wu, Shou-Shu Gong

Published May 23, 2026• 0 citations
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Abstract

We investigate the ground-state phase diagram of the $S=1$ and $S=3/2$ Heisenberg model on the two-dimensional Shastry-Sutherland lattice (SSL) using density matrix renormalization group (DMRG) and cluster mean-field theory (CMFT). Between the dimer phase and Néel antiferromagnetic phases, we identify two intermediate phases: a mixed plaquette-dimer (MPD) phase and a spiral phase. These phases are characterized via bond energies and spin-spin correlation functions; phase boundaries are located from the ground-state energy derivative and entanglement entropy. The MPD phase exhibits strong intradimer correlations and weak tetramerization on the empty plaquettes, and its transitions to the dimer and spiral phases are first order. Combining our results with the known boundaries for $S=1/2$ and the classical limit $S\to\infty$, we construct a global $S$-$g$ phase diagram. This diagram reveals the progressive suppression of quantum effects with increasing $S$ and offers a theoretical framework for larger-$S$ SSL materials.

DOI
10.48550/arxiv.2605.24409

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Spiral and Mixed Plaquette-Dimer Phases in the S=1S=1S=1 and 3/23/23/2 Shastry-Sutherland Heisenberg Model
We investigate the ground-state phase diagram of the S=1S=1S=1 and S=3/2S=3/2S=3/2 Heisenberg model on the two-dimensional Shastry-Sutherland lattice (SSL) using density matrix renormalization group (DMRG) and cluster mean-field theory (CMFT). Between the dimer phase and Néel antiferromagnetic phases, we identify two intermediate phases: a mixed plaquette-dimer (MPD) phase and a spiral phase. These phases are characterized via bond energies and spin-spin correlation functions; phase boundaries are located from the ground-state energy derivative and entanglement entropy. The MPD phase exhibits strong intradimer correlations and weak tetramerization on the empty plaquettes, and its transitions to the dimer and spiral phases are first order. Combining our results with the known boundaries for S=1/2S=1/2S=1/2 and the classical limit S→∞S\to\inftyS→∞, we construct a global SSS-ggg phase diagram. This diagram reveals the progressive suppression of quantum effects with increasing SSS and offers a theoretical framework for larger-SSS SSL materials.
Frustrated spin-1/2 model with all-antiferromagnetic exchange on Shastry-Sutherland lattice (SSL) has been extensively explored, and in this work we study the quantum phase diagram of isotropic Heisenberg spin- 1 / 2 model on the SSL with ferromagnetic exchange interactions along leg, and antiferromagnetic couplings along the diagonal bonds ( J ). Using density matrix renormalization group (DMRG) and exact diagonalization calculations, we identify four distinct ground-state (gs) phases for this frustrated spin-1/2 model: stripe ( π , 0 ) , stripe ( 0 , π ) , ferromagnetic, and spiral-dimer phases. In the spiral-dimer phase the gs can exhibit dimer formation along the diagonal bonds with or without spins spiral along the x axis or y axis in different parameter regime and these states are connected through crossovers. There is a continuous transition between stripe with a long-range spin-spin correlations and spiral-dimer phase with a short-range correlations. An effective spin parameter is introduced to accurately determine the phase boundaries. Our DMRG results differ significantly from previous Schwinger boson mean-field theory predictions. The spiral phase occurs in a narrow range of the parameter space and shows short-range correlations in the system.
We investigate the ground-state phase diagram of the SSS=1/2 XXZ model on the two-dimensional Shastry-Sutherland lattice using exact diagonalization (ED), density-matrix renormalization group (DMRG), and cluster mean-field theory (CMFT) with DMRG as a solver. In the isotropic case (Δ=1Δ=1Δ=1), CMFT results reveal an intermediate empty plaquette (EP) phase that has a lower energy than the full plaquette (FP) phase. However, due to mean-field artifacts, CMFT alone is not suitable for accurately determining phase boundaries. Therefore, we combined three methods to map out the reliable phase diagram. Our calculations show that the EP phase narrows as ΔΔΔ deviates from unity and eventually vanishes. More importantly, we identify a spiral phase at small ΔΔΔ, which has not been reported in previous studies. This phase is clearly captured by DMRG simulations on long cylindrical geometries. The competition between the EP, spiral, and xyxyxy-AFM phases near their boundaries provides a plausible explanation for the emergent spin-liquid-like behavior in RE2_22​Be2_22​GeO2_22​, while shedding new light on the role of XXZ anisotropy in the Shastry-Sutherland XXZ model.
The ground state (gs) of antiferromagnetically coupled dimers on the Shastry-Sutherland lattice (SSL) stabilizes many exotic phases and has been extensively studied. The gs properties of ferromagnetically coupled dimers on SSL are equally important but unexplored. In this model the exchange coupling along the xxx-axis (JxJ_xJx​) and yyy-axis (JyJ_yJy​) are ferromagnetic and the diagonal exchange coupling (JJJ) is antiferromagnetic. In this work we explore the quantum phase diagram of ferromagnetically coupled dimer model numerically using density matrix renormalization group (DMRG) method. We note that in JxJ_xJx​-JyJ_yJy​ parameter space this model exhibits six interesting phases:(I) stripe (0,π)(0,π)(0,π), (II) stripe (π,0)(π,0)(π,0), (III) perfect dimer, (IV) XXX-spiral, (V) YYY-spiral and (VI) ferromagnetic phase. Phase boundaries of these quantum phases are determined using the correlation functions and gs energies. We also notice the correlation length in this system is less than four lattice units in most of the parameter regimes. The non-collinear behaviour in XXX-spiral and YYY-spiral phase and the dependence of pitch angles on model parameters are also studied.
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