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arXiv:2503.20122

Deconfined Gapless phases and criticalities in Shastry-Sutherland Antiferromagnet

Chen, Lvcheng, Zheng-Xin Liu

Published Mar 26, 2025• 0 citations
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Abstract

Antiferromagnets on the Shastry-Sutherland lattice have attracted lots of research interest due to the possible existence of deconfined criticality. In the present work, we study the $J_1$-$J_2$-$J_r$ model using Variational Monte Carlo (VMC) method, where $J_1$, $J_2$, $J_r$ stand for the nearest-neighbor, next nearest neighbor and ring exchange interactions respectively. An empty plaquette (EP) phase with spontaneous mirror symmetry breaking is reproduced. However, the EP phase in the VMC approach is $Z_2$ deconfined and have Majorana-type gapless spinon excitations, which is qualitatively different from the EP phase in literature. The central observation of the present study is the gapless $Z_2$ Quantum spin liquid phase resulting from the competition between the EP phase, the full plaquette (FP) phase and the antiferromagnetic Néel phase. While the phase transition from the $Z_2$ QSL phase to the EP phase is likely of Landau-Ginzburg type, the continuous transitions to the confined FP and Néel phases are exotic and need to be further explored.

DOI
10.48550/arxiv.2503.20122

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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.
We study the ground-state phase diagram of the Shastry-Sutherland model by using a variational optimization of the infinite tensor network states, and identify a weakly first-order transition between the plaquette valence bond solid and the antiferromagnetic states. The full plaquette state is found to strongly compete with the empty plaquette ground state, and can be stabilized as the ground state when a staggered ring-exchange interaction preserving the Shastry-Sutherland lattice symmetry is introduced. We propose the triple point where the full plaquette, empty plaquette, and antiferromagnetic phases meet as a deconfined quantum critical point (DQCP). The analysis of susceptibilities provides evidence of an emergent SO(5)\text{SO}(5)SO(5) symmetry at this point. These results shed light on the study of DQCP in quantum magnets and provide a way to understand the proximate DQCP signatures in recent experiments on SrCu2(BO3)2{\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}SrCu2​(BO3​)2​.
Based on a special variant of plaquette expansion, an operator is constructed whose eigenvalues give the low-energy singlet spectrum of spin-12\frac1221​ Heisenberg antiferromagnet on square lattice with nearest- and frustrating next-nearest-neighbor exchange couplings J1J_1J1​ and J2J_2J2​. It is well known that a non-magnetic phase arises in this model at 0.4≲J2/J1≲0.60.4\lesssim J_2/J_1\lesssim 0.60.4≲J2​/J1​≲0.6 sandwiched by two Neel ordered phases. In agreement with previous results, we observe a first-order quantum phase transition (QPT) at J2≈0.64J1J_2\approx 0.64J_1J2​≈0.64J1​ from the non-magnetic phase to the Neel one. Large gap (≳0.4J1\gtrsim0.4J_1≳0.4J1​) is found in the singlet spectrum at J2<0.64J1J_2<0.64J_1J2​<0.64J1​ that excludes a gapless spin-liquid state at 0.4≲J2/J1≲0.60.4\lesssim J_2/J_1\lesssim 0.60.4≲J2​/J1​≲0.6 and the deconfined quantum criticality scenario for the QPT to another Neel phase. We observe a first-order QPT at J2≈0.55J1J_2\approx 0.55J_1J2​≈0.55J1​ presumably between two non-magnetic phases.