Unifying Dirac Spin Liquids on Square and Shastry-Sutherland Lattices via Fermionic Deconfined Criticality

We present a fermionic gauge theory for deconfined quantum criticality on the Shastry-Sutherland lattice and reveal its shared low-energy field-theoretic structure with the square lattice. Starting from an SU(2) $π$-flux parent state, we construct a continuum theory of Dirac spinons coupled to an SU(2) gauge field and adjoint Higgs fields whose condensates drive transitions to a staggered-flux U(1) spin liquid and a gapless $\mathbb{Z}{2}$ Dirac spin liquid. While the Shastry-Sutherland lattice permits additional symmetry-allowed fermion bilinears compared to the square lattice, the quantum field theories are identical up to additional irrelevant terms. Consequently, the Higgs potential structure and the leading low-energy theory coincide with the square-lattice case at the quantum critical point. The SO(5) critical point is expected to realize conformal deconfined criticality: we analyze it in a large flavor expansion, calculate its critical exponents, and identify the Yukawa coupling between the fermions and Higgs fields as the relevant perturbation that destabilizes it, consistent with pseudocritical behavior observed in recent Monte Carlo studies. We show that the emergent SO(5) order parameter acquires a large anomalous dimension at the critical point, leading to strongly enhanced Néel and VBS susceptibilities-a hallmark of fermionic deconfined quantum criticality consistent with numerical studies. Our results place recent numerical evidence for a gapless $\mathbb{Z}{2}$ Dirac spin liquid on the Shastry-Sutherland lattice within a controlled field-theoretic framework and demonstrate that fermionic deconfined criticality on the square lattice-including critical exponents and stability-extends to frustrated lattices with reduced symmetry.

💡 Research Summary

This paper develops a fermionic gauge‑theory description of deconfined quantum criticality on the Shastry‑Sutherland lattice and demonstrates that its low‑energy field‑theoretic structure is essentially identical to that previously established for the square lattice. Starting from an SU(2) π‑flux “parent” spin‑liquid state, the authors construct a continuum theory in which massless Dirac spinons are minimally coupled to an emergent SU(2) gauge field and to three real adjoint Higgs fields. Condensation of these Higgs fields reduces the gauge symmetry either to U(1) (producing a staggered‑flux U(1) spin liquid) or to Z₂ (producing a gapless Z₂ Dirac spin liquid, denoted Z3000).

Because the Shastry‑Sutherland lattice has fewer point‑group symmetries than the square lattice, its projective symmetry group (PSG) permits additional fermion bilinears and gradient terms. The authors perform a systematic PSG analysis and show that all such extra operators have scaling dimensions that render them irrelevant at the putative critical point. Consequently, the leading part of the continuum Lagrangian – the Dirac fermions, the SU(2) gauge field, the three Higgs fields, and their Yukawa couplings – is identical to the square‑lattice theory and enjoys a global SO(5) symmetry that rotates the Néel vector and the VBS order‑parameter tensor into one another.

The paper then carries out a controlled large‑N_f, N_b expansion (with N_f = 2 fundamental Dirac flavors and N_b = 2 adjoint Higgs fields). One‑loop calculations of the fermion and boson self‑energies yield renormalization‑group (RG) equations for the gauge coupling g and the Yukawa coupling λ_Y. The gauge coupling flows to a stable infrared fixed point g* ∝ √ε (ε = 4 − d), while λ_Y is weakly relevant: β(λ_Y) ≈ ε λ_Y − C λ_Y³. At the fixed point with exact SO(5) symmetry the anomalous dimension of the SO(5) order parameter is found to be large (η_O ≈ 1.1), implying strongly enhanced Néel and VBS susceptibilities, a hallmark of fermionic deconfined criticality that has been observed in recent Monte‑Carlo studies of J‑Q models.

Because λ_Y ultimately destabilizes the SO(5) fixed point at the lowest energies, the theory predicts a pseudocritical regime: over a broad intermediate energy window the system behaves as if it were at a conformal SO(5) fixed point before flowing away. This scenario explains the “walking” behavior and the apparent emergent SO(5) symmetry reported in numerical simulations on both square and Shastry‑Sutherland lattices.

The authors also discuss experimental relevance. In the real material SrCu₂(BO₃)₂, hydrostatic pressure tunes the ratio J_d/J_s, which in the gauge‑theory language corresponds to varying the Higgs condensates. The theory predicts a sequence of phases—Néel → Z₂ Dirac spin liquid → VBS—accessible by pressure, with characteristic signatures such as anomalous heat‑capacity scaling, enhanced spin‑structure factor at the Néel and VBS wavevectors, and possible detection of gapless Dirac spinons via thermal transport.

In summary, the work establishes that the fermionic deconfined critical point with SO(5) symmetry, previously studied on the square lattice, extends unchanged (up to irrelevant operators) to the frustrated Shastry‑Sutherland geometry. It provides analytical expressions for critical exponents, clarifies the role of Yukawa couplings as the leading destabilizing perturbation, and connects these field‑theoretic results to recent numerical evidence for a gapless Z₂ Dirac spin liquid and pseudocritical behavior in frustrated quantum magnets.