Unifying Dirac spin liquids on square and Shastry–Sutherland lattices via fermionic deconfined criticality

Abstract

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 \mathrm{SU}(2) S U ( 2 ) \pi π -flux parent state, we construct a continuum theory of Dirac spinons coupled to an \mathrm{SU}(2) S U ( 2 ) gauge field and adjoint Higgs fields whose condensates drive transitions to a staggered-flux \mathrm{U}(1) U ( 1 ) spin liquid and a gapless \mathbb{Z}_{2} 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 \mathrm{SO}(5) S O ( 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 \mathrm{SO}(5) S O ( 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} 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.

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BibTeX RIS

BibTeX

@article{feuerpfeil2026unifying,
  title = {{Unifying Dirac spin liquids on square and Shastry–Sutherland lattices via fermionic deconfined criticality}},
  author = {Andreas Feuerpfeil and Leyna Shackleton and Atanu Maity and Ronny Thomale and Subir Sachdev and Yasir Iqbal},
  journal = {SciPost},
  year = {2026},
  month = nov,
  doi = {10.21468/scipostphys.21.5.111},
  url = {http://scipost.org/SciPostPhys.21.5.111},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - Unifying Dirac spin liquids on square and Shastry–Sutherland lattices via fermionic deconfined criticality
AU  - Andreas Feuerpfeil
AU  - Leyna Shackleton
AU  - Atanu Maity
AU  - Ronny Thomale
AU  - Subir Sachdev
AU  - Yasir Iqbal
PY  - 2026
DA  - 2026/11/03
JO  - SciPost
DO  - 10.21468/scipostphys.21.5.111
UR  - http://scipost.org/SciPostPhys.21.5.111
AB  - 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 \mathrm{SU}(2) S U ( 2 ) \pi π -flux parent state, we construct a continuum theory of Dirac spinons coupled to an \mathrm{SU}(2) S U ( 2 ) gauge field and adjoint Higgs fields whose condensates drive transitions to a staggered-flux \mathrm{U}(1) U ( 1 ) spin liquid and a gapless \mathbb{Z}_{2} 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 \mathrm{SO}(5) S O ( 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 \mathrm{SO}(5) S O ( 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} 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.
SN  - 2542-4653
ER  -

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