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

TL;DR

This paper develops a unified fermionic gauge theory framework for deconfined quantum criticality on both square and Shastry-Sutherland lattices, revealing shared low-energy structures and critical behaviors, and connecting numerical findings with field-theoretic models.

Contribution

It introduces a continuum fermionic gauge theory for the Shastry-Sutherland lattice, showing its equivalence to the square lattice case at criticality, and analyzes the critical exponents and stability of the SO(5) deconfined critical point.

Findings

Shared low-energy field-theoretic structure between square and Shastry-Sutherland lattices.

Identification of the SO(5) critical point as a conformal deconfined criticality.

Enhanced Néel and VBS susceptibilities consistent with fermionic deconfined quantum 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 SU(2) $\pi$-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 N\'eel 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.