Spin excitations of the Shastry-Sutherland model -- altermagnetism and deconfined quantum criticality

TL;DR

The paper investigates the PVBS-to-AFM transition in the frustrated spin-1/2 Shastry–Sutherland model to identify spectral signatures of a deconfined quantum critical point (DQCP) with emergent symmetry. Using state-of-the-art $i$PEPS$ tensor-network methods, ground and excited states are computed to obtain the dynamical structure factors and track low-energy modes across the transition. The AFM phase exhibits altermagnetic behavior with two split chiral magnons, while the PVBS phase hosts a triplet and a singlet mode; near the transition, the Higgs, triplet, and singlet gaps soften and their velocities converge, with four modes becoming degenerate at $(J/J')_c\approx 0.79$, signaling an emergent $O(4)$ DQCP. These results provide a concrete spectral fingerprint of deconfined criticality in a spin model and offer concrete guidance for experimental detection in SrCu$_2$(BO$_3$)$_2$ via INS and RIXS, highlighting the broader relevance to symmetry-enhanced quantum phase transitions.

Abstract

Frustrated quantum magnets can host a variety of exotic spin excitations, including fractionalized spin excitations coupled to emergent gauge fields at deconfined quantum critical points (DQCPs) and chiral magnons in altermagnets. Here, we investigate the spin excitation spectra of the highly frustrated $S=1/2$ antiferromagnetic (AFM) Shastry-Sutherland model, focusing on the evolution of low-energy collective modes from the Néel AFM phase to the plaquette valence bond solid (PVBS). We demonstrate that the AFM state exhibits altermagnetic behavior, characterized by a non-relativistic splitting between two chiral magnon bands. Furthermore, we identify two additional low-energy excitations: a Higgs mode in the longitudinal excitation channel and an $S=0$ excitation with vanishing spectral weight. As the system approaches the AFM-to-PVBS transition, both these modes soften along with the lowest-energy triplet and singlet modes in the PVBS state. The closing gap of the Higgs mode, combined with the nearly degenerate velocities of $S=1$ and $S=0$ excitations, provides spectral evidence that the AFM-to-PVBS transition is proximate to a DQCP with emergent $O(4)$ symmetry. Our results help clarify the spectral signature of a broad class of symmetry enhanced quantum phase transitions including deconfined quantum criticality.

Figures (11)

• Figure 1: (a): Sketch of the SS lattice and the corresponding altermagnetism. The two sublattices of the Néel state are connected by a $C_4$ rotation of the lattice about the center of the empty plaquette (without the dimer bond). A time-reversal symmetry then recovers the Néel order. (b): Sketched phase diagram of the SS model with $J/J^\prime$. The $J/J^\prime$ values at the two transitions are taken from Ref. Xi2023. (c): LSW dispersion in the AFM state of the SS model showing the chiral magnon bands with a non-zero splitting along the M$^\prime$-$\Gamma$-M direction of the Brillouin zone. $\mathcal{L}$($\mathcal{R}$) refers to the left(right)-handed chiral magnon bands.
• Figure 2: (a): Spin DSF in the AFM phase of the SS model calculated by the LSW theory. The inset shows high symmetric directions of the Brillouin zone. (b): Total spin DSF ($\mathcal{S}^{xx+yy+zz}$) in the AFM phase calculated by the iPEPS method with $D=3$ at $J/J^\prime=1.1$. (c): The transverse component ($\mathcal{S}^{xx+yy}$) of the results in (b). (d): The longitudinal component ($\mathcal{S}^{zz}$) of the results in (b). The red, black, and white lines with dots in (b) and (d) label the magnon, Higgs, and $S=0$ modes, respectively.
• Figure 3: (a): Spin DSF in the plaquette phase calculated by the iPEPS method with $D=3$ at $J/J^\prime=0.7$. The white line with dots shows the lowest singlet excitation. The magenta dashed line labels the dispersion of the triplet excitations in the bond-operator theory. (b): $J/J^\prime$ dependence of extracted gaps at the M point of the Brillouin zone for several low-energy excitation modes in the plaquette phase, including, from bottom to top, a triplet (in red), a singlet (in black), and a 7-fold multiplet (in blue). The results are obtained by the iPEPS method with $D=5$. The dashed line shows the gap of the triplet excitations in the bond-operator theory.
• Figure 4: (a): Evolution of low-energy collective (Higgs and Goldstone) modes across a DQCP with emergent O(4) symmetry. In the PVBS phase, the singlet (S) and triplet (T) modes serve as the Higgs and Goldstone modes associated with the emergent O(4) symmetry. In the AFM phase the Higgs mode (H) turns to a spin longitudinal mode (in black) whereas the singlet (S$^\prime$) and two magnon (M) modes constitute as the Goldstone modes. The DQCP is characterized by simultaneous gap closing of all four modes. (b): Similar to (a), but across a first-order transition with emergent O(4) symmetry. Contrast to the DQCP scenario, the gap of the Higgs mode keeps to be finite across the first-order transition. (c): Gaps at the M point of the triplet (T) and singlet (S) modes in the plaquette phase and of the magnons (M), the Higgs mode (H), and the singlet mode (S$^\prime$) with $J/J^\prime$, obtained in the iPEPS calculation with $D=5$. A simultaneous softening of all modes with gaps close to the magnon gap takes place near the PVBS-to-AFM transition at $(J/J^\prime)_c\approx0.79$. (d): Finite-$D$ analysis on the crossing points of the triplet, Higgs, and magnon modes. In the large-$D$ limit, all crossing points are close and can be extrapolated to $(J/J^\prime)_c\approx0.79$, suggesting the existence of a DQCP. (e): Finite $D$ analysis of the Higgs gap, $\Delta$, at the crossing point with the magnon mode, showing the closure of the Higgs gap in the large $D$ limit. (f): Evolution of the velocities $c$ with $J/J^\prime$ for the singlet mode in the PVBS phase together with the Higgs and magnon modes in the AFM phases. $c$ of the these modes coincide at $(J/J^\prime)_c$. For each mode, $c$ is extracted by fitting the dispersion along the M to X direction with $\omega(\mathbf{q})=\sqrt{\Delta^2+c^2q^2}$.
• Figure 5: (a): The iPEPS setup in the calculation of the ground state of the SS model. The tensors are arranged at the sites of the SS lattice. The bright-colored sites indicate a $2\times2$ unit cell used in the calculation. (b): Illustration of the single-mode iPEPS ansatz for the calculation of excited states. In each term of the summation, a single local tensor $A_\alpha$ located at site $r$ belonging to a specified sublattice is modified to a different tensor $B_{\alpha}$. Here $\alpha=1,2,3,4$, corresponding to a $2\times 2$ unit cell.