Spin Excitations and Their Implications for Deconfined Quantum Criticality in the Shastry-Sutherland Model

Core Concepts

The Shastry-Sutherland model exhibits nearly deconfined excitations near the transition between plaquette and antiferromagnetic phases, suggesting proximity to a deconfined quantum critical point, but the transition remains weakly first-order due to the altermagnetic nature of the antiferromagnetic state.

Abstract

• Bibliographic Information: Chen, H., Duan, G., Liu, C., Cui, Y., Yu, W., Xie, Z. Y., & Yu, R. (2024). Spin excitations of the Shastry-Sutherland model – altermagnetism and proximate deconfined quantum criticality. arXiv preprint arXiv:2411.00301v1.
• Research Objective: This study investigates the nature of the phase transition between the plaquette and antiferromagnetic states in the Shastry-Sutherland model by examining spin excitations.
• Methodology: The researchers employ the infinite projected entangled pair state (iPEPS) method to calculate the ground and excited states of the model. They analyze the spin dynamical structure factor (DSF) to characterize the spin excitations. Additionally, they compare their findings with linear spin wave (LSW) and bond-operator theories.
• Key Findings: The study reveals the presence of nearly deconfined excitations near the plaquette-to-antiferromagnetic transition, evidenced by the softening of both the Higgs mode in the antiferromagnetic phase and the triplet mode in the plaquette phase. However, a finite splitting persists between the two chiral Goldstone modes at the transition point due to the altermagnetic nature of the antiferromagnetic state.
• Main Conclusions: The authors conclude that the plaquette-to-antiferromagnetic transition in the Shastry-Sutherland model is weakly first-order, proximate to a deconfined quantum critical point. The altermagnetism, characterized by the non-relativistic splitting of magnon bands, serves as a sensitive probe for the proximate deconfined quantum criticality.
• Significance: This research provides valuable insights into the complex interplay between altermagnetism and deconfined quantum criticality in quantum magnetism. The findings contribute to the ongoing debate surrounding the existence of deconfined quantum critical points in quantum spin models.
• Limitations and Future Research: Further investigation into the influence of spin frustration on the phase transition is suggested. Additionally, experimental verification of the theoretical predictions, such as the splitting of magnon bands, is encouraged.

Stats

J/J’ ≈ 0.68: Approximate value of the coupling ratio at the dimer-to-plaquette transition.
J/J’ ∼ 0.8: Approximate value of the coupling ratio at the plaquette-to-AFM transition.
D = 5: Maximum bond dimension used in the iPEPS calculations for excited states.
(J/J′)c ≈ 0.79: Critical coupling ratio for the plaquette-to-AFM transition.

Quotes

Key Insights Distilled From

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

by Hongyu Chen,... at arxiv.org 11-04-2024

https://arxiv.org/pdf/2411.00301.pdf

Deeper Inquiries

How would the inclusion of further neighbor interactions or anisotropy in the Shastry-Sutherland model affect the nature of the phase transition and the properties of the excitations?

Answer:
Introducing further neighbor interactions or anisotropy in the Shastry-Sutherland model can significantly impact the delicate balance of competing phases and the nature of the excitations.
Further neighbor interactions:

Shifting phase boundaries: Including interactions beyond nearest-neighbor couplings (like next-nearest-neighbor or inter-dimer interactions) can shift the phase boundaries between the dimer-singlet, plaquette VBS, and antiferromagnetic phases. This is because these additional interactions can either enhance or frustrate the dominant correlations responsible for each phase.
Stabilizing new phases: In some cases, further neighbor interactions might even stabilize entirely new phases not present in the original model. For example, introducing a frustrating next-nearest-neighbor interaction could potentially stabilize a quantum spin liquid phase.
Modifying excitation spectra: The excitation spectra would also be modified. The dispersion relations of the magnons, triplons (triplet excitations in the VBS phase), and any other emergent excitations would be altered due to the modified interactions. The energy gaps and the nature of the splitting between different modes could also change.
Anisotropy:

Breaking symmetries: Introducing anisotropy, such as exchange anisotropy (different coupling strengths for different spin components) or single-ion anisotropy, breaks the SU(2) spin symmetry of the model. This can have profound consequences on the nature of the phases and excitations.
Lifting degeneracies: Anisotropy can lift the degeneracy of certain excitations. For example, in the antiferromagnetic phase, a single-ion anisotropy can introduce a gap in the Goldstone mode spectrum.
Favoring specific order: Depending on the type of anisotropy, it can favor specific types of magnetic order. For instance, an easy-axis anisotropy would favor Ising-like order, while an easy-plane anisotropy would favor XY-like order.
Impact on the phase transition:
The nature of the plaquette-to-AFM transition, particularly its proximity to the deconfined quantum critical point (DQCP), could be significantly affected by these modifications.

First-order transition: Further neighbor interactions or anisotropy could potentially enhance the weakly first-order nature of the transition, pushing it further away from the DQCP.
New universality class: Alternatively, they could drive the transition towards a different universality class, potentially even realizing a true DQCP with different emergent symmetries.
In summary, introducing further neighbor interactions or anisotropy in the Shastry-Sutherland model provides a rich playground for exploring new quantum phases and transitions. It allows for fine-tuning the competition between different ground states and investigating the emergence of exotic excitations and potentially novel critical behavior.

Could the observed nearly deconfined excitations be a finite-size effect of the numerical simulations, and would a true deconfined quantum critical point emerge in the thermodynamic limit?

Answer:
The question of whether the observed nearly deconfined excitations in the Shastry-Sutherland model are a finite-size effect or a signature of a proximate deconfined quantum critical point (DQCP) is a crucial one. While the iPEPS method used in the study simulates infinite systems, it employs a finite bond dimension (D) which effectively limits the entanglement entropy and can introduce finite-size effects.
Arguments for finite-size effects:

Gap closing: The study observes that the gaps of both the Higgs mode and the triplet mode decrease rapidly as the transition is approached, coming very close to the gap of the Goldstone modes. This gap closing could be accelerated in the thermodynamic limit (D → ∞), potentially leading to a true DQCP where all three modes become gapless and degenerate.
Emergent symmetry: The proximity of the crossing points of these modes to the transition point in the large-D limit suggests an emergent symmetry, potentially the O(4) symmetry associated with the DQCP.
Arguments against finite-size effects:

Finite splitting: Despite the gap closing, the splitting between the two Goldstone modes, a consequence of altermagnetism, remains finite at the transition point even when extrapolating to the large-D limit. This suggests that the O(4) symmetry is not fully restored, indicating a weakly first-order transition instead of a true DQCP.
Small but finite gap: The extrapolation of the energy of the crossing point between the Higgs mode and the triplet mode to the large-D limit reveals a small but finite gap (approximately 0.05J'). This non-zero gap at the transition further supports the weakly first-order nature.
Conclusion:
While the numerical evidence points towards a proximate DQCP, definitively concluding whether a true DQCP emerges in the thermodynamic limit requires further investigation.

Higher bond dimensions: Performing simulations with even higher bond dimensions could provide more conclusive evidence by examining the scaling behavior of the gaps and the splitting of the Goldstone modes.
Alternative approaches: Employing complementary numerical techniques, such as Quantum Monte Carlo methods (where applicable) or large-scale DMRG calculations, could help validate the iPEPS results and shed further light on the nature of the transition.
Therefore, while the observed nearly deconfined excitations are suggestive of a proximate DQCP, it remains an open question whether a true DQCP with fully deconfined excitations exists in the thermodynamic limit of the Shastry-Sutherland model.

What are the broader implications of understanding and potentially manipulating altermagnetism for technological applications, particularly in spintronics or quantum information processing?

Answer:
Altermagnetism, with its unique symmetry properties and the intriguing properties it induces, holds significant potential for technological applications, particularly in spintronics and quantum information processing.
Spintronics:

Spin currents: The chiral magnons in altermagnets, as highlighted in the paper, can carry spin currents. This opens up possibilities for developing novel spintronic devices that utilize these spin currents for information transmission and processing.
Spin Nernst effect: The paper suggests that altermagnetism can lead to a sizable spin Nernst effect, where a temperature gradient can generate a transverse spin current. This effect could be utilized for spin current generation and manipulation in spin caloritronic devices.
Anomalous Hall effect: Altermagnets can exhibit an anomalous Hall effect even in the absence of net magnetization, providing new mechanisms for Hall-effect-based spintronic devices.
Quantum information processing:

Protected qubits: The unique symmetry properties of altermagnets could potentially be exploited to create protected qubits, the building blocks of quantum computers. The specific symmetries could offer protection against certain types of noise and decoherence, enhancing qubit coherence times.
Topological spintronics: The interplay between altermagnetism and topology could lead to the realization of topological spin textures, such as skyrmions, which are promising candidates for information storage and processing in future spintronic devices.
Novel quantum materials: Understanding altermagnetism can guide the search and design of new quantum materials with tailored magnetic properties for specific spintronic and quantum information applications.
Manipulation of altermagnetism:

Strain engineering: Applying strain to altermagnetic materials can modify their magnetic anisotropy and potentially control the splitting of the magnon bands, enabling dynamic control over spin currents and other relevant properties.
Electric field control: In some altermagnets, electric fields could be used to manipulate the magnetic order and the associated spin excitations, offering a pathway towards electrically controlled spintronic devices.
Optical control: Ultrafast lasers could potentially be employed to switch the magnetic state of altermagnets or excite specific spin wave modes, enabling high-speed operation in spintronic and quantum information devices.
Challenges and outlook:
While the field of altermagnetism is relatively new, its potential for technological applications is immense. However, several challenges need to be addressed:

Material realization: Identifying and synthesizing new materials that exhibit robust altermagnetism at practical temperatures is crucial.
Control and manipulation: Developing efficient methods to control and manipulate the magnetic properties of altermagnets is essential for device applications.
Integration: Integrating altermagnetic materials into existing or future spintronic and quantum information platforms is a significant challenge.
Overcoming these challenges will pave the way for a new generation of spintronic and quantum information technologies based on the unique properties of altermagnetism.