Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4

Abstract: We analyze the effect of quenched disorder on spin-1/2 quantum magnets in which magnetic frustration promotes the formation of local singlets. Our results include a theory for 2d valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids. We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-1/2 moments. This renormalizes the lattice into a strongly random spin network with interesting low-energy excitations. Similarly when short-ranged valence bonds would be pinned by stronger disorder, we find that this putative glass is unstable to defects that carry spin-1/2 magnetic moments, and whose residual interactions decide the ultimate low energy fate. Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets with spin-1/2 per statistical unit cell. These conjectures are supported by an argument for 1d spin chains. We apply insights from this study to the phenomenology of YbMgGaO$_4$, a recently discovered triangular lattice spin-1/2 insulator which was proposed to be a quantum spin liquid. We instead explore a description based on the present theory. Experimental signatures, including unusual specific heat, thermal conductivity, and dynamical structure factor, and their behavior in a magnetic field, are predicted from the theory, and compare favorably with existing measurements on YbMgGaO$_4$ and related materials.

Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO$_4$

The paper "Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO$_4" explores the intriguing effects of quenched disorder on spin-1/2 quantum magnets. It addresses how disorder interacts with magnetic frustration to influence local singlet formation and investigates the consequences on specific materials such as YbMgGaO$_4$.

Core Contributions

1. Theoretical Framework for Random Magnets: The authors present a comprehensive theory for two-dimensional (2D) valence-bond solids (VBS) under weak bond randomness. They delve into different disorder regimes and theorize connections with quantum spin liquids. One focal point is understanding how VBS phases are destabilized when subjected to quenched disorder, inevitably leading to topological defects that carry spin-1/2 moments. This results in a transformation into a strongly random spin network with novel low-energy excitations.

2. Impact on Quantum Spin Liquids: Interestingly, when VBS order is destroyed, it forms defect networks that reinforce randomness in spin distributions, potentially hinting at exotic phases resembling quantum spin liquids. The destruction of long-range VBS order induces defects such as vortices with protected spin-1/2 cores, resulting in low-energy excitations in the system.

3. Phenomenological Description of YbMgGaO$_4$: A practical application of the theory is directed at YbMgGaO$_4$, a notable material identified as a triangular lattice spin-1/2 insulator. This material was previously thought to be a quantum spin liquid, but the authors propose an alternative description based on their theoretical insights. The anomalous heat capacity, thermal conductivity, and structure factor measurements in this material suggest a complex interplay of disorder and frustration that aligns with the theory's predictions for defect-induced excitations.

Numerical Results and Claims

The paper makes ambitious conjectures, backed by rigorous arguments and supporting numerical assessments, regarding the stability and transformation of VBS phases in disordered settings. Notably, it conjectures Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets, claiming that spin-1/2 moments per unit cell impose limits on achievable phases, dictating the presence of unavoidable defect-induced excitations. These conjectures are supported through evidence from one-dimensional spin chains and applied to two-dimensional systems.

Implications

1. Theoretical Implications: One potential avenue is extending these theories to other 2D frustrated systems, where disorder interactions can lead to surprising destabilization of magnetic orders, hinting at spin-liquid-like behaviors without requiring complete absence of order.

2. Experimental Realization: By considering the YbMgGaO$_4$ as a prototypical example, the theoretical conclusions offer frameworks to interpret experimental observations, especially for other triangular lattice systems with intrinsic disorder.

3. Future Directions in Spin Systems: The multifaceted insights enrich the understanding of magnetism and disorder, proposing novel ways to approach material synthesis and quantum computation architectures by leveraging unpredictability from disorder.

Conclusion

This paper provides a robust theoretical basis for describing the effects of disorder in quantum magnets, highlighting the unique pathways through which topological defects and randomness converge to create novel excitations. By applying these insights concretely to systems like YbMgGaO$_4$, it extends the theoretical model into practical narratives essential for tackling contemporary challenges in material science. Future work could potentiate new experimental methodologies to explore these nontrivial states further, with a focus on high-resolution measurements or new computational paradigms to accurately capture the weak disorder dynamics in real-world systems.