Researchers have uncovered a pathway to creating three-dimensional quantum spin liquids, materials exhibiting exotic properties with potential applications in quantum computing. Anna Sandberg from Stockholm University, Lukas Rødland from the Max Planck Institute for the Science of Light, and Maria Hermanns from Stockholm University, alongside their colleagues, detail how spin-orbital liquids offer an exactly solvable route to these complex states of matter. Their work demonstrates that these models host a rich variety of metallic phases, including topological Fermi surfaces and Weyl semimetals, and establishes a unified framework for understanding metals within fractionalized spin liquids, representing a significant advance in the field of condensed matter physics.
This work details exactly solvable models built upon spin-orbital liquids, extending beyond the well-known Kitaev model and opening pathways to novel phases of matter.
Researchers demonstrate that these models, realizable on both three- and four-coordinated lattices, host a diverse range of gapless Majorana metals characterized by topological Fermi surfaces, nodal lines, and Weyl semimetal phases. The study establishes a framework for understanding three-dimensional Majorana metals within fractionalized spin liquids, revealing how these materials can support multiple itinerant Majorana flavors, up to three, depending on the lattice structure.
These Majorana fermions, quasiparticles that are their own antiparticles, exhibit unique behavior and contribute to the topological properties of the materials. Analysis of model stability under realistic perturbations reveals predictable splitting patterns and topological transitions driven by symmetry breaking and flavor mixing, providing a unified organizing principle for these complex systems.
Specifically, the research focuses on constructing spin-orbital Hamiltonians using higher-dimensional Clifford-algebra representations. These representations allow for the creation of models with either three or two itinerant Majorana flavors, depending on whether the lattice is three- or four-coordinated.
The resulting phases are not merely theoretical constructs; they are demonstrably rich in topological features, including Fermi surfaces, nodal lines, and Weyl points, all of which are crucial for potential applications in quantum technologies. The investigation goes beyond simply identifying these phases, delving into their robustness against external influences.
By analyzing the models’ response to physically motivated perturbations, scientists have mapped out generic splitting patterns and topological transitions, providing a comprehensive understanding of how these materials behave under varying conditions. This detailed analysis yields a unifying framework for understanding three-dimensional Majorana metals, paving the way for the design and discovery of new quantum materials with tailored properties.
Construction and characterisation of solvable spin-orbital liquids on three- and four-coordinated lattices
Spin-orbital liquids represent an exactly solvable pathway to three-dimensional Z2 quantum spin liquids extending beyond the original Kitaev model. The research constructs these models utilising higher-dimensional Clifford-algebra representations, enabling their realisation on both three- and four-coordinated lattices and generating phases with three and two itinerant flavors.
Detailed analysis reveals these models host a rich variety of gapless metals, specifically characterised by topological Fermi surfaces, nodal lines, and Weyl semimetal phases. The study systematically investigates the stability of these structures under physically motivated perturbations, identifying generic splitting patterns and topological transitions driven by symmetry breaking and flavor mixing.
This work yields a unified framework for understanding three-dimensional metals within fractionalised spin liquids. To achieve this, the researchers focused on lattices, both three- and four-coordinated, as representative examples of generic behaviour in three-dimensional spin-orbital liquids. For each lattice configuration, the low-energy properties and robust nodal structures of the itinerant Majorana fermions were determined.
The response of these systems to various physically motivated perturbations was also studied to understand their behaviour under realistic conditions. This involved a comprehensive exploration of symmetry implementation and the effects of symmetry breaking on the resulting phases. The methodology establishes a foundation for exploring more realistic and complex settings beyond the simplified toy models currently available for quantum spin liquids.
Majorana fermion flavours and topological phases in three-dimensional quantum spin liquids
Researchers detail the properties of spin-orbital liquids, demonstrating exactly solvable routes to three-dimensional Z2 quantum spin liquids extending beyond the original Kitaev model. These models, built from higher-dimensional Clifford-algebra representations, give rise to phases with either three or two itinerant Majorana fermion flavors depending on the lattice structure.
Analysis reveals the presence of topological Fermi surfaces, nodal lines, and Weyl semimetal phases within these gapless metals. Specifically, the work establishes that for lattices with three-fold coordination, the models host three itinerant Majorana flavors. Conversely, four-coordinated lattices exhibit only two itinerant Majorana flavors, a direct consequence of the relationship between the number of flavors and the lattice’s coordination number.
The study systematically explores the low-energy properties and robust nodal structures of these itinerant fermions across various lattice types. Investigations into physically motivated perturbations reveal generic splitting patterns and topological transitions driven by symmetry breaking and flavor mixing.
These transitions yield a unified framework for understanding three-dimensional metals within fractionalized spin liquids. The models utilize Γ matrices, higher-dimensional representations of the Clifford algebra, to preserve solvability while increasing the local Hilbert space. Representations with q = 1 act on a four-dimensional Hilbert space, naturally interpreted as a combination of spin and orbital degrees of freedom.
For three-coordinated lattices, the Hamiltonian takes the form described by equation (5), exhibiting an emergent SO(3) symmetry and manifesting in three identical itinerant Majoranas. This construction, analogous to the original Kitaev model but with an increased number of itinerant Majorana fermions, enriches the possible band structures and topological features. The research provides a foundation for future investigations into three-dimensional quantum spin liquids and their potential material realizations.
Topological metallic phases within solvable three-dimensional spin liquids
Researchers have identified an exactly solvable route to three-dimensional quantum spin liquids, extending the original Kitaev model to encompass spin-orbital liquids. These novel materials are constructed using higher-dimensional Clifford-algebra representations and can be realised on lattices with either three or four coordinating bonds, resulting in phases exhibiting three or two itinerant flavours.
Investigations reveal these models host a diverse range of gapless metallic states, notably characterised by topological Fermi surfaces, nodal lines, and Weyl semimetal phases. Analysis of the stability of these structures under physically relevant perturbations demonstrates generic splitting patterns and topological transitions driven by symmetry breaking and flavour mixing.
This work establishes a unified framework for understanding three-dimensional metals within fractionalised spin liquids, providing a basis for classifying their behaviour. The authors acknowledge that while the topological Fermi surfaces persist even with substantial perturbations, their detailed geometry is significantly deformed.
Future research could explore the behaviour of these systems under more complex perturbations or investigate the potential for driving transitions into different quantum spin liquid regimes. These findings are significant as they offer a pathway towards understanding and potentially realising exotic quantum states of matter with unique electronic properties.
The identification of topological features within these spin liquids suggests potential applications in spintronics and quantum computation, where robust and topologically protected electronic states are highly desirable. The established framework for classifying three-dimensional metals in fractionalised spin liquids provides a valuable tool for guiding future materials discovery and characterisation.