Quantum Spin Liquids (1601.03742v1)

Abstract: Quantum spin liquids may be considered "quantum disordered" ground states of spin systems, in which zero point fluctuations are so strong that they prevent conventional magnetic long range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons that are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments to study quantum spin liquids, and to the diverse probes used therein.

• The paper introduces a robust theoretical framework for quantum spin liquids by emphasizing many-body entanglement and topological order.
• The paper applies models such as the toric code, U(1) and Z2 gauge theories, and parton construction to elucidate exotic quantum phenomena.
• The paper discusses experimental challenges and material candidates, outlining future directions for identifying unambiguous QSL signatures.

Overview of Quantum Spin Liquids and Their Theoretical Framework

Quantum Spin Liquids (QSLs) represent a fascinating class of quantum phases in condensed matter systems, characterized by their lack of conventional magnetic order, even at absolute zero temperature. These states are defined by their significant many-body entanglement, often leading to exotic phenomena such as non-local excitations and topological orders. This summary explores the foundational concepts, theoretical models, and potential experimental signatures of QSLs, as well as their role within the broader framework of condensed matter physics.

Defining Features of Quantum Spin Liquids

QSLs are identified by their highly entangled ground states, which resist any smooth transformation into a product state over finite regions of the system. This high degree of entanglement facilitates unique physical properties, such as non-local excitations and topological orders that are robust against local perturbations. The concept of topological order, a central theme in the paper of QSLs, signifies an intricate form of quantum order that extends beyond the Landau paradigm of symmetry-breaking order parameters.

Theoretical Models and Analytical Tools

1. Toric Code and Topological Phases: Kitaev's toric code provides a paradigmatic model of a QSL with topological order. It supports emergent excitations known as anyons, which exhibit non-trivial mutual statistics that cannot be generated by any local Hamiltonian. These anyons are pivotal in understanding the topological properties of the system.
2. Gauge Theories: A significant feature of QSLs is their description through gauge theories, such as U(1) and Z2 lattice gauge theories. These theories capture the emergent gauge structures in QSLs and facilitate the understanding of non-local excitations in terms of gauge charges and fluxes. For instance, the stability of the Coulomb phase in U(1) gauge theory in three dimensions and its relation to photon-like excitations underscores the richness of QSLs as physical systems.
3. Parton Construction: The parton approach, involving the fractionalization of spin operators into fermionic or bosonic constituents, provides a versatile method to potentially capture the dynamics and ground states of QSLs. Parton mean field theories and variational wavefunctions employing Gutzwiller projections are tools that have been applied to suggest and explore possible QSL candidates for various lattice geometries.

Symmetry, Fractionalization, and Constraints

The topological nature of QSLs is intimately linked with their symmetry properties. Symmetries can impose significant constraints on the possible ground states and excitations through the Lieb-Schultz-Mattis type theorems, which ascertain that fully gapped states in half-integer spin systems must exhibit non-trivial topological order or be gracefully degenerate. Understanding how symmetries are projectively realized in QSLs (fractionalization of quantum numbers) remains an active area of research, leading to classifications of symmetric and symmetry-enriched topological (SET) states.

Experimental Considerations and Material Realizations

Identifying QSLs in real materials remains a challenging but rewarding endeavor. Promising candidates include materials with frustrated geometries, spin-orbit coupled systems, and compounds near the Mott transition. Key experimental signatures of QSLs are the absence of long-range magnetic order, fractionalized excitations observable in neutron scattering, persistently dynamic spin correlations, and unconventional responses to magnetic fields. Current materials considered for QSL studies include honeycomb iridates, organic Mott insulators, and certain rare-earth pyrochlores, each with unique characteristics and challenges.

Conclusion and Future Directions

The paper of QSLs is a vibrant and evolving field, promising further insights into quantum entanglement, topological phases, and potentially revolutionary applications such as quantum computing. Future research will explore the interplay between quantum entanglement, symmetry, and exotic quantum phases, while experimental advancements aim to unearth new materials and experimental techniques that can provide unambiguous evidence for the existence of QSLs. As the field progresses, it is positioned to offer profound contributions to our understanding of complex quantum systems and their manifestations in nature.