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arXiv:2310.19577 · Contemporary Physics

Quantum spin liquids

Tom Lancaster

Published Apr 3, 2023• 20 citations
arXivHTMLPDF

Abstract

A glance at recent research on magnetism turns up a curious set of articles discussing, or claiming evidence for, a state of matter called a quantum spin liquid (QSL). These articles are notable in their invocation of exotic notions of topological physics, quantum entanglement, fractional quantum numbers, anyon statistics and gauge field theories. So what is a QSL and why do we need this complicated technical vocabulary to describe it? Our aim in this article is to introduce some of these concepts and provide a discussion of what a QSL is, where it might occur in Nature and why it is of interest. As we'll see, this is a rich subject which is still in development, and unambiguous evidence for the realisation of the QSL state in a magnetic material remains hotly debated. However, the payoff in terms of the special nature of quantum entanglement in the QSL, and its diverse spectrum of unusual excitations and topological status will (at least to some extent) justify the need to engage with some powerful, occasionally abstract, technical material.

DOI
10.1080/00107514.2023.2284522

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A glance at recent research on magnetism turns up a curious set of articles discussing, or claiming evidence for, a state of matter called a quantum spin liquid (QSL). These articles are notable in their invocation of exotic notions of topological physics, quantum entanglement, fractional quantum numbers, anyon statistics and gauge field theories. So what is a QSL and why do we need this complicated technical vocabulary to describe it? Our aim in this article is to introduce some of these concepts and provide a discussion of what a QSL is, where it might occur in Nature and why it is of interest. As we'll see, this is a rich subject which is still in development, and unambiguous evidence for the realisation of the QSL state in a magnetic material remains hotly debated. However, the payoff in terms of the special nature of quantum entanglement in the QSL, and its diverse spectrum of unusual excitations and topological status will (at least to some extent) justify the need to engage with some powerful, occasionally abstract, technical material.
Quantum Spin Liquids Quantum spin liquids (QSLs) possess magnetic interactions that, even at absolute zero temperature, remain in a disordered liquid-like spin state. It is very difficult to prove unambiguously that a material is a QSL, because there is always a possibility that it can become ordered below the lowest measured temperature. Barkeshli et al. used quantum field theory to propose a direct way to identify a QSL by placing it in contact with other exotic materials, such as superconductors or magnets. The theory predicted that, at such a boundary, electrons entering the QSL would turn into excitations lacking charge or lacking spin. Future experiments may be able to detect this transmutation. Science , this issue p. [722][1] [1]: /lookup/doi/10.1126/science.1253251
Abstract Quantum spin liquids (QSLs) give rise to exotic emergent particles by weaving intricate entanglement patterns in the underlying electrons. Bipartite measures between subregions can detect the presence of anyons, but little is known about the full entanglement structure of QSLs. Here, we study the multiparty entanglement of QSLs via entanglement microscopy. We find that in contrast to conventional matter, the genuine multiparty entanglement (GME) between spins is absent in the smallest subregions, a phenomenon we call ``entanglement frustration.'' Instead, GME is more collective, and arises solely in loops. By exploiting exact results and large-scale numerics, we confirm these properties in various gapped and gapless QSLs realized in physically motivated Hamiltonians, as well as with string-net wavefunctions hosting abelian or non-abelian anyons. Our results shed new light on the phase diagram of Kitaev’s honeycomb model in a Zeeman field, and the Kagome Heisenberg model under various perturbations. Going beyond QSLs, we provide evidence that entanglement loops are a universal property of quantum gauge theories. This leads to a new understanding of fractionalization, and the means by which gauge bosons encode quantum information.
Electrons have three quantized properties-charge, spin, and Fermi statistics-that are directly responsible for a vast array of phenomena. Here we show how these properties can be coherently and dynamically stripped from the electron as it enters a certain exotic state of matter known as a quantum spin liquid (QSL). In a QSL, electron spins collectively form a highly entangled quantum state that gives rise to the fractionalization of spin, charge, and statistics. We show that certain QSLs host distinct, topologically robust boundary types, some of which allow the electron to coherently enter the QSL as a fractionalized quasi-particle, leaving its spin, charge, or statistics behind. We use these ideas to propose a number of universal, conclusive experimental signatures that would establish fractionalization in QSLs.
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, which is 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, which 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 in relation to study quantum spin liquids, and to the diverse probes used therein.
Quantum Materials Materials with interacting quantum spins that nevertheless do not order magnetically down to the lowest temperatures are candidates for a materials class called quantum spin liquids (QSLs). QSLs are characterized by long-range quantum entanglement and are tricky to study theoretically; an even more difficult task is to experimentally prove that a material is a QSL. Broholm et al. take a broad view of the state of the field and comment on the upcoming challenges. Science , this issue p. [eaay0668][1] [1]: /lookup/doi/10.1126/science.aay0668
Abstract In condensed matter physics there is a novel phase termed ‘quantum spin liquid’, in which strong quantum fluctuations prevent long-range magnetic order from being estab lished, and so electron spins do not form an ordered pattern but remain liquid-like even at absolute zero temperature. Such a phase is not involved in any spontaneous symmetry breaking and local order parameter, and to understand it is beyond conventional phase transition theory. Due to the rich physics and exotic properties of quantum spin liquids, such as long-range entanglement and fractional quantum excitations, which are believed to hold great potential for quantum communication and computation, they have been intensively studied since the concept was proposed in 1973 by P.W. Anderson. Currently, experimental identification of a quantum spin liquid remains a great challenge. Here, we highlight some interesting experimental progress that has been made recently. We also discuss outstanding issues and raise questions that we consider to be important for future research.