Case for a U ( 1 ) π Quantum Spin Liquid Ground State in the Dipole-Octupole Pyrochlore Ce 2 Zr 2 O 7
Not Available
Smith, E. M. (ORCID:0000000220543585)↗
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The Search for a Quantum Spin Liquid: K 2 UTe 3 [Slides]
Abstract not provided.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Detecting fractionalization in critical spin liquids using color centers
Quantum spin liquids are highly entangled ground states of insulating spin systems, in which magnetic ordering is prevented down to the lowest temperatures due to quantum fluctuations. One of the most extraordinary characteristics of quantum spin liquid phases is their ability to support fractionalized, low-energy quasiparticles known as spinons, which carry spin-1/2 but bear no charge. Relaxometry based on color centers in crystalline materials—of which nitrogen-vacancy (NV) centers in diamond are a well-explored example—provides an exciting new platform to probe the spin spectral functions of magnetic materials with both energy and momentum resolution and to search for signatures of these elusive, fractionalized excitations. In this work, we theoretically investigate the color-center relaxometry of two archetypal quantum spin liquids: the two-dimensional U(1) quantum spin liquid with a spinon Fermi surface and the spin-1/2 antiferromagnetic spin chain. The former is characterized by a metallic, spin-split ground state of mobile, interacting spinons, which closely resembles a spin-polarized Fermi liquid ground state but with neutral quasiparticles. We show that the observation of the Stoner continuum and the collective spin wave mode in the spin spectral function would provide a strong evidence for the existence of spinons and fractionalization. In one dimension, mobile spinons form a Luttinger liquid ground state. We show that the spin spectral function exhibits strong features representing the collective density and spin-wave modes, which are broadened in an algebraic fashion with an exponent characterized by the Luttinger parameter. The possibilities of measuring these collective modes and detecting the power-law decay of the spectral weight using NV relaxometry are discussed. We also examine how the transition rates are modified by marginally irrelevant operators in the Heisenberg limit. Published by the American Physical Society 2024
Takei, So (ORCID:0000000191771895)↗
Coexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet
We study the ground-state properties of a spin-1 Heisenberg model on a square lattice with the first- and second-nearest-neighbor antiferromagnetic couplings $J_1$ and $J_2$ and a three-spin scalar chirality term $J_\chi$. Using the density matrix renormalization group calculation, we map out a global phase diagram including various magnetic order phases and an emergent quantum spin liquid phase. The nature of the spin liquid is identified as a bosonic non-Abelian Moore-Read state from the fingerprint of the entanglement spectra and identification of a full set of topological sectors. We further unveil a stripe magnetic order coexisting with this spin liquid. Furthermore, our results not only establish a rare example of non-Abelian spin liquids in simple spin systems but also demonstrate the coexistence of fractionalized excitations and magnetic order beyond mean-field descriptions.
2-dimensional systems↗
Tensor network investigation of the double layer Kagome compound Ca 10 Cr 7 O 28
Quantum spin liquids are exotic quantum phases of matter that do not order even at zero temperature. While there are several toy models and simple Hamiltonians that could host a quantum spin liquid as their ground state, it is very rare to find actual, realistic materials that exhibit their properties. At the same time, the classical simulation of such instances of strongly correlated systems is intricate and reliable methods are scarce. Here, in this work, we investigate the quantum magnet Ca 10 Cr 7 O 28 that has recently been discovered to exhibit properties of a quantum spin liquid in inelastic neutron scattering experiments. This compound has a distorted bilayer Kagome lattice crystal structure consisting of Cr 5+ ions with spin- moments. Coincidentally, the lattice structure renders a tensor network algorithm in 2D applicable that can be seen as a new variant of a projected entangled simplex state algorithm in the thermodynamic limit. In this first numerical investigation of this material that takes into account genuine quantum correlations, good agreement with the experimental findings is found. Our study contributes to uplifting tensor networks from conceptual tools to methods to describe real two-dimensional quantum materials.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Chiral spin liquid and quantum phase diagram of spin- 1 2 J 1 − J 2 − J χ model on the square lattice
Not Available
Zhang, Xiao-Tian (ORCID:0000000339451135)↗
Spinon mediation of witness spin dynamics in herbertsmithite
The kagome lattice of spin-1/2 copper atoms in herbertsmithite is conjectured to sustain a quantum spin liquid state with spinon quasiparticles. Ideally, the kagome crystal planes are each separated by a plane of spinless zinc atoms. However, in real crystals, some spin-1/2 copper atoms substitute randomly onto these inter-kagome zinc sites. Here we reconceptualize such ‘impurity’ atoms as quantum witness spins whose dynamics is designed to probe the spin liquid state. We then introduce spin noise spectroscopy to measure the frequency and temperature dependence of witness spin dynamics, demonstrating that their phenomenology is consistent with extensive interactions between witness spins mediated by propagation of spinons through a quantum spin liquid. Ultimately, a sharp transition occurs at around 260 mK, below which the properties of both spin noise and magnetic susceptibility suggest that the witness spins form a spin glass phase. Among the theoretical models considered, we demonstrate that our observations are only consistent with spinon-mediated interactions between witness spins by either a Z 2 or U(1) quantum spin liquid, with the former model more closely matching the data. Our work demonstrates that quantum mechanical witness spins may now conceivably be used as a widely applicable probe of quantum spin liquid physics.
Takahashi, Hiroto [University of Oxford (United Ki↗
Phonon dynamics in the site-disordered Kitaev spin liquid
The Kitaev honeycomb model provides a paradigmatic example of an exactly solvable quantum spin liquid (QSL), where spins fractionalize into itinerant Majorana fermions coupled to a static background of ℤ 2 gauge fluxes. This model has attracted significant interest due to its potential experimental realization in spin-orbit Mott insulators like 𝛼−RuCl 3 . Among various experimental techniques, ultrasound measurements of sound attenuation have emerged as a promising approach to detect spin fractionalization in these materials. However, deviations from the ideal Kitaev model, often due to disorder, introduce localized modes that dominate the low-energy physics. To investigate these effects, we calculate the sound attenuation coefficient in the site-disordered Kitaev honeycomb model under an applied magnetic field that breaks time-reversal symmetry. Our analysis reveals that quasilocalized modes from quasivacancies impact the phonon self-energy, yet the sound attenuation coefficient maintains its sixfold symmetry and linear temperature dependence at low temperatures, even with disorder. This robustness underscores sound attenuation's reliability as a probe for spin fractionalization. As a result, we show that this linear behavior persists under an external field and in the random-flux sector, highlighting the persistent influence of fractionalized excitations, despite disorder.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Probing topological spin liquids on a programmable quantum simulator
Synthesizing topological order Topologically ordered matter exhibits long-range quantum entanglement. However, measuring this entanglement in real materials is extremely tricky. Now, two groups take a different approach and turn to synthetic systems to engineer the topological order of the so-called toric code type (see the Perspective by Bartlett). Satzinger et al . used a quantum processor to study the ground state and excitations of the toric code. Semeghini et al . detected signatures of a toric code–type quantum spin liquid in a two-dimensional array of Rydberg atoms held in optical tweezers. —JS
Science & Technology - Other Topics↗
Momentum-independent magnetic excitation continuum in the honeycomb iridate H 3 LiIr 2 O 6
Understanding the interplay between the inherent disorder and the correlated fluctuating-spin ground state is a key element in the search for quantum spin liquids. H 3 LiIr 2 O 6 is considered to be a spin liquid that is proximate to the Kitaev-limit quantum spin liquid. Its ground state shows no magnetic order or spin freezing as expected for the spin liquid state. However, hydrogen zero-point motion and stacking faults are known to be present. The resulting bond disorder has been invoked to explain the existence of unexpected low-energy spin excitations, although data interpretation remains challenging. Here, we use resonant X-ray spectroscopies to map the collective excitations in H 3 LiIr 2 O 6 and characterize its magnetic state. In the low-temperature correlated state, we reveal a broad bandwidth of magnetic excitations. The central energy and the high-energy tail of the continuum are consistent with expectations for dominant ferromagnetic Kitaev interactions between dynamically fluctuating spins. Furthermore, the absence of a momentum dependence to these excitations are consistent with disorder-induced broken translational invariance. Our low-energy data and the energy and width of the crystal field excitations support an interpretation of H 3 LiIr 2 O 6 as a disordered topological spin liquid in close proximity to bond-disordered versions of the Kitaev quantum spin liquid.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Proximate spin liquid and fractionalization in the triangular antiferromagnet KYbSe 2
The Heisenberg triangular-lattice quantum spin liquid and its phase transitions to nearby magnetic orders have received much theoretical attention, but clear experimental manifestations of these states are rare. Here we demonstrate that a spin-half delafossite material, namely, KYbSe 2 , shows close proximity to the triangular-lattice Heisenberg quantum spin liquid. Using neutron scattering, we identify a diffuse continuum with a sharp lower bound within the measured spectra. Applying entanglement witnesses to the data indicates multipartite entanglement spread between its neighbours, and an analysis of its magnetic-exchange couplings reveals close proximity to the theoretical quantum spin-liquid phase. The key features of the data are reproduced by Schwinger boson theory and tensor network calculations with a substantial next-nearest-neighbour coupling. The strength of the dynamical structure factor at the Brillouin-zone K point shows a scaling collapse down to 0.3 K, indicating the existence of a second-order quantum phase transition. Finally, comparing this with previous theoretical work suggests that the proximate phase at a larger next-nearest-neighbour coupling is a gapped $\mathbb{Z}_{2}$ spin liquid, resolving a long-debated issue. Similar content being viewed by others
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Symmetric U(1) and Z 2 spin liquids on the pyrochlore lattice
The geometrically frustrated three-dimensional pyrochlore lattice has been long predicted to host a quantum spin liquid, an intrinsic long-range entangled state with fractionalized excitations. To date, most proposals for pyrochlore materials have focused on quantum spin ice, a U(1) quantum spin liquid whose only low energy excitations are emergent photons of Maxwell type. Here, we explore the possibility of finding pyrochlore quantum spin liquids whose low energy theories go beyond this standard one. We give a complete classification of symmetric U ( 1 ) and Z 2 spin liquids on the pyrochlore lattice within the projective symmetry group framework for fermionic spinons. We find 18 U ( 1 ) spin liquids and 28 Z 2 spin liquids that preserve pyrochlore space-group symmetry while, upon further imposing time-reversal symmetry, the numbers of classes become 16 and 48, respectively. For each class, the most general symmetry-allowed spinon mean-field Hamiltonian is given. Interestingly, we find that several U(1) spin liquid classes possess an unusual gapless multi-nodal-line structure (“nodal star”) in the spinon bands, which is protected by the projective actions of the threefold rotation and screw symmetries of the pyrochlore space group. Through a simple model, we study the effect of gauge fluctuations on such a nodal star spin liquid and propose that the leading terms in the low temperature specific heat have the scaling form C / T ~ T + T / ln T , in contrast to the form C / T ~ T 2 of the standard U(1) pyrochlore spin liquid with gapped spinons.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Global quantum phase diagram and non-Abelian chiral spin liquid in a spin- 3 2 square-lattice antiferromagnet
Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin-$\frac{1}{2}$ systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in a spin-$\frac{3}{2}$ Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density-matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of the Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian chiral spin liquid emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Finally, our numerical discovery of an exotic quantum spin liquid in a spin-$\frac{3}{2}$ system suggests a route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds.
2-dimensional systems↗
Disorder-induced spin-cluster magnetism in a doped kagome spin liquid candidate
The search for new quantum spin liquid materials relies on systems with strong frustration such as spins on an ideal kagome lattice. However, lattice imperfections can have substantial effects which are as yet not well understood. In recent work, the two-dimensional kagome system YCu 3 (OH) 6 [(Cl 𝑥 Br (1−𝑥) ) 3−𝑦 (OH) 𝑦 ] has emerged as a leading candidate hosting a Dirac spin liquid which appears to survive at least for 𝑥 < 0.4, associated with alternating-bond-hexagon (ABH) disorder. Here in magnetic samples with 𝑥 = 0.58, 𝑦 = 0.1 we report unusual in-plane ferromagnetic canting (FM) of the in-plane antiferromagnet (AFM), with an unusually wide regime of short-ranged order, and propose theoretical models to explain this behavior. First, we show that Kitaev-type exchanges naturally arise on the kagome lattice to second order in the known Dzyaloshinskii-Moriya exchanges, and that these interactions can produce the unusual in-plane FM canting from antichiral AFM. Second, we propose a phenomenological model of weakly FM-canted spin clusters to describe the short-ranged regime and analyze quantum fluctuations in an ABH toy model to show how ABH disorder can stabilize this regime. Here, the combination of experimental observation and theory suggests that kagome-Kitaev interactions and ABH disorder are necessary for describing the magnetic fluctuations in this family of materials, with potential implications for the proposed proximate spin liquid phase.
Seth, Arnab [Georgia Institute of Technology, Atla↗
Chiral spin liquid and quantum phase transition in the triangular-lattice Hofstadter-Hubbard model
Recent advances in moiré engineering motivate the study of lattice models of strongly correlated electrons subjected to substantial orbital magnetic flux. We analyze the triangular-lattice Hofstadter-Hubbard model at one-quarter flux quantum per plaquette and a density of one electron per site, where a chiral spin liquid phase may exist between weak-coupling integer quantum Hall and strong-coupling 120° antiferromagnetic phases. Here, we use matrix product state methods and analytical arguments to investigate this model compactified to cylinders of finite circumference. We uncover a glide particle-hole symmetry operation which, we argue, is spontaneously broken at the quantum Hall to spin liquid transition on odd-circumference cylinders. We numerically verify the spontaneous symmetry breaking and further demonstrate that this transition is associated with algebraic long-range correlations of various spin-singlet, charge-neutral operators. For even-circumference cylinders, the transition becomes a crossover associated with a large correlation length that grows substantially with circumference. Our findings suggest that in the two-dimensional limit, the transition to a chiral spin liquid phase is continuous and features critical fluctuations of the current.
Divic, Stefan [University of Pennsylvania, Philade↗
Magnetic dilution in the triangular lattice antiferromagnet NaYb 1−𝑥 Lu 𝑥 O 2
The delafossitelike compound NaYbO 2 hosts a triangular lattice of Yb 3+ moments and is a promising candidate for the realization of a quantum spin liquid ground state—an exotic, quantum-disordered magnetic phase featuring long-range entanglement of spins. Tuning this system away from this quantum-disordered regime toward classical order or spin freezing is a powerful approach to shed light on the nature of the parent ground state. Here we leverage the substitution of nonmagnetic Lu 3+ onto the Yb 3+ sites to study the effects of magnetic disorder in NaYbO 2 using low-temperature ac susceptibility, heat capacity, and muon spin relaxation (𝜇SR) measurements. Here, our 𝜇SR measurements reveal resilient, correlated magnetic fluctuations that persist to at least 15% dilution, precluding conventional spin freezing and magnetic inhomogeneity. Heat capacity and magnetic susceptibility resolve a rapid suppression of the field-induced “up-up-down” magnetic order upon dilution and a crossover in the power-law behavior of the low-temperature magnetic excitations associated with the zero-field quantum disordered ground state. Taken together, these results support the notion of a robust network of entangled moments in NaYbO 2 and provide experimental validation of several models of a Heisenberg triangular lattice antiferromagnet in the presence of disorder.
Muon spin relaxation & rotation↗
Weak-field induced nonmagnetic state in a Co-based honeycomb
Layered honeycomb magnets are of interest as potential realizations of the Kitaev quantum spin liquid (KQSL), a quantum state with long-range spin entanglement and an exactly solvable Hamiltonian. Conventional magnetically ordered states are present for all currently known candidate materials, however, because non-Kitaev terms in the Hamiltonians obscure the Kitaev physics. Current experimental studies of the KQSL are focused on 4 d or 5 d transition metal–based honeycombs, in which strong spin-orbit coupling can be expected, yielding Kitaev interaction that dominates in an applied magnetic field. In contrast, for 3 d -based layered honeycomb magnets, spin-orbit coupling is weak, and thus, Kitaev physics should be substantially less accessible. Here, we report our studies on BaCo 2 (AsO 4 ) 2 , for which we find that the magnetic order associated with the non-Kitaev interactions can be fully suppressed by a relatively low magnetic field, yielding a nonmagnetic material and implying the presence of strong magnetic frustration and weak non-Kitaev interactions.
Science & Technology - Other Topics↗
Probing fractional statistics in quantum simulators of spin liquid Hamiltonians
Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realise and investigate topological quantum spin liquid phases. This new and exciting direction brings about important research questions on how to probe and determine the presence of such exotic, highly entangled phases in a noisy quantum environment. One of the most promising tools is investigating the behaviour of the topological excitations, and in particular their fractional statistics. In this work we put forward a generic route to achieve this, and we illustrate it in the specific case of \mathbb{Z}_2 ℤ 2 topological spin liquids implemented with the aid of combinatorial gauge symmetry. We design a convenient architecture to study signatures of fractional statistics via quasiparticle interferometry, and we assess its robustness to diagonal and off-diagonal disorder, as well as to dephasing - effects that are generally pervasive in current quantum programmable devices. Interestingly, when turned on its head, our scheme provides a remarkably clear test of the “quantumness” of these devices, with robust signatures that crucially hinge on quantum coherence and quantum interference effects, and cannot be mimicked by classical stochastic processes.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗