Topological Spin Liquid Research Articles

Emerging Anomalous Hall Effect in (111)‐Oriented Artificial Iridate Honeycomb Lattices

AbstractComplex Ir oxides provide a promising platform for investigating cooperativity and competition between Mott physics and spin‐orbit coupling in condensed matter physics. These materials have the potential to reveal intriguing phases, such as topological phases and the Kitaev spin liquid state, an exactly solvable S = 1/2 spin model describing Ir4+ ions on a 2D honeycomb lattice. However, experimental confirmation of such phases in iridate films has been hindered by the difficulty of preparing (111)‐oriented samples of the perovskite phase. Herein, by constructing SrIrO3/SrTiO3 superlattices on SrTiO3 (111) substrates, (111)‐oriented perovskite phase SrIrO3 films are achieved with the unprecedentedly large thickness of 6 unit cells. Electrical and magnetic characterizations reveal that these films exhibit anomalous Hall insulating behavior, significant charge fluctuations, and long‐range antiferromagnetic order. Moreover, these properties can be tuned by varying the thickness of the SrIrO₃ layer. These emergent phenomena underscore the complex interactions among spin‐orbit coupling, electron–electron correlations, and crystal structure in (111)‐oriented artificial iridate honeycomb lattices. Further, spin fractionalization and topological quantum spin liquid may be achieved by tuning the spin–orbit coupling and crystal field intensity from interface engineering.

Variational MonteCarlo Study of the 1/9-Magnetization Plateau in Kagome Antiferromagnets.

Motivated by very recent experimental observations of the 1/9-magnetization plateaus in YCu_{3}(OH)_{6+x}Br_{3-x} and YCu_{3}(OD)_{6+x}Br_{3-x}, our study delves into the magnetic-field-induced phase transitions in the nearest-neighbor antiferromagnetic Heisenberg model on the kagome lattice using the variational MonteCarlo technique. We uncover a phase transition from a zero-field Dirac spin liquid to a field-induced magnetically disordered phase that exhibits the 1/9-magnetization plateau. Through a comprehensive analysis encompassing the magnetization distribution, spin correlations, chiral order parameter, topological entanglement entropy, ground-state degeneracy, Chern number, and excitation spectrum, we pinpoint the phase associated with this magnetization plateau as a chiral Z_{3} topological quantum spin liquid and elucidate its diverse physical properties.

Non-Abelian Anyons in Periodically Driven Abelian Spin Liquids.

We show that non-Abelian anyons can emerge from an Abelian topologically ordered system subject to local time-periodic driving. This is illustrated with the toric-code model, as the canonical representative of a broad class of Abelian topological spin liquids. The Abelian anyons in the toric code include fermionic and bosonic quasiparticle excitations which see each other as π fluxes; namely, they result in the accumulation of a π phase if wound around each other. Non-Abelian behavior emerges because the Floquet modulation can engineer a nontrivial band topology for the fermions, inducing their fractionalization into Floquet-Majorana modes bound to the bosons. The latter then develop non-Abelian character akin to vortices in topological superconductors, realizing Ising topological order. Our findings shed light on the nonequilibrium physics of driven topologically ordered quantum matter and may facilitate the observation of non-Abelian behavior in engineered quantum systems.

Quantum state preparation of topological chiral spin liquids via Floquet engineering

Quantum state preparation of topological chiral spin liquids via Floquet engineering

Classification of Symmetry-Enriched Topological Quantum Spin Liquids

We present a systematic framework to classify symmetry-enriched topological quantum spin liquids in two spatial dimensions. This framework can deal with all topological quantum spin liquids, which may be either Abelian or non-Abelian and chiral or nonchiral. It can systematically treat a general symmetry, which may include both lattice symmetry and internal symmetry, may contain antiunitary symmetry, and may permute anyons. The framework applies to all types of lattices and can systematically distinguish different lattice systems with the same symmetry group using their quantum anomalies, which are sometimes known as Lieb-Schultz-Mattis anomalies. We apply this framework to classify U(1)2N chiral states and non-Abelian Ising(ν) states enriched by a p6×SO(3) or p4×SO(3) symmetry and ZN topological orders and U(1)2N×U(1)−2N topological orders enriched by a p6m×SO(3)×Z2T, p4m×SO(3)×Z2T, p6m×Z2T, or p4m×Z2T symmetry, where p6, p4, p6m, and p4m are lattice symmetries while SO(3) and Z2T are spin rotation and time-reversal symmetries, respectively. In particular, we identify symmetry-enriched topological quantum spin liquids that are not easily captured by the usual parton-mean-field approach, including examples with the familiar Z2 topological order. Published by the American Physical Society 2024

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}_2ℤ2 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.

Momentum-independent magnetic excitation continuum in the honeycomb iridate H3LiIr2O6

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. H3LiIr2O6 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 H3LiIr2O6 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 H3LiIr2O6 as a disordered topological spin liquid in close proximity to bond-disordered versions of the Kitaev quantum spin liquid.

Network construction of non-Abelian chiral spin liquids

We use a network of chiral junctions to construct a family of topological chiral spin liquids in two spatial dimensions. The chiral spin liquid phase harbors SU(2)_kk anyons, which stem from the underlying SU(2)_kk WZW models that describe the constituent spin chains of the network. The network exhibits quantized spin and thermal Hall conductances. We illustrate our construction by inspecting the topological properties of the SU(2)_22 model. We find that this model has emergent Ising anyons, with spinons acting as vortex excitations that bind Majorana zero modes. We also show that the ground state of this network is threefold degenerate on the torus, asserting its non-Abelian character. Our results shed new light on the stability of non-Abelian topological phases in artificial quantum materials.

Epitaxial growth, optical and electrical conductivity of the metallic pyrochlore Bi2Ru2O7 on Y-stabilized ZrO2 substrate

Epitaxial heterostructures composed of complex correlated metal oxides, grown along specific crystallographic orientations, offer a route to investigating emergent phenomena such as topological states and spin liquids through geometrical lattice engineering. A2Ru2O7 pyrochlore ruthenates, in particular, exhibit a metal–insulator transition with varying A cation, whose mechanism is not fully understood. We report on the epitaxial growth, and structural and electrical properties of metallic pyrochlore bismuth ruthenate heterostructures, grown along both the [001] and [111] directions. Ordered pyrochlore thin films were obtained with a highly oriented texture along the [001] and [111] crystallographic directions. Density functional theory calculations of the electronic band structure and density of states indicated that Bi2Ru2O7 is semimetallic and that hybridization of the Ru 4d and Bi 6p orbitals via the anion network at the Fermi energy was responsible for the metallicity. Electrical conductivity measurements confirmed that the compound is weakly metallic, in agreement with the reported conductivity for the stoichiometric bulk compound. The carrier concentration and mobility of the electrons compared favorably with previous reports on bulk material and indicate strong electron–electron interactions. The measured and computed optical conductivities were found to share coincident spectral features and confirm the electronic correlation. Comparison of the electrical and optical properties of the two distinct orientations indicates differences that cannot be attributed to differences in crystalline quality or dislocations and may indicate anisotropy in the electronic structure of Bi2Ru2O7. This study will enable access to the kagome lattice arising naturally in the 111 planes of the pyrochlore B cation sublattice, which may be used to uncover emergent topological properties.

Gauge-Theoretic Origin of Rydberg Quantum Spin Liquids.

Recent atomic physics experiments and numerical works have reported complementary signatures of the emergence of a topological quantum spin liquid in models with blockade interactions. However, the specific mechanism stabilizing such a phase remains unclear. Here, we introduce an exact relation between an Ising-Higgs lattice gauge theory on the kagome lattice and blockaded models on Ruby lattices. This relation elucidates the origin of previously observed topological spin liquids by directly linking the latter to a deconfined phase of a solvable gauge theory. By means of exact diagonalization and unbiased quantum MonteCarlo simulations, we show that the deconfined phases extend in a broad region of the parameter space; these states are characterized by a large ground state overlap with resonating valence bond wave functions. These blockaded models include both creation or annihilation and hopping dynamics, and can be experimentally realized with Rydberg-dressed atoms, offering novel and controllable platforms for the engineering and characterization of spin liquid states.

Dynamical Preparation of Quantum Spin Liquids in Rydberg Atom Arrays.

We theoretically analyze recent experiments [Semeghini etal., Science 374, 1242 (2021)SCIEAS0036-807510.1126/science.abi8794] demonstrating the onset of a topological spin liquid using a programmable quantum simulator based on Rydberg atom arrays. In the experiment, robust signatures of topological order emerge in out-of-equilibrium states that are prepared using a quasiadiabatic state preparation protocol. We show theoretically that the state preparation protocol can be optimized to target the fixed point of the topological phase-the resonating valence bond state of hard dimers-in a time that scales linearly with the number of atoms. Moreover, we provide a two-parameter variational manifold of tensor network states that accurately describe the many-body dynamics of the preparation process. Using this approach we analyze the nature of the nonequilibrium state, establishing the emergence of topological order.

Nuclear spin polarization and control in hexagonal boron nitride

Electron spins in van der Waals materials are playing a crucial role in recent advances in condensed-matter physics and spintronics. However, nuclear spins in van der Waals materials remain an unexplored quantum resource. Here we report optical polarization and coherent control of nuclear spins in a van der Waals material at room temperature. We use negatively charged boron vacancy ([Formula: see text]) spin defects in hexagonal boron nitride to polarize nearby nitrogen nuclear spins. We observe the Rabi frequency of nuclear spins at the excited-state level anti-crossing of [Formula: see text] defects to be 350 times larger than that of an isolated nucleus, and demonstrate fast coherent control of nuclear spins. Further, we detect strong electron-mediated nuclear-nuclear spin coupling that is five orders of magnitude larger than the direct nuclear-spin dipolar coupling, enabling multi-qubit operations. Our work opens new avenues for the manipulation of nuclear spins in van der Waals materials for quantum information science and technology.

Anomalous Dimensions of Monopole Operators at the Transitions between Dirac and Topological Spin Liquids

Monopole operators are studied in a large family of quantum critical points between Dirac and topological quantum spin liquids (QSLs): chiral and Z$_{2}$ QSLs. These quantum phase transitions are described by conformal field theories (CFTs): quantum electrodynamics in 2+1 dimensions with 2N flavors of two-component massless Dirac fermions and a four-fermion interaction. For the transition to a chiral spin liquid, it is the Gross-Neveu interaction (QED$_{3}$-GN), while for the transitions to Z$_{2}$ QSLs it is a superconducting pairing term with general spin/valley structure (generalized QED$_{3}$-Z$_{2}$GN). Using the state-operator correspondence, we obtain monopole scaling dimensions to sub-leading order in 1/N. For monopoles with a minimal topological charge q=1/2, the scaling dimension is 2N*0.26510 at leading-order, with the quantum correction being 0.118911(7) for the chiral spin liquid, and 0.102846(9) for the simplest Z$_{2}$ case (the expression is also given for a general pairing term). Although these two anomalous dimensions are nearly equal, the underlying quantum fluctuations possess distinct origins. The analogous result in QED$_{3}$ is also obtained and we find a sub-leading contribution of -0.038138(5), which differs slightly from the value first obtained in the literature. The scaling dimension of a QED$_{3}$-GN monopole with minimal charge is very close to the scaling dimensions of other operators predicted to be equal by a conjectured duality between QED$_{3}$-GN with 2N=2 flavors and the CP$^{1}$ model. Additionally, non-minimally charged monopoles on both sides of the duality have similar scaling dimensions. By studying the large-q asymptotics of the scaling dimensions in QED$_{3}$, QED$_{3}$-GN, and QED$_{3}$-Z$_{2}$GN we verify that the constant O(q$^{0}$) coefficient precisely matches the universal non-perturbative prediction for CFTs with a global U(1) symmetry.

Perfect flat band with chirality and charge ordering out of strong spin-orbit interaction

Spin-orbit interaction has established itself as a key player in the emergent phenomena in modern condensed matter, including topological insulator, spin liquid and spin-dependent transports. However, its function is rather limited to adding topological nature to band kinetics, leaving behind the growing interest in the direct interplay with electron correlation. Here, we prove by our spinor line graph theory that a very strong spin-orbit interaction realized in 5d pyrochlore electronic systems generates multiply degenerate perfect flat bands. Unlike any of the previous flat bands, the electrons in this band localize in real space by destructively interfering with each other in a spin selective manner governed by the SU(2) gauge field. These electrons avoid the Coulomb interaction by self-organizing their localized wave functions, which may lead to a flat-band state with a stiff spin chirality. It also causes perfectly trimerized charge ordering, which may explain the recently discovered exotic low-temperature insulating phase of CsW2O6.

Quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field

The quantum Monte Carlo method on asymptotic Lefschetz thimbles is a numerical algorithm devised specifically for alleviation of the sign problem appearing in the simulations of quantum many-body systems. In this method, the sign problem is alleviated by shifting the integration domain for the auxiliary fields, appearing for example in the conventional determinant quantum Monte Carlo method, from real space to an appropriate manifold in complex space. Here we extend this method to quantum spin models with generic two-spin interactions, by using the Hubbard-Stratonovich transformation to decouple the exchange interactions and the Popov-Fedotov transformation to map the quantum spins to complex fermions. As a demonstration, we apply the method to the Kitaev model in a magnetic field whose ground state is predicted to deliver a topological quantum spin liquid with non-Abelian anyonic excitations. To illustrate how the sign problem is alleviated in this method, we visualize the asymptotic Lefschetz thimbles in complex space, together with the saddle points and the zeros of the fermion determinant. We benchmark our method in the low-temperature region in a magnetic field and show that the sign of the action is recovered considerably and unbiased numerical results are obtained with sufficient precision.

Topological chiral spin liquids and competing states in triangular lattice SU(N) Mott insulators

SU($N$) Mott insulators have been proposed and/or realized in solid-state materials and with ultracold atoms on optical lattices. We study the two-dimensional SU($N$) antiferromagnets on the triangular lattice. Starting from an SU($N$) Heisenberg model with the fundamental representation on each site in the large-$N$ limit, we perform a self-consistent calculation and find a variety of ground states including the valence cluster states, stripe ordered states with a doubled unit-cell and topological chiral spin liquids. The system favors a cluster or ordered ground state when the number of flavors $N$ is less than 6. It is shown that, increasing the number of flavors enhances quantum fluctuations and eventually transfer the clusterized ground states into a topological chiral spin liquids. This chiral spin liquid ground state has an equivalent for the square lattice SU($N$) magnets. We further identify the corresponding lowest competing states that represent another distinct type of chiral spin liquid states. We conclude with a discussion about the relevant systems and the experimental probes.

Multiple spin-orbit excitons in \u03b1-RuCl3 from bulk to atomically thin layers

The van der Waals Kitaev magnet α-RuCl3 has recently garnered considerable attention due to its possible realization of topological spin liquids. Combining Raman spectroscopy with numerical calculations, we report here the thickness dependence of electronic structure and ensuing low-energy excitations for exfoliated α-RuCl3. We observe two pronounced peaks at A1 = 249 meV and A2 = 454 meV, which are assigned to single and double spin-orbit (SO) excitons, respectively. Our numerical calculations support this interpretation by reproducing their spectral energy and shape with the electronic parameters: SO coupling λ = 140 meV, Hund’s coupling JH = 350 meV, and on-site Coulomb interaction U = 2.35 eV. The multiple SO excitons persist down to a single layer, whereas their peaks shift slightly to lower energy. For frequencies below 350 cm−1, both a magnetic continuum and phonons show noticeable thickness dependence. These results demonstrate that a SO entangled jeff = 1/2 picture remains valid in a monolayer limit despite the presence of lattice distortions.

Generic field-driven phenomena in Kitaev spin liquids: Canted magnetism and proximate spin liquid physics

Topological spin liquids in two spatial dimensions are stable phases in the presence of a small magnetic field, but may give way to field-induced phenomena at intermediate field strengths. Sandwiched between the low-field spin liquid physics and the high-field spin-polarized phase, the exploration of magnetic phenomena in this intermediate regime however often remains elusive to controlled analytical approaches. Here we numerically study such intermediate-field magnetic phenomena for two representative Kitaev models (on the square-octagon and decorated honeycomb lattice) that exhibit either Abelian or non-Abelian topological order in the low-field limit. Using a combination of exact diagonalization and density matrix renormalization group techniques, as well as linear spin-wave theory, we establish the generic features of Kitaev spin liquids in an external magnetic field. While ferromagnetic models typically exhibit a direct transition to the polarized state at a relatively low field strength, antiferromagnetic couplings not only substantially stabilizes the topological spin liquid phase, but generically lead to the emergence of a distinct field-induced intermediate regime, separated by a crossover from the high-field polarized regime. Our results suggest that, for most lattice geometries, this regime generically exhibits significant spin canting, antiferromagnetic spin-spin correlations, and an extended proximate spin liquid regime at finite temperatures. Notably, we identify a symmetry obstruction in the original honeycomb Kitaev model that prevents, at least for certain field directions, the formation of such canted magnetism without breaking symmetries -- consistent with the recent numerical observation of an extended gapless spin liquid in this case.

Topological Z2 invariant in Kitaev spin liquids: Classification of gapped spin liquids beyond projective symmetry group

A projective symmetry group (PSG) has been regarded as a classification theory of spin liquids. However, it does not include a symmetry-protected topological order of fermionic spinon excitations, and thus the classification of gapped spin liquids is incomplete. We demonstrate the classification beyond PSG by utilizing the Kitaev model on the squareoctagon lattice, where two gapped spin liquids are distinguished by a topological $Z_2$ invariant. This $Z_2$ invariant can be defined solely by the time-reversal and translation symmetries on condition that the time-reversal symmetry is implemented projectively. Thus, it is a hidden class of topological Kitaev spin liquids with helical edge states, which has been ignored for a long time. This suggests that there exists an unknown classification scheme of gapped spin liquids beyond PSG.

Topological superconductivity in a van der Waals heterostructure.

Exotic states such as topological insulators, superconductors and quantum spin liquids are often challenging or impossible to create in a single material1-3. For example, it is unclear whether topological superconductivity, which has been suggested to be a key ingredient for topological quantum computing, exists in any naturally occurring material4-9. The problem can be circumvented by deliberately selecting the combination of materials in heterostructures so that the desired physics emerges from interactions between the different components1,10-15. Here we use this designer approach to fabricate van der Waals heterostructures that combine a two-dimensional (2D) ferromagnet with a superconductor, and we observe 2D topological superconductivity in the system. We use molecular-beam epitaxy to grow 2D islands of ferromagnetic chromium tribromide16 on superconducting niobium diselenide. We then use low-temperature scanning tunnelling microscopy and spectroscopy to reveal the signatures of one-dimensional Majorana edge modes. The fabricated 2D van der Waals heterostructure provides a high-quality, tunable system that can be readily integrated into device structures that use topological superconductivity. The layered heterostructures can be readily accessed by various external stimuli, potentially allowing external control of 2D topological superconductivity through electrical17, mechanical18, chemical19 or optical means20.