Two-dimensional Spin Research Articles

Two-dimensional spin models with macroscopic degeneracy

We consider a class of anisotropic spin- models with competing ferro- and antiferromagnetic interactions on two-dimensional Tasaki and kagome lattices consisting of corner sharing triangles. For certain values of the interactions the ground state is macroscopically degenerated in zero magnetic field. In this case the ground state manifold consists of isolated magnons as well as the bound magnon complexes. The ground state degeneracy is estimated using a special form of exact wave function which admits arrow configuration representation on two-dimensional lattice. The comparison of this estimate with the result for some special exactly solved models shows that the used approach determines the number of the ground states with exponential accuracy. It is shown that the main contribution to the ground state degeneracy and the residual entropy is given by the bound magnon complexes.

Spatial order in a two-dimensional spin–orbit-coupled spin-1/2 condensate: superlattice, multi-ring and stripe formation

We demonstrate the formation of stable spatially-ordered states in a uniform and also trapped quasi-two-dimensional (quasi-2D) Rashba or Dresselhaus spin–orbit (SO) coupled pseudo spin-1/2 Bose–Einstein condensate using the mean-field Gross–Pitaevskii equation. For weak SO coupling, one can have a circularly-symmetric (0, +1)- or (0, −1)-type multi-ring state with intrinsic vorticity, for Rashba or Dresselhaus SO coupling, respectively, where the numbers in the parentheses denote the net angular momentum projection in the two components, in addition to a circularly-asymmetric degenerate state with zero net angular momentum projection. For intermediate SO couplings, in addition to the above two types, one can also have states with stripe pattern in component densities with no periodic modulation in total density. The stripe state continues to exist for large SO coupling. In addition, a new spatially-periodic state appears in the uniform system: a superlattice state, possessing some properties of a supersolid, with a square-lattice pattern in component densities and also in total density. In a trapped system the superlattice state is slightly different with multi-ring pattern in component density and a square-lattice pattern in total density. For an equal mixture of Rashba and Dresselhaus SO couplings, in both uniform and trapped systems, only stripe states are found for all strengths of SO couplings. In a uniform system all these states are quasi-2D solitonic states.

A reconfigurable spin ice

Magnetism Spin ices, magnetic systems in which local spins respect the so-called ice rules, can occur in natural materials or be engineered in patterned arrays. King et al. used superconducting qubits to implement a two-dimensional artificial spin ice. By changing the strength and ratio of spin couplings, the researchers were able to access a variety of ground states. Arranging the boundary spins in an antiferromagnetic configuration and then flipping one of those spins generated a magnetic monopole in the system's interior. Science , abe2824, this issue p. [576][1] [1]: /lookup/doi/10.1126/science.abe2824

Qubit spin ice.

Artificial spin ices are frustrated spin systems that can be engineered, in which fine tuning of geometry and topology has allowed the design and characterization of exotic emergent phenomena at the constituent level. Here, we report a realization of spin ice in a lattice of superconducting qubits. Unlike conventional artificial spin ice, our system is disordered by both quantum and thermal fluctuations. The ground state is classically described by the ice rule, and we achieved control over a fragile degeneracy point, leading to a Coulomb phase. The ability to pin individual spins allows us to demonstrate Gauss's law for emergent effective monopoles in two dimensions. The demonstrated qubit control lays the groundwork for potential future study of topologically protected artificial quantum spin liquids.

Continuous control of classical-quantum crossover by external high pressure in the coupled chain compound CsCuCl3

In solid materials, the parameters relevant to quantum effects, such as the spin quantum number, are basically determined and fixed at the chemical synthesis, which makes it challenging to control the amount of quantum correlations. We propose and demonstrate a method for active control of the classical-quantum crossover in magnetic insulators by applying external pressure. As a concrete example, we perform high-field, high-pressure measurements on CsCuCl3, which has the structure of weakly-coupled spin chains. The magnetization process experiences a continuous evolution from the semi-classical realm to the highly-quantum regime with increasing pressure. Based on the idea of "squashing” the spin chains onto a plane, we characterize the change in the quantum correlations by the change in the value of the local spin quantum number of an effective two-dimensional model. This opens a way to access the tunable classical-quantum crossover of two-dimensional spin systems by using alternative systems of coupled-chain compounds.

Long-lived coherence in driven many-spin systems: from two to infinite spatial dimensions

Long-lived coherences, emerging under periodic pulse driving in the disordered ensembles of strongly interacting spins, offer immense advantages for future quantum technologies, but the physical origin and the key properties of this phenomenon remain poorly understood. We theoretically investigate this effect in ensembles of different dimensionality, and predict existence of the long-lived coherences in all such systems, from two-dimensional to infinite-dimensional (where every spin is coupled to all others with similar strength), which are of particular importance for quantum sensing and quantum information processing. We explore the transition from two to infinite dimensions, and show that the long-time coherence dynamics in all dimensionalities is qualitatively similar, although the short-time behavior is drastically different, exhibiting dimensionality-dependent singularity. Our study establishes the common physical origin of the long-lived coherences in different dimensionalities, and suggests that this effect is a generic feature of the strongly coupled spin systems with positional disorder. Our results lay out foundation for utilizing the long-lived coherences in a range of application, from quantum sensing with two-dimensional spin ensembles, to quantum information processing with the infinitely-dimensional spin systems in the cavity-QED settings.

The time-averaged spin-Hall conductivity in two-dimensional spin–orbit coupled systems: the role of spin dynamics

We investigate the spin-Hall conductivity (SHC) in the two-dimensional spin–orbit coupled systems by taking spin precession into account. The influence of spin precession on the spin-Hall current in the presence of disorder is investigated. Perturbation method leads to the result that the spin dynamics is composed of Larmor (periodic) and non-Larmor (non-periodic) precession. The non-Larmor component of spin is found to be the same result obtained from the Kubo formula in the short time limit. The Larmor component of spin, i.e., spin precession in the unperturbed system, was neglected in the previous studies, but it plays an important role in the linear response theory. The Larmor precession of spin should be zero after time average over several complete periods because there is no specific orientation perpendicular to the plane. By using the requirement of vanishing time-averaged Larmor precession of spin, we calculate the time-averaged non-Larmor SHC for k-cubic Rashba system by using the conventional definition of the spin current. Our result is 2.1(q/8π) which is very close to the experimental value 2.2(q/8π) by Wunderlich et al [2005 Phys. Rev. Lett. 94, 047204], where −q is the electric charge.

Host-Guest Interaction in Ethylene and Ethane Separation on Zeolitic Imidazolate Frameworks as Revealed by Solid-State NMR Spectroscopy.

The separation of ethane/ethylene mixture by using metal-organic frameworks (MOFs) as adsorbents is strongly associated with the pore size-sieving effect and the adsorbent-adsorbate interaction. Herein, solid-state NMR spectroscopy is utilized to explore the host-guest interaction and ethane/ethylene separation mechanism on zeolitic imidazolate frameworks (ZIFs). Preferential access to the ZIF-8 and ZIF-8-90 frameworks by ethane compared to ethylene is directly visualized from two-dimensional 1 H-1 H spin diffusion MAS NMR spectroscopy and further verified by computational density distributions. The 1 H MAS NMR spectroscopy provides an alternative for straightforwardly extracting the adsorption selectivity of ethane/ethylene mixture at 1.1∼9.6 bar in ZIFs, which is consistent with the IAST predictions.

Generating a Topological Anomalous Hall Effect in a Nonmagnetic Conductor: An In-Plane Magnetic Field as a Direct Probe of the Berry Curvature

We demonstrate that the Berry curvature monopole of nonmagnetic two-dimensional spin-3/2 holes leads to a novel Hall effect linear in an applied in-plane magnetic field B_{∥}. Remarkably, all scalar and spin-dependent disorder contributions vanish to leading order in B_{∥}, while there is no Lorentz force and hence no ordinary Hall effect. This purely intrinsic phenomenon, which we term the anomalous planar Hall effect (APHE), provides a direct transport probe of the Berry curvature accessible in all p-type semiconductors. We discuss experimental setups for its measurement.

Tailoring Dzyaloshinskii\u2013Moriya interaction in a transition metal dichalcogenide by dual-intercalation

Dzyaloshinskii–Moriya interaction (DMI) is vital to form various chiral spin textures, novel behaviors of magnons and permits their potential applications in energy-efficient spintronic devices. Here, we realize a sizable bulk DMI in a transition metal dichalcogenide (TMD) 2H-TaS2 by intercalating Fe atoms, which form the chiral supercells with broken spatial inversion symmetry and also act as the source of magnetic orderings. Using a newly developed protonic gate technology, gate-controlled protons intercalation could further change the carrier density and intensely tune DMI via the Ruderman–Kittel–Kasuya–Yosida mechanism. The resultant giant topological Hall resistivity {rho }_{{xy}}^{T} of 1.41{mathrm{mu}} Omega cdot {{mathrm{cm}}} at {V}_{g}=-5.2{mathrm{V}} (about 424 % larger than the zero-bias value) is larger than most known chiral magnets. Theoretical analysis indicates that such a large topological Hall effect originates from the two-dimensional Bloch-type chiral spin textures stabilized by DMI, while the large anomalous Hall effect comes from the gapped Dirac nodal lines by spin–orbit interaction. Dual-intercalation in 2H-TaS2 provides a model system to reveal the nature of DMI in the large family of TMDs and a promising way of gate tuning of DMI, which further enables an electrical control of the chiral spin textures and related electromagnetic phenomena.

Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits.

In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the buildup of spatiotemporal correlation functions in one- and two-dimensional quantum spin systems, where we particularly scrutinize the inevitable impact of errors present in any realistic implementation. Importantly, we find that the hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, which opens the door to reach nontrivial time scales with a small number of gates. While errors within the random circuit are shown to be irrelevant, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.

Supersolid-like states in a two-dimensional trapped spin–orbit-coupled spin-1 condensate

We study supersolid-like states in a quasi-two-dimensional trapped Rashba and Dresselhaus spin–orbit (SO) coupled spin-1 condensate. For small strengths of SO coupling γ (γ ⪅ 0.75), in the ferromagnetic phase, circularly-symmetric (0, ±1, ±2)- and (∓1, 0, ±1)-type states are formed where the numbers in the parentheses denote the angular momentum of the vortex at the center of the components and where the upper (lower) sign correspond to Rashba (Dresselhaus) coupling; in the antiferromagnetic phase, only (∓1, 0, ±1)-type states are formed. For large strengths of SO coupling, supersolid-like superlattice and superstripe states are formed in the ferromagnetic phase. In the antiferromagnetic phase, for large strengths of SO coupling, supersolid-like superstripe and multi-ring states are formed. For an equal mixture of Rashba and Dresselhaus SO couplings, only a superstripe state is found. All these states are found to be dynamically stable and hence accessible in an experiment and will enhance the fundamental understanding of crystallization onto radially periodic states in solids.

Monopole hierarchy in transitions out of a Dirac spin liquid

Quantum spin liquids host novel emergent excitations, such as monopoles of an emergent gauge field. Here, we study the hierarchy of monopole operators that emerges at quantum critical points (QCPs) between a two-dimensional Dirac spin liquid and various ordered phases. This is described by a confinement transition of quantum electrodynamics in two spatial dimensions (QED3 Gross–Neveu theories). Focusing on a spin ordering transition, we get the scaling dimension of monopoles at leading order in a large-N expansion, where 2N is the number of Dirac fermions, as a function of the monopole’s total magnetic spin. Monopoles with a maximal spin have the smallest scaling dimension while monopoles with a vanishing magnetic spin have the largest one, the same as in pure QED3. The organization of monopoles in multiplets of the QCP’s symmetry group SU(2) × SU(N) is shown for general N.

An entropic simulational study of the spin-1 Baxter–Wu model in a crystal field

We investigate the critical behavior of the two-dimensional spin-1 Baxter–Wu model in a crystal field using entropic sampling simulations, based on the Wang–Landau method, with the joint density of states. We obtain the temperature–crystal field phase diagram, which includes a tetracritical line ending at a pentacritical point. A finite-size scaling analysis of the maximum of the specific heat, while changing the crystal field anisotropy, is used to obtain a precise location of the pentacritical point. Our results give the critical temperature and crystal field as Tpc=0.98030(10) and Dpc=1.68288(62). We also detect that at the first-order region of the phase diagram, the specific heat exhibits a double peak structure as in the Schottky-like anomaly, which is associated with an order–disorder transition.

Renormalization of concurrence and quantum Fisher information in two-dimensional XXZ model

We investigate two-dimensional anisotropic spin- $$\frac{1}{2}$$ lattice for XXZ model using concurrence and quantum Fisher information. The model is solved by using quantum renormalization group method and observed the quantum phase transition in thermodynamic limit. After sufficient iterations of quantum renormalization group, the concurrence and quantum Fisher information both attain two different saturated values that represent two different phases, the Neel phase and the spin fluid phase. The first-order derivative and the scaling behavior of both the concurrence and the quantum Fisher information are studied. At phase transition point, the non-analytic behavior of the derivative as a function of lattice size is discussed. Moreover, we observe that the scaling exponent for the concurrence and the quantum Fisher information describe the correlation length of the model at the critical point.

Efficient Tensor Network Ansatz for High-Dimensional Quantum Many-Body Problems.

We introduce a novel tensor network structure augmenting the well-established tree tensor network representation of a quantum many-body wave function. The new structure satisfies the area law in high dimensions remaining efficiently manipulatable and scalable. We benchmark this novel approach against paradigmatic two-dimensional spin models demonstrating unprecedented precision and system sizes. Finally, we compute the ground state phase diagram of two-dimensional lattice Rydberg atoms in optical tweezers observing nontrivial phases and quantum phase transitions, providing realistic benchmarks for current and future two-dimensional quantum simulations.

New effective precession spin for modeling multimodal gravitational waveforms in the strong-field regime

Accurately modeling the complete gravitational-wave signal from precessing binary black holes through the late inspiral, merger, and ringdown remains a challenging problem. The lack of analytic solutions for the precession dynamics of generic double-spin systems, and the high dimensionality of the problem, obfuscate the incorporation of strong-field spin-precession information into semianalytic waveform models used in gravitational-wave data analysis. Previously, an effective precession spin ${\ensuremath{\chi}}_{p}$ was introduced to reduce the number of spin degrees of freedom. Here, we show that ${\ensuremath{\chi}}_{p}$ alone does not accurately reproduce higher-order multipolar modes, in particular the ones that carry strong imprints due to precession such as the (2,1)-mode. To improve the higher-mode content, and in particular to facilitate an accurate incorporation of precession effects in the strong-field regime into waveform models, we introduce a new dimensional reduction through an effective precession spin vector, ${\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\chi}}}_{\ensuremath{\perp}}$, which takes into account precessing spin information from both black holes. We show that this adapted effective precession spin (i) mimics the precession dynamics of the fully precessing configuration remarkably well, (ii) captures the signature features of precession in higher-order modes, and (iii) reproduces the final state of the remnant black hole with high accuracy for the overwhelming majority of configurations. We demonstrate the efficacy of this two-dimensional precession spin in the strong-field regime, paving the path for meaningful calibration of the precessing sector of semianalytic waveform models with a faithful representation of higher-order modes through merger and the remnant black hole spin.

Ordering behavior of the two-dimensional Ising spin glass with long-range correlated disorder.

The standard short-range two-dimensional Ising spin glass is numerically well accessible, in particular, because there are polynomial-time ground-state algorithms. On the other hand, in contrast to higher dimensional spin glasses, it does not exhibit a rich behavior, i.e., no ordered phase at finite temperature. Here, we investigate whether long-range correlated bonds change this behavior. This would still keep the model numerically well accessible while exhibiting a more interesting behavior. The bonds are drawn from a Gaussian distribution with a two-point correlation for bonds at distance r that decays as (1+r^{2})^{-a/2}, a≥0. We study numerically with exact algorithms the ground-state and domain-wall excitations. Our results indicate that the inclusion of bond correlations still does not lead to a spin-glass order at any finite temperature. A further analysis reveals that bond correlations have a strong effect at local length scales, inducing ferro- and antiferromagnetic domains into the system. The length scale of ferro- and antiferromagnetic order diverges exponentially as the correlation exponent approaches a critical value, a→a_{crit}=0. Thus, our results suggest that the system becomes a ferro- or antiferromagnet only in the limit a→0.

Mirror symmetry breaking in a model insulating cuprate

Understanding the complex phase diagram of cuprate superconductors is an outstanding challenge. The most actively studied questions surround the nature of the pseudogap and strange metal states and their relationship to superconductivity. In contrast, there is general agreement that the low energy physics of the Mott insulating parent state is well captured by a two-dimensional spin $S$ = 1/2 antiferromagnetic (AFM) Heisenberg model. However, recent observations of a large thermal Hall conductivity in several parent cuprates appear to defy this simple model and suggest proximity to a magneto-chiral state that breaks all mirror planes perpendicular to the CuO$_2$ layers. Here we use optical second harmonic generation to directly resolve the point group symmetries of the model parent cuprate Sr$_2$CuO$_2$Cl$_2$. We report evidence of an order parameter $\Phi$ that breaks all perpendicular mirror planes and is consistent with a magneto-chiral state in zero magnetic field. Although $\Phi$ is clearly coupled to the AFM order parameter, we are unable to realize its time-reversed partner ($-\Phi$) by thermal cycling through the AFM transition temperature ($T_{\textrm{N}}$ $\approx$ 260 K) or by sampling different spatial locations. This suggests that $\Phi$ onsets above $T_{\textrm{N}}$ and may be relevant to the mechanism of pseudogap formation.

Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry

We carefully study how the fermion-fermion interactions affect the low-energy states of a two-dimensional spin-1/2 fermionic system on the kagomé lattice with a quadratic band crossing point. With the help of the renormalization group approach, we can treat all kinds of fermionic interactions on the same footing and then establish the coupled energy-dependent flows of fermionic interaction parameters via collecting one-loop corrections, from which a number of interesting results are extracted in the low-energy regime. At first, various sorts of fermion-fermion interactions furiously compete with each other and are inevitably attracted by certain fixed point in the parameter space, which clusters into three qualitatively distinct regions relying heavily upon the structure parameters of materials. In addition, we notice that an instability accompanied by some symmetry breaking is triggered around different sorts of fixed points. Computing and comparing susceptibilities of twelve potential candidates indicates that charge density wave always dominates over all other instabilities. Incidently, there exist several subleading ones including the x-current, bond density, and chiral plus s-wave superconductors. Finally, we realize that strong fluctuations nearby the leading instability prefer to suppress density of states and specific heat as well compressibility of quasiparticles in the lowest-energy limit.