Spin Operators Research Articles

Two-loop supergravity on AdS5×S5 from CFT

We describe a construction of the two-loop amplitude of four graviton supermultiplets in AdS5×S5. We start from an ansatz for a preamplitude from which we generate the full amplitude under the action of a specific Casimir operator. The ansatz captures a recent ansatz of Huang and Yuan and we confirm their result through similar constraints. The form of the result suggests that all ambiguities are captured by the preamplitude which determines the result up to tree-level ambiguities only. We identify a class of four-dimensional ‘zigzag’ integrals which are perfectly adapted to describing the leading logarithmic discontinuity to all orders. We also observe that a bonus crossing symmetry of the preamplitude follows from the transformation properties of the Casimir operator. Combined with the zigzag integrals this allows us to construct a crossing symmetric function with the correct leading logarithmic discontinuities in all channels.From the two-loop result we extract an explicit expression for the two-loop correction to the anomalous dimensions of twist-four operators of generic spin which includes dependence on (alternating) nested harmonic sums up to weight three. We also revisit the prescription of the bulk-point limit of AdS amplitudes and show how it recovers the full flat-space amplitude, not just its discontinuity. With this extended notion of the bulk-point limit we reproduce the scale-dependent logarithmic threshold terms of type IIB string theory in flat-space.

Spinning gluons from the QCD light-ray OPE

We study the transverse spin structure of the squeezed limit of the three-point energy correlator, leftlangle mathrm{mathcal{E}}left({overrightarrow{n}}_1right)mathrm{mathcal{E}}left({overrightarrow{n}}_2right)mathrm{mathcal{E}}left({overrightarrow{n}}_3right)rightrangle . To describe its all orders perturbative behavior, we develop the light-ray operator product expansion (OPE) in QCD. At leading twist the iterated OPE of mathrm{mathcal{E}}left({overrightarrow{n}}_iright) operators closes onto light-ray operators {mathbbm{O}}^{left[Jright]}left(overrightarrow{n}right) with spin J, and transverse spin j = 0, 2. We compute the mathrm{mathcal{E}}left({overrightarrow{n}}_1right)mathrm{mathcal{E}}left({overrightarrow{n}}_2right) , mathrm{mathcal{E}}left({overrightarrow{n}}_1right){mathbbm{O}}^{left[Jright]}left({overrightarrow{n}}_2right) and {mathbbm{O}}^{left[{J}_1right]}left({overrightarrow{n}}_1right){mathbbm{O}}^{left[{J}_2right]}left({overrightarrow{n}}_2right) OPEs as analytic functions of J, which allows for the description of arbitrary squeezed limits of N -point correlators in QCD. We use these results with J = 3 to reproduce the perturbative expansion in the squeezed limit of the three-point correlator, as well as to resum the leading twist singular structure for both quark and gluon jets, including transverse spin contributions, as required for phenomenological applications. Finally, we briefly comment on the transverse spin structure at higher twists, and show that to all orders in the twist expansion the highest transverse spin contributions are universal between quark and gluon jets, and are descendants of the leading twist transverse spin-2 operator, allowing their resummation into a simple two-dimensional Euclidean conformal block. Due to the general applicability of our results to arbitrary correlation functions of energy flow operators, we anticipate that they can be widely applied to improving our understanding of jet substructure at the LHC.

Origin of nonsymmorphic bosonization formulas in generalized antiferromagnetic Kitaev spin- 12 chains from a renormalization-group perspective

Recently, in the Luttinger liquid phase of the one-dimensional generalized antiferromagnetic Kitaev spin-1/2 model, it has been found that the Abelian bosonization formulas of the local spin operators only respect the exact discrete nonsymmorphic symmetry group of the model, not the emergent U(1) symmetry. In this work, we perform a renormalization group (RG) study to provide explanations for the origin of the U(1) breaking terms in the bosonization formulas. We find that the lack of U(1) symmetry originates from the wave-function renormalization effects in the spin operators along the RG flow induced by the U(1) breaking interactions in the microscopic Hamiltonian. In addition, the RG analysis can give predictions to the signs and order of magnitudes of the coefficients in the bosonization formulas. Our work is helping to understand the rich nonsymmorphic physics in one-dimensional Kitaev spin models.

Geometric integration of classical spin dynamics via a mean-field Schrödinger equation

The Landau-Lifshitz equation describes the time evolution of magnetic dipoles and can be derived by taking the classical limit of a quantum mechanical spin Hamiltonian. To take this limit, one constrains the many-body quantum state to a tensor product of coherent states, thereby neglecting entanglement between sites. Expectation values of the quantum spin operators produce the usual classical spin dipoles. One may also consider expectation values of polynomials of the spin operators, leading to quadrupole and higher-order spin moments, which satisfy a dynamical equation of motion that generalizes the Landau-Lifshitz dynamics [Zhang and Batista, Phys. Rev. B 104, 104409 (2021)]. Here we reformulate the dynamics of these ${N}^{2}\ensuremath{-}1$ generalized spin components as a mean-field Schr\"odinger equation on the $N$-dimensional coherent state. This viewpoint suggests efficient integration methods that respect the local symplectic structure of the classical spin dynamics.

The 2PM Hamiltonian for binary Kerr to quartic in spin

From the S-matrix of spinning particles, we extract the 2 PM conservative potential for binary spinning black holes up to quartic order in spin operators. An important ingredient is the exponentiated gravitational Compton amplitude in the classical spin-limit for all graviton helicity sectors. The validity of the resulting Hamiltonian is verified by matching to known lower spin order results, as well as direct computation of the 2PM impulse and spin kicks from the eikonal phase and that from the test black hole scattering based on Mathisson-Papapetrou-Dixon equations.

High-fidelity control of spin ensemble dynamics via artificial intelligence: from quantum computing to NMR spectroscopy and imaging.

High-fidelity control of spin ensemble dynamics is essential for many research areas, spanning from quantum computing and radio-frequency (RF) engineering to NMR spectroscopy and imaging. However, attaining robust and high-fidelity spin operations remains an unmet challenge. Using an evolutionary algorithm and artificial intelligence (AI), we designed new RF pulses with customizable spatial or temporal field inhomogeneity compensation. Compared with the standard RF shapes, the new AI-generated pulses show superior performance for bandwidth, robustness, and tolerance to field imperfections. As a benchmark, we constructed a spin entanglement operator for the weakly coupled two-spin-1/2 system of 13CHCl3, achieving high-fidelity transformations under multiple inhomogeneity sources. We then generated band-selective and ultra-broadband RF pulses typical of biomolecular NMR spectroscopy. When implemented in multipulse NMR experiments, the AI-generated pulses significantly increased the sensitivity of medium-size and large protein spectra relative to standard pulse sequences. Finally, we applied the new pulses to typical imaging experiments, showing a remarkable tolerance to changes in the RF field. These AI-generated RF pulses can be directly implemented in quantum information, NMR spectroscopy of biomolecules, magnetic resonance imaging techniques for in vivo and materials sciences.

Anomaly-induced vacuum effective action with torsion: Covariant solution and ambiguities

The conformal anomaly in curved spacetime with antisymmetric torsion is reconsidered, taking into account new important details. We formulate, for the first time, the covariant solution of the anomaly-induced effective action. The covariant effective action includes local terms corresponding to total derivatives in the conformal anomaly. The contribution of massless fermions to these terms is characterized by multiplicative anomaly, coming from two different choices of doubling for the spinor operator. On the other hand, the nonlocal part of anomaly-induced action is free of ambiguities and admits a low-energy limit, similar to the effective potential in the metric-scalar theory.

Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Starting from the hamiltonian for the Heisenberg ferromagnet which comprise randomly distributed nonmagnetic ions as impurities in a Bravais lattice, we express the spin operators by means of the Dyson–Maleev transformation in terms of the Bose operators of the second quantization. Then by using methods of quantum statistical field theory, we derive the partition function and the free energy for the system. We adopt the Matsubara thermal perturbation method to a portion of the hamiltonian which describes the interaction between magnons and the stationary field of nonmagnetic ions. Upon averaging over all possible distributions of impurities, we express the free energy of the system as a function of the mean impurity concentration. Subsequently, we set up the double-time single particle Green function at temperature T in the momentum space in terms of magnon operators and derive the equation of motion for the Green function through the Heisenberg equation of motion and then solve the resulting equation. From this, we calculate the self-energy and then the spectral density function for the system. We apply the formalism to the case of the simple cubic lattice and compute the density of states, the spectral density function and the lifetime of the magnons as a function of energy for several values of the mean concentration of nonmagnetic ions in the ferromagnetic lattice. We calculate the magnon energy spectrum as a function of the average impurity concentration fraction c, which shows that for low lying states, the excitation energy increases continuously with c in the studied range 0.1≤c≤0.7. We also use the spectral density function to compute some thermodynamical quantities through the magnon occupation number. We have obtained closed form expressions for the configurationally averaged physical quantities of interest in a unified fashion as functions of the mean concentration of nonmagnetic impurities c to any order of c applicable below a critical percolation concentration cp. The quantities of interest comprise the thermodynamic potential (free energy), the spin-wave self-energy and the spectral density function from which other quantities can be derived.

Heteronuclear decoupling with rotor-synchronized phase-alternated cycles.

A new heteronuclear decoupling pulse sequence is introduced, dubbed ROtor-Synchronized Phase-Alternated Cycles (ROSPAC). It is based on a partial refocusing of the coherences (spin operator products or cross-terms) [Filip et al., J. Mag. Reson. 176, 2 (2005)] responsible for transverse spin-polarization dephasing, on the irradiation of a large pattern of radio-frequencies, and on a significant minimization of the cross-effects implying 1H chemical-shift anisotropy. Decoupling efficiency is analyzed by numerical simulations and experiments and compared to that of established decoupling sequences [swept-frequency two-pulse phase-modulated (TPPM), TPPM, small phase incremental alternation (SPINAL), refocused Continuous-wave (CWApa), and Rotor-Synchronized Hahn-Echo pulse train (RS-HEPT)]. It was found that ROSPAC offers good 1H offset robustness for a large range of chemical shifts and low radio-frequency (RF) powers, and performs very well in the ultra-fast magic-angle spinning (MAS) regime, where it is almost independent from RF power and permits it to avoid rotary-resonance recoupling conditions (v1 = nvr, n = 1, 2). It has the advantage that only the pulse lengths require optimization and has a low duty cycle in the pulsed decoupling regime. The efficiency of the decoupling sequence is demonstrated on a model microcrystalline sample of the model protein domain GB1 at 100kHz MAS at 18.8T.

The discrete Chebyshev–Meckler–Mermin–Schwarz polynomials and spin algebra

The polynomials discovered by Chebyshev and subsequently related to spin transition probabilities by Meckler [Meckler, Phys. Rev. 111, 1447 (1958)] and Mermin and Schwarz [Found. Phys. 12, 101 (1982)] are studied, and their application to phase space representations of spin states and operators is examined. In particular, a formula relating the end-point value of the polynomials to scale factors relating different phase space representations of spherical harmonic operators is found. This formula is applied to illustrative calculations of Wigner functions for a single spin and the singlet state of a pair of spins.

CIM-Spin: A Scalable CMOS Annealing Processor With Digital In-Memory Spin Operators and Register Spins for Combinatorial Optimization Problems

Recently, annealing processors based on the Ising model have received rising attention as efficient alternative hardware for solving combinatorial optimization problems. After mapping a problem to the hardware Ising model, we can observe the natural convergence behavior of the Ising model and find potential solutions to the problem. The quantum annealing processor has shown effectiveness in finding better solutions to the problems by using quantum bits (qubits) with annealing based on their quantum tunneling behaviors. However, the annealing processor based on the emerging quantum technology faces challenges such as limited scalability, high energy consumption, and operating costs due to the extremely low operating temperature. As a low-cost alternative, a CMOS annealing processor has been recently developed and drawn increasing attention thanks to the advantages over its quantum counterpart, including better scalability and lower energy consumption. In this work, we present a digital CMOS annealing processor with in-memory spin operators and register spins. The proposed CMOS annealing processor achieves > <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10\times $ </tex-math></inline-formula> energy efficiency and faster operation than state-of-the-art works.

The spin-1 XYZ model with Dzyaloshinskii–Moriya interaction

The spin-1 XYZ model is studied in terms of a mean-field (MF) approach by introducing the spin operators on honeycomb lattice. The considered Hamiltonian consists of a bilinear exchange interaction parameter (Jz) and a single-ion anisotropy (Dz) only along the z-axis, in addition to the Dzyaloshinskii–Moriya interaction (Δm). The external magnetic field is introduced in all three dimensions and their behaviors are examined on the components of magnetization. Then the thermal behaviors of magnetizaitons are investigated in detail to obtain the phase diagrams on the (Dz/J,kT/J) and (Δm/J,kT/J) planes when the external magnetic field components are turned off. It is found that the model gives both first- and second-order phase transitions in addition to a few types critical points including the tricritical and bicritical points.

One-to-one correspondence between thermal structure factors and coupling constants of general bilinear Hamiltonians.

A theorem that establishes a one-to-one relation between zero-temperature static spin-spin correlators and coupling constants for a general class of quantum spin Hamiltonians bilinear in the spin operators has been recently established by Quintanilla, using an argument in the spirit of the Hohenberg-Kohn theorem in density functional theory. Quintanilla's theorem gives a firm theoretical foundation to quantum spin Hamiltonian learning using spin structure factors as input data. Here we extend the validity of the theorem in two directions. First, following the same approach as Mermin, the proof is extended to the case of finite-temperature spin structure factors, thus ensuring that the application of this theorem to experimental data is sound. Second, we note that this theorem applies to all types of Hamiltonians expressed as sums of bilinear operators, so that it can also relate the density-density correlators to the Coulomb matrix elements for interacting electrons in the lowest Landau level.

Hermitian matrix definiteness from quantum phase estimation

An algorithm to classify a general Hermitian matrix according to its signature (positive semi-definite, negative or indefinite) is presented. It builds on the Quantum Phase Estimation algorithm, which stores the sign of the eigenvalues of a Hermitian matrix in one ancillary qubit. The signature of the matrix is extracted from the mean value of a spin operator in this single ancillary qubit. The algorithm is probabilistic, but it shows good performance, achieving 97% of correct classifications with few qubits. The computational cost scales comparably to the classical one in the case of a generic matrix, but improves significantly for restricted classes of matrices like $k$-local or sparse hamiltonians.

Quantum field theory for spin operator of the photon

All elementary particles in nature can be classified as fermions with half-integer spin and bosons with integer spin. Within quantum electrodynamics (QED), even though the spin of the Dirac particle is well defined, there exist open questions on the quantized description of spin of the gauge field particle -- the photon. Using quantum field theory, we discover the quantum operators for the spin angular momentum (SAM) $\boldsymbol{S}_{M}=(1/c)\int d^{3}x\boldsymbol{\pi}\times\boldsymbol{A}$ and orbital angular momentum (OAM) $\boldsymbol{L}_{M}=-(1/c)\int d^{3}x\pi^{\mu}\boldsymbol{x}\times\boldsymbol{\nabla}A_{\mu}$ of the photon, where $\pi^{\mu}$ is the conjugate canonical momentum of the gauge field $A^{\mu}$. We also reveal a perfect symmetry between the angular momentum commutation relations for Dirac fields and Maxwell fields. We derive the well-known OAM and SAM of classical electromagnetic fields from the above defined quantum operators. Our work shows that the spin and OAM operators commute which is important for simultaneously observing and separating the SAM and OAM. The correct commutation relations of orbital and spin angular momentum of the photon have applications in quantum optics, topological photonics as well as nanophotonics and can be extended in the future for the spin structure of nucleons.

Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations

The Kitaev model on the honeycomb lattice, while being integrable via the spin-fermion mapping, has generally resisted an analytical treatment of the far-from-equilibrium dynamics due to the extensive number of relevant configurations of conserved charges. Here we study a close proxy of this model, the isotropic Kitaev spin-1/2 model on the Bethe lattice. Instead of relying on the spin-fermion mapping, we take a straightforward approach of solving Heisenberg equations for a tailored subset of spin operators. The simplest operator in this subset corresponds to the energy contribution of a single bond direction. As an example, we calculate the time-dependent expectation value of this observable for a factorized translation-invariant (or staggered-translation-invariant) initial state with arbitrary initial (staggered) polarization.

Hilbert Space Structure of the Low Energy Sector of U(N) Quantum Hall Ferromagnets and Their Classical Limit

Using the Lieb–Mattis ordering theorem of electronic energy levels, we identify the Hilbert space of the low energy sector of U(N) quantum Hall/Heisenberg ferromagnets at filling factor M for L Landau/lattice sites with the carrier space of irreducible representations of U(N) described by rectangular Young tableaux of M rows and L columns, and associated with Grassmannian phase spaces U(N)/U(M)×U(N−M). We embed this N-component fermion mixture in Fock space through a Schwinger–Jordan (boson and fermion) representation of U(N)-spin operators. We provide different realizations of basis vectors using Young diagrams, Gelfand–Tsetlin patterns and Fock states (for an electron/flux occupation number in the fermionic/bosonic representation). U(N)-spin operator matrix elements in the Gelfand–Tsetlin basis are explicitly given. Coherent state excitations above the ground state are computed and labeled by complex (N−M)×M matrix points Z on the Grassmannian phase space. They adopt the form of a U(N) displaced/rotated highest-weight vector, or a multinomial Bose–Einstein condensate in the flux occupation number representation. Replacing U(N)-spin operators by their expectation values in a Grassmannian coherent state allows for a semi-classical treatment of the low energy (long wavelength) U(N)-spin-wave coherent excitations (skyrmions) of U(N) quantum Hall ferromagnets in terms of Grasmannian nonlinear sigma models.

Quantum spin solver near saturation: QS3

We develop a program package named QS3▪ based on the (thick-restart) Lanczos method for analyzing spin-1/2 XXZ-type quantum spin models on spatially uniform/non-uniform lattices near fully polarized states, which can be mapped to dilute hardcore Bose systems. All calculations in QS3, including eigenvalue problems, expectation values for one/two-point spin operators, and static/dynamical spin structure factors, are performed in the symmetry-adapted bases specified by the number N↓ of down spins and the wave number k associated with the translational symmetry without using the bit representation for specifying spin configurations. Because of these treatments, QS3 can support large-scale quantum systems containing more than 1000 sites with dilute N↓. We show the benchmark results of QS3 for the low-energy excitation dispersion of the isotropic Heisenberg model on the 10×10×10 cubic lattice, the static and dynamical spin structure factors of the isotropic Heisenberg model on the 10×10 square lattice, and the open-MP parallelization efficiency on the supercomputer (Ohtaka) based on AMD Epyc 7702 installed at the Institute for the Solid State Physics (ISSP). Theoretical backgrounds and the user interface of QS3 are also described. Program summaryProgram Title: QS3CPC Library link to program files:https://doi.org/10.17632/yc6jytvf8v.1Developer's repository link:https://github.com/QS-Cube/EDLicensing provisions: MITProgramming language: Fortran90External routines/libraries: BLAS, LAPACKNature of problem: Physical properties (such as total energy, magnetic moment, two-point spin correlation function, and dynamical structure factor)Solution method: Application software based on the full diagonalization method and the exact diagonalization method using the Lanczos and thick-restart Lanczos techniques for quantum spin S=1/2 models such as the XXZ model.Restrictions: Spin S=1/2 systems with U(1) symmetry.Unusual features: Massively large quantum spin systems with U(1) symmetry near the saturation field can be solved with or without considering translational symmetry, which is difficult to treat using standard exact diagonalization libraries with the bit representation for specifying spin configurations.

Metrological Characterization of Non-Gaussian Entangled States of Superconducting Qubits.

Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterizes the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalization of the RSP with respect to nonlinear observables and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, we report the characterization of multiparticle entangled states generated during its nonlinear dynamics. First, selecting ten qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89_{-0.29}^{+0.28} dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.

Dynamical Collective Excitations and Entanglement of Two Strongly Correlated Rydberg Superatoms

Based on the dipole blockade effect and with the aid of the superatom (SA) model, we propose a scheme to investigate the correlated evolution of two Rydberg sub-superatoms (SSAs), formed by two spatially separated atomic Rydberg sub-ensembles but in the same blockade region. Starting from the pure separable states, we investigate the in-phase or anti-phase correlated dynamics and explore how two Rydberg SSAs entangle with each other mediated by a single Rydberg excitation. Starting from the entangled states, we discuss the robustness of the system against decoherence induced by the dephasing rate. Our results show that both the correlated evolution of two Rydberg SSAs and their collective-state entanglement are usually sensitive to the number of each Rydberg SSA. This allows us to coherently manipulate the Rydberg ensemble over long distances from the single-quantum level to the mesoscopic level by changing the number of atoms. Furthermore, the method for dividing an SA into two SSAs and obtaining their spin operators without any approximation can be readily generalized to the case of many SSAs. It may have potential promising applications in quantum information processing and provide an attractive platform to study the quantum-classical correspondence, many-body physics and so on.