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Results for “Spin operator”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Computation of the expectation value of the spin operator S^ 2 for the spin-flip Bethe–Salpeter equation

Spin-flip (SF) methods applied to excited-state approaches like the Bethe–Salpeter equation allow access to the excitation energies of open-shell systems, such as molecules and defects in solids. The eigenstates of these solutions, however, are generally not eigenstates of the spin operator S^ 2 . Even for simple cases where the excitation vector is expected to be, for example, a triplet state, the value of S^ 2 may be found to differ from 2.00; this difference is called 'spin contamination'. The expectation values S^ 2 must be computed for each excitation vector, to assist with the characterization of the particular excitation and to determine the amount of spin contamination of the state. Here, our aim is to provide for the first time in the SF methods literature a comprehensive resource on the derivation of the formulas for S^ 2 as well as its computational implementation. After a brief discussion of the theory of the SF Bethe–Salpeter equation (BSE) and some examples further illustrating the need for calculating S^ 2 , we present the derivation for the general equation for computing S^ 2 with the eigenvectors from an SF-BSE calculation, how it is implemented in a Python script, and timing information on how this calculation scales with the size of the SF-BSE Hamiltonian.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Open-system spin transport and operator weight dissipation in spin chains

Here, we use nonequilibrium steady states to study the effect of dissipation-assisted operator evolution (DAOE) on the scaling behavior of transport in one-dimensional spin chains. We consider three models in the XXZ family: the XXZ model with staggered anisotropy, which is chaotic; XXZ model with no external field and tunable interaction, which is Bethe-ansatz integrable and (in the zero interaction limit) free-fermion integrable; and the disordered XY model, which is free-fermion integrable and Anderson localized. We find evidence that DAOE's effect on transport is controlled by its effect on the system's conserved quantities. To the extent that DAOE preserves those symmetries, it preserves the scaling of the system's transport properties; to the extent it breaks those conserved quantities, it pushes the system towards diffusive scaling of transport.

1-dimensional spin chains↗
DOE OSTI2022

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 –1 generalized spin components as a mean-field Schrödinger equation on the N-dimensional coherent state. Furthermore, this viewpoint suggests efficient integration methods that respect the local symplectic structure of the classical spin dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

A model of randomly-coupled Pauli spins

Abstract We construct a model of Pauli spin operators with all-to-all 4-local interactions by replacing Majorana fermions in the SYK model with spin operators. Equivalently, we replace fermions with hard-core bosons. We study this model numerically and compare the properties with those of the SYK model. We observe a striking quantitative coincidence between the spin model and the SYK model, which suggests that this spin model is strongly chaotic and, perhaps, can play some role in holography. We also discuss the path-integral approach with multi-local fields and the possibility of quantum simulations. This model may be an interesting target for quantum simulations because Pauli spins are easier to implement than fermions on qubit-based quantum devices.

Physics↗
DOE OSTI2022

Universal quantum operation of spin-3/2 Blume-Capel chains

We propose a logical qubit based on the Blume-Capel model: A higher-spin generalization of the Ising chain which allows for an on-site anisotropy-preserving rotational invariance around the Ising axis. We show that such a spin-3/2 Blume-Capel model can also support localized Majorana zero modes at the ends of the chain. Inspired by known braiding protocols of these Majorana zero modes, upon appropriate manipulation of the system parameters, we demonstrate a set of universal gate operations which act on qubits encoded in the doubly degenerate ground states of the chain.

1-dimensional spin chains↗
DOE OSTI2021

Spin-Coherent Transport under Strong Spin-Orbit Interaction (Final Technical Report)

The major goals of the project consisted of acquiring insight in spin-dependent quantum coherent electronic transport phenomena arising from spin-orbit interaction, via experiments on semiconductor heterostructures and thin film semimetals patterned into mesoscopic and nanoscale geometries. The solid-state physics findings contain insight potentially useful for the creation of new quantum states of matter, for spin operations in quantum information processing, for future spin electronics, and for other future functionalities of power-saving electronic devices. The subject was of fundamental interest, but was also of long-term applied interest for quantum devices, spintronics devices, and general electronic devices. The experiments were conducted by low-temperature electronic magnetotransport in nanoscale structures of length scales similar to the quantum phase- and spin-coherence lengths and the carrier mean-free paths in the materials. Emphasis was placed on quantum coherence and spin coherence, to understand coherent spin-dependent electronic processes, on transport of electrons with very long mean-free path (ballistic transport), on the transfer of electron spin to nuclear spin (dynamic nuclear spin polarization in bismuth), and on the study of materials with quantum states emerging from spin-orbit interaction and electron-electron interaction (bismuth iridates). In two-dimensional electron systems in quantum wells of the narrow-bandgap semiconductors InAs and InGaAs the objectives included the characterization of quantum states arising from the Aharonov-Casher quantum-mechanical phase as an electromagnetic dual of the Aharonov-Bohm phase. Objectives also included quantum electronic transport at the mesoscopic scale on the semimetal bismuth in thin film form, and particularly on its strongly spin-orbit coupled surface states. An almost-strain-free method was developed to grow high-quality bismuth thin films. Devices fabricated on these films were then used to study a novel nuclear spin torque, whereby the bismuth carrier spin was transferred to the bismuth nuclei by the agency of both spin-orbit interaction and hyperfine interaction. Aspects of ballistic transport were studied in GaAs/AlGaAs heterostructures of very high mobility, and a hitherto unsuspected similarity was discovered between ballistic transport and hydrodynamic transport, of potential use in future power-saving electronic devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Closed-form expressions for unitaries of spin-adapted fermionic operators

One of the open challenges in quantum computing simulations of problems of chemical interest is the proper enforcement of spin symmetry. Efficient quantum circuits implementing unitaries generated by spin-adapted operators remain elusive, while naïve Trotterization schemes break spin symmetry. Here, in this work, we analyze the mathematical structure of spin-adapted operators and derive closed-form expressions for unitaries generated by singlet spin-adapted generalised single and double excitations. These results represent significant progress toward the economical enforcement of spin symmetry in quantum simulations.

fermionic algebra↗
DOE OSTI2022

Celestial operator product expansions and w 1+∞ symmetry for all spins

The operator product expansion of massless celestial primary operators of arbitrary spin is investigated. Poincaré symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading singular terms at tree-level in a holomorphic limit. The symmetry constraints are solved by an Euler beta function with arguments that depend simply on the right-moving conformal weights of the operators in the product. These symmetry-derived coefficients are shown not only to match precisely those arising from momentum-space tree-level collinear limits, but also to obey an infinite number of additional symmetry transformations that respect the algebra of w 1+∞ . In tree-level minimally-coupled gravitational theories, celestial currents are constructed from light transforms of conformally soft gravitons and found to generate the action of w 1+∞ on arbitrary massless celestial primaries. Results include operator product expansion coefficients for fermions as well as those arising from higher-derivative non-minimal couplings of gluons and gravitons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Asymptotic optimality of twist-untwist protocols for Heisenberg scaling in atom-based sensing

Twist-untwist protocols for quantum metrology consist of a serial application of (1) unitary nonlinear dynamics (e.g., spin squeezing or Kerr nonlinearity), (2) parameterized dynamics U ( φ ) (e.g., a collective rotation or phase space displacement), and (3) time reversed application of step 1. Such protocols are known to produce states that allow Heisenberg scaling for experimentally accessible estimators of φ even when the nonlinearities are applied for times much shorter than required to produce Schrödinger cat states. In this work, we prove that, asymptotically in the number of particles, twist-untwist protocols provide the lowest estimation error among quantum metrology protocols that utilize two calls to a weakly nonlinear evolution and a readout involving only first and second moments of a total spin operator n → · J → . We consider the following physical settings: all-to-all interactions generated by one-axis twisting J z 2 (e.g., interacting Bose gases), constant finite range spin-spin interactions of distinguishable or bosonic atoms (e.g., trapped ions or Rydberg atoms, or lattice bosons). In these settings, we further show that the optimal twist-untwist protocols asymptotically achieve 85% and 92% of the respective quantum Cramér-Rao bounds. We show that the error of a twist-untwist protocol can be decreased by a factor of L without an increase in the noise of the spin measurement if the twist-untwist protocol can be noiselessly iterated as an L layer quantum alternating operator ansatz.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Two-dimensional coherent spectrum of high-spin models via a quantum computing approach

Here in this work we present and benchmark a quantum computing approach to calculate the two-dimensional coherent spectrum (2DCS) of high-spin models. Our approach is based on simulating their real-time dynamics in the presence of several magnetic field pulses, which are spaced in time. We utilize the adaptive variational quantum dynamics simulation algorithm for the study due to its compact circuits, which enables simulations over sufficiently long times to achieve the required resolution in frequency space. Specifically, we consider an antiferromagnetic quantum spin model that incorporates Dzyaloshinskii-Moriya interactions and single-ion anisotropy. The obtained 2DCS spectra exhibit distinct peaks at multiples of the magnon frequency, arising from transitions between different eigenstates of the unperturbed Hamiltonian. By comparing the one-dimensional coherent spectrum with 2DCS, we demonstrate that 2DCS provides a higher resolution of the energy spectrum. We further investigate how the quantum resources scale with the magnitude of the spin using two different binary encodings of the high-spin operators: the standard binary encoding and the Gray code. At low magnetic fields both encodings require comparable quantum resources, but at larger field strengths the Gray code is advantageous. Numerical simulations for spin models with increasing number of sites indicate a polynomial system-size scaling for quantum resources. Lastly, we compare the numerical 2DCS with experimental results on a rare-earth orthoferrite system. The observed strength of the magnonic high-harmonic generation signals in the 2DCS of the quantum high-spin model aligns well with the experimental data, showing significant improvement over the corresponding mean-field results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Lyapunov growth in quantum spin chains

The Ising spin chain with longitudinal and transverse magnetic fields is often used in studies of quantum chaos, displaying both chaotic and integrable regions in its parameter space. However, even at a strongly chaotic point this model does not exhibit Lyapunov growth of the commutator squared of spin operators, as this observable saturates before exponential growth can manifest itself (even in situations where a spatial suppression factor makes the initial commutator small). In this work, we extend this model from the spin 1/2 Ising model to higher spins, demonstrate numerically that a window of exponential growth opens up for sufficiently large spin, and extract a quantity which corresponds to a notion of a Lyapunov exponent. In the classical infinite-spin limit, we identify and compute the appropriate classical analog of the commutator squared, and show that the corresponding exponent agrees with the infinite-spin limit extracted from the quantum spin chain.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Renormalized classical theory of quantum magnets

Here, we derive a renormalized classical spin (RCS) theory for 𝑆 >1/2 quantum magnets by constraining a generalized classical theory that includes all multipolar fluctuations to a reduced CP 1 phase space of dipolar SU(2) coherent states. When the spin Hamiltonian $\hat{ℋ}$(𝑆) is linear in the spin operators $\hat{𝑺}$ 𝑗 for each lattice site 𝑗, the RCS Hamiltonian $\tilde{ℋ}$ cl coincides with the usual classical model ℋ cl = lim 𝑆→∞⁡ $\hat{ℋ}$(𝑆). In the presence of nonlinear terms, however, the RCS theory is more accurate than ℋ cl . For the many materials modeled by spin Hamiltonians with (nonlinear) single-ion anisotropy terms, the use of the RCS theory is essential to accurately model phase diagrams and to extract the correct Hamiltonian parameters from neutron-scattering data.

magnetic anisotropy↗
DOE OSTI2024

Two-point sum-rules in three-dimensional Yang-Mills theory

We compute the stress-tensor two-point function in three-dimensional Yang-Mills theory to three-loops in perturbation theory. Using its calculable shape at high momenta, we test the notion that its Borel transform is saturated at low energies by the lowest glueball state(s). This assumption provides relatively stable estimates for the mass of the lightest glueball that we compare with lattice simulations. We also provide estimates for the coupling of the lightest glueball to the stress tensor. Along the way, we comment on the extent that such estimates are non-rigorous. Lastly, we discuss the possibility of applying the sum-rule analysis to two-point functions of higher-spin operators and obtain a crude approximation for the glueball couplings to these operators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

An effective field theory for non-maximal quantum chaos

In non-maximally quantum chaotic systems, the exponential behavior of out-of-time-ordered correlators (OTOCs) results from summing over exchanges of an infinite tower of higher “spin” operators. We construct an effective field theory (EFT) to capture these exchanges in (0 + 1) dimensions. The EFT generalizes the one for maximally chaotic systems, and reduces to it in the limit of maximal chaos. The theory predicts the general structure of OTOCs both at leading order in the 1/N expansion (N is the number of degrees of freedom), and after resuming over an infinite number of higher order 1/N corrections. These general results agree with those previously explicitly obtained in specific models. We also show that the general structure of the EFT can be extracted from the large q SYK model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Angular fractals in thermal QFT

We show that thermal effective field theory controls the long-distance expansion of the partition function of a d-dimensional QFT, with an insertion of any finite-order spatial isometry. Consequently, the thermal partition function on a sphere displays a fractal-like structure as a function of angular twist, reminiscent of the behavior of a modular form near the real line. As an example application, we find that for CFTs, the effective free energy of even-spin minus odd-spin operators at high temperature is smaller than the usual free energy by a factor of 1/2 d . Near certain rational angles, the partition function receives subleading contributions from “Kaluza-Klein vortex defects” in the thermal EFT, which we classify. We illustrate our results with examples in free and holographic theories, and also discuss nonperturbative corrections from worldline instantons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗