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DOE OSTI2025

Control simulations of many-body quantum systems by a synergism of discrete real-time learning and optimal control theory

We present a self-consistent algorithm for optimal control simulations of many-body quantum systems. The algorithm features a two-step synergism that combines discrete real-time machine learning (DRTL) with Quantum Optimal Control Theory (QOCT) using the time-dependent Schrödinger equation. Specifically, in step (1), DRTL is employed to identify a compact working space (i.e., the important portion of the Hilbert space) for the time evolution of the many-body quantum system in the presence of a control field (i.e., the initial or previously updated field), and in step (2), QOCT utilizes the DRTL-determined working space to find a newly updated control field for a chosen objective. Steps 1 and 2 are iterated until a self-consistent control objective value is reached such that the resulting optimal control field yields the same targeted objective value when the corresponding working space is systematically enlarged. Furthermore, to demonstrate this two-step self-consistent DRTL-QOCT synergistic algorithm, we perform optimal control simulations of strongly interacting 1D as well as 2D Heisenberg spin systems. In both scenarios, only a single spin (at the left end site for 1D and the upper left corner site for 2D) is driven by the time-dependent control fields to create an excitation at the opposite site as the target. It is found that, starting from all spin-down zero excitation states, the synergistic method is able to identify working spaces and convergence of the desired controlled dynamics with just a few iterations of the overall algorithm. In the cases studied, the dimensionality of the working space scales only quasi-linearly with the number of spins.

Artificial neural networks↗

DOE OSTI2024

Implementation of a laser–neutron pump–probe capability for inelastic neutron scattering

Knowledge about nonequilibrium dynamics in spin systems is of great importance to both fundamental science and technological applications. Inelastic neutron scattering (INS) is an indispensable tool to study spin excitations in complex magnetic materials. However, conventional INS spectrometers currently only perform steady-state measurements and probe averaged properties over many collision events between spin excitations in thermodynamic equilibrium, while the exact picture of re-equilibration of these excitations remains unknown. In this paper, we report on the design and implementation of a time-resolved laser–neutron pump–probe capability at hybrid spectrometer (beamline 14-B) at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory. This capability allows us to excite out-of-equilibrium magnons with a nanosecond pulsed laser source and probe the resulting dynamics using INS. Here, we discussed technical aspects to implement such a capability in a neutron beamline, including choices of suitable neutron instrumentation and material systems, laser excitation scheme, experimental configurations, and relevant firmware and software development to allow for time-synchronized pump–probe measurements. We demonstrated that the laser-induced nonequilibrium structure factor is able to be resolved by INS in a quantum magnet. In conclusion, the method developed in this work will provide SNS with advanced capabilities for performing out-of-equilibrium measurements, opening up an entirely new research direction to study out-of-equilibrium phenomena using neutrons.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Temperature-Dependent Spin-Lattice Relaxation of the Nitrogen-Vacancy Spin Triplet in Diamond

Spin-lattice relaxation within the nitrogen-vacancy (NV) center’s electronic ground-state spin triplet limits its coherence times, and thereby impacts its performance in quantum applications. We report measurements of the relaxation rates on the NV center’s $|m_s = 0 \rangle ↔ |m_s = ± 1 \rangle$ and $|m_s = -1 \rangle ↔ |m_s = + 1\rangle$ transitions as a function of temperature from 9 to 474 K in high-purity samples. We show that the temperature dependencies of the rates are reproduced by an ab initio theory of Raman scattering due to second-order spin-phonon interactions, and we discuss the applicability of the theory to other spin systems. Using a novel analytical model based on these results, we suggest that the high-temperature behavior of NV spin-lattice relaxation is dominated by interactions with two groups of quasilocalized phonons centered at 68.2(17) and 167(12) meV.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Coherent control of strongly interacting spins in the solid-state

The major goal of this project is to develop coherent interacting spin systems in the solid state, based on rare earth ions. By leveraging the ability to controllably incorporate rare earth ions such as Er into a solid-state host, and maintain individual-ion addressability below the diffraction limit based on inhomogeneous broadening, we aim to create strongly interacting electron spin clusters with individual-site control. Performing spectroscopy of these strongly interacting systems will shed light on their fundamental properties, as well as enable applications to quantum information science, in particular quantum networks that are also enabled by a telecom-band spin-photon interface in Er.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

A high-performance implementation of atomistic spin dynamics simulations on x86 CPUs

Atomistic spin dynamics simulations provide valuable information about the energy spectrum of magnetic materials in different phases, allowing one to identify instabilities and the nature of their excitations. However, the time cost of evaluating the dynamical correlation function S(q,t) increases quadratically as the number of spins N, leading to significant computational effort, making the simulation of large spin systems very challenging. In this work, here, we propose to use a highly optimized general matrix multiply (GEMM) subroutine to calculate the dynamical spin-spin correlation function that can achieve near-optimal hardware utilization. Furthermore, we fuse the element-wise operations in the calculation of S(q,t) into the in-house GEMM kernel, which results in further performance improvements of 44\% - 71\% on several relatively large lattice sizes when compared to the implementation that uses the GEMM subroutine in OpenBLAS, which is the state-of-the-art open source library for Basic Linear Algebra Subroutine (BLAS).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Geometrical Frustration and Planar Triangular Antiferromagnetism in Quasi-Three-Dimensional Artificial Spin Architecture

We present a realization of highly frustrated planar triangular antiferromagnetism achieved in a quasi-three-dimensional artificial spin system consisting of monodomain Ising-type nanomagnets lithographically arranged onto a deep-etched silicon substrate. We demonstrate how the three-dimensional spin architecture results in the first direct observation of long-range ordered planar triangular antiferromagnetism, in addition to a highly disordered phase with short-range correlations, once competing interactions are perfectly tuned. Finally, our work demonstrates how escaping two-dimensional restrictions can lead to new types of magnetically frustrated metamaterials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Detecting fractionalization in critical spin liquids using color centers

Quantum spin liquids are highly entangled ground states of insulating spin systems, in which magnetic ordering is prevented down to the lowest temperatures due to quantum fluctuations. One of the most extraordinary characteristics of quantum spin liquid phases is their ability to support fractionalized, low-energy quasiparticles known as spinons, which carry spin-1/2 but bear no charge. Relaxometry based on color centers in crystalline materials—of which nitrogen-vacancy (NV) centers in diamond are a well-explored example—provides an exciting new platform to probe the spin spectral functions of magnetic materials with both energy and momentum resolution and to search for signatures of these elusive, fractionalized excitations. In this work, we theoretically investigate the color-center relaxometry of two archetypal quantum spin liquids: the two-dimensional U(1) quantum spin liquid with a spinon Fermi surface and the spin-1/2 antiferromagnetic spin chain. The former is characterized by a metallic, spin-split ground state of mobile, interacting spinons, which closely resembles a spin-polarized Fermi liquid ground state but with neutral quasiparticles. We show that the observation of the Stoner continuum and the collective spin wave mode in the spin spectral function would provide a strong evidence for the existence of spinons and fractionalization. In one dimension, mobile spinons form a Luttinger liquid ground state. We show that the spin spectral function exhibits strong features representing the collective density and spin-wave modes, which are broadened in an algebraic fashion with an exponent characterized by the Luttinger parameter. The possibilities of measuring these collective modes and detecting the power-law decay of the spectral weight using NV relaxometry are discussed. We also examine how the transition rates are modified by marginally irrelevant operators in the Heisenberg limit. Published by the American Physical Society 2024

Takei, So (ORCID:0000000191771895)↗

DOE OSTI2025

Extended molecular eigenmodes treatment of dipole–dipole NMR relaxation in real fluids

Traditional models of NMR relaxation fail to account for the complex, multi-exponential behavior of the autocorrelation function in realistic systems characterized by soft-interactions and molecules that are chemically and physically complex. Here, in this study, we describe the relative diffusion of the spin dipoles by means of a Fokker–Planck equation that includes an interaction potential of mean force to account for the response of the physical/chemical environment around the dipoles. By numerically solving the Fokker–Planck equation for the diffusion propagator, we estimate dipole–dipole NMR relaxation for like- and unlike-spin systems via its eigenmode solution. We test the model against molecular simulations of diffusing dipoles with harmonic potentials and also validate using experimental longitudinal relaxation data from real systems, including Gd(III)–aqua and Gd(III)–DO3A–butrol complexes, the latter being an important MRI contrast agent. Using this novel approach, we predict both the inner- and outer-shell contributions to the relaxivity rates with excellent accuracy at frequencies relevant to MRI. We also show that, under the appropriate assumptions, our framework naturally recovers the Bloembergen–Purcell–Pound, the Solomon–Bloembergen–Morgan, and the Hwang–Freed models. Our implementation is general and publicly available for application to a broad range of systems.

Pinheiro dos Santos, Thiago J. [Rice Univ., Housto↗

DOE OSTI2023

Quantum spin helices more stable than the ground state: Onset of helical protection

Topological magnetic structures are promising candidates for resilient information storage. An elementary example is spin helices in one-dimensional easy-plane quantum magnets. To quantify their stability, we numerically implement the stochastic Schrödinger equation and time-dependent perturbation theory for spin chains with fluctuating local magnetic fields. Here, we find two classes of quantum spin helices that can reach and even exceed ground-state stability: spin-current-maximizing helices and, for fine-tuned boundary conditions, the recently discovered “phantom helices.” Beyond that, we show that the helicity itself (left or right rotating) is even more stable. We explain these findings by separated helical sectors and connect them to topological sectors in continuous spin systems. The resulting helical protection mechanism is a promising phenomenon for stabilizing helical quantum structures, e.g., in ultracold atoms and solid-state systems. We also identify a third type of phantom helix in the system.

1-dimensional spin chains↗

DOE OSTI2026

A Dipolar Chiral Spin Liquid on the Breathed Kagome Lattice

Continuous control over lattice geometry, when combined with long-range interactions, offers a powerful yet underexplored tool to generate highly frustrated quantum spin systems. By considering long-range dipolar antiferromagnetic interactions on a breathed Kagome lattice, we demonstrate how these tools can be leveraged to stabilize a chiral spin liquid. We support this prediction with large-scale density-matrix renormalization group calculations and explore the surrounding phase diagram, identifying a route to adiabatic preparation via a locally varying magnetic field. At the same time, we identify the relevant low-energy degrees of freedom in each unit cell, providing a complementary language to study the chiral spin liquid. Finally, we carefully analyze its stability and signatures in finite-sized clusters, proposing direct, experimentally viable measurements of the chiral edge mode in both Rydberg atom and ultracold polar molecule arrays.

Machado↗

DOE OSTI2024

Quantum spatial search with multiple excitations

Spatial search is the problem of finding a marked vertex in a graph. A continuous-time quantum walk in the single-excitation subspace of an $n$ spin system solves the problem of spatial search by finding the marked vertex in $O(\sqrt{n})$ time. Here, we investigate a natural extension of the spatial search problem, marking multiple vertices of a graph, which are still marked with local fields. We prove that a continuous-time quantum walk in the $k$-excitation subspace of $n$ spins can determine the binary string of $k$ marked vertices with an asymptotic fidelity in time $O(\sqrt{n})$, despite the size of the state space growing as $O(n^k)$. Numerically, we show that this algorithm can be implemented with interactions that decay as $1/r^\alpha$, where $r$ is the distance between spins, and an $\alpha$ that is readily available in current ion trap systems.

Lewis, Dylan↗

DOE OSTI2024

Density-matrix mean-field theory

Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short in capturing quantum fluctuations, which restricts their applicability to systems with significant quantum effects. In this article, we propose an improved mean-field theory, density-matrix mean-field theory (DMMFT). DMMFT constructs effective Hamiltonians, incorporating quantum environments shaped by entanglements, quantified by the reduced density matrices. Therefore, it offers a systematic and unbiased approach to account for the effects of fluctuations and entanglements in quantum ordered phases. As demonstrative examples, we show that DMMFT can not only quantitatively evaluate the renormalization of order parameters induced by quantum fluctuations, but can also detect the topological quantum phases. Additionally, we discuss the extensions of DMMFT for systems at finite temperatures and those with disorders. Our work provides an efficient approach to explore phases exhibiting unconventional quantum orders, which can be particularly beneficial for investigating frustrated spin systems in high spatial dimensions.

Physics↗

DOE OSTI2022

Coexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet

We study the ground-state properties of a spin-1 Heisenberg model on a square lattice with the first- and second-nearest-neighbor antiferromagnetic couplings $J_1$ and $J_2$ and a three-spin scalar chirality term $J_\chi$. Using the density matrix renormalization group calculation, we map out a global phase diagram including various magnetic order phases and an emergent quantum spin liquid phase. The nature of the spin liquid is identified as a bosonic non-Abelian Moore-Read state from the fingerprint of the entanglement spectra and identification of a full set of topological sectors. We further unveil a stripe magnetic order coexisting with this spin liquid. Furthermore, our results not only establish a rare example of non-Abelian spin liquids in simple spin systems but also demonstrate the coexistence of fractionalized excitations and magnetic order beyond mean-field descriptions.

2-dimensional systems↗

DOE OSTI2022

Superconductivity in a system of interacting spinful semions

Noninteracting particles obeying certain fractional statistics have been predicted to exhibit superconductivity. We discuss the issue in an attractively interacting system of spinful semions on a lattice by numerically investigating the presence of off-diagonal long-range order at zero temperature. For this purpose we construct a Hubbard model wherein two semions with opposite spin can virtually coincide while maintaining consistency with the fractional braiding statistics. Clear off-diagonal long-range order is seen in the strong coupling limit, consistent with the expectation that a pair of semions obeys Bose statistics. We find that the semion system behaves similarly to a system of fermions with the same attractive Hubbard U interaction for a wide range of U, suggesting that semions also undergo a BCS to BEC crossover as a function of U.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Quantum liquid from strange frustration in the trimer magnet Ba4Ir3O10

Abstract Quantum spin systems such as magnetic insulators usually show magnetic order, but such classical states can give way to quantum liquids with exotic entanglement through two known mechanisms of frustration: geometric frustration in lattices with triangle motifs, and spin-orbit-coupling frustration in the exactly solvable quantum liquid of Kitaev’s honeycomb lattice. Here we present the experimental observation of a new kind of frustrated quantum liquid arising in an unlikely place: the magnetic insulator Ba 4 Ir 3 O 10 where Ir 3 O 12 trimers form an unfrustrated square lattice. The crystal structure shows no apparent spin chains. Experimentally we find a quantum liquid state persisting down to 0.2 K that is stabilized by strong antiferromagnetic interaction with Curie–Weiss temperature ranging from −766 to −169 K due to magnetic anisotropy. The anisotropy-averaged frustration parameter is 2000, seldom seen in iridates. Heat capacity and thermal conductivity are both linear at low temperatures, a familiar feature in metals but here in an insulator pointing to an exotic quantum liquid state; a mere 2% Sr substitution for Ba produces long-range order at 130 K and destroys the linear-T features. Although the Ir 4+ (5d 5 ) ions in Ba 4 Ir 3 O 10 appear to form Ir 3 O 12 trimers of face-sharing IrO 6 octahedra, we propose that intra-trimer exchange is reduced and the lattice recombines into an array of coupled 1D chains with additional spins. An extreme limit of decoupled 1D chains can explain most but not all of the striking experimental observations, indicating that the inter-chain coupling plays an important role in the frustration mechanism leading to this quantum liquid.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Contributing to Sunny open source code

The Sunny package is an existing open source software to support the simulation of magnetic spin systems. It is available online under the MIT license here: https://github.com/SunnySuite/Sunny.jl The package aims to include the following features: - Analysis for symmetry-allowed interactions - Monte Carlo algorithms for simulating equilibrium configurations. - Schemes for integrating spin dynamics. - Inference of model Hamiltonians - Support for generalized SU(N) spins - Tools for interpreting experimental data, such as diffraction data, magnetization curves, and heat capacity data

Barros, Kipton↗

DOE OSTI2025

Laboratory Testing to Assess the Feasibility of Polyurethane Flat Belts for Marine Energy Applications

Polyurethane flat belts have received limited scientific attention as load-bearing elements in marine energy systems, particularly in applications involving dynamic tensile and bending loads. This study evaluates their potential as a replacement for traditional wire ropes in marine energy applications, with a focus on their ability to be integrated into winch-driven wave energy converters where bending and tensile stresses can make long-term operation difficult. Polyurethane belts are hypothesized to offer enhanced fatigue resistance due to their reduced thickness in the bending plane and therefore lower bending stresses. This research involves a series of tests utilizing the National Renewable Energy Laboratory’s (NREL) Large-Amplitude Motion Platform to replicate the dynamic conditions experienced by mooring lines of winch-based point-absorber-type marine energy converters. The conditions tested include unequal coiling and uncoiling tensions and load cases resulting from the device’s unconstrained movement relative to its anchor, such as twisting and off-axis loading. Results from this study show that polyurethane flat belts can achieve more than 198 percent of the fatigue life of a conventional wire rope under similar load profiles. The stress concentrations resulting from off-axis loading and cumulative twist beyond the system’s allowable limits have been identified as potential failure modes for flat belt mooring lines used in winch-driven wave energy converters deployed in ocean environments. To mitigate these risks, the use of anti-spin systems and fairleads designed to accommodate off-axis loading while limiting twist accumulation is recommended.

13 HYDRO ENERGY↗

DOE OSTI2021

Quantifying and Controlling Entanglement in the Quantum Magnet Cs 2 CoCl 4

The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs 2 CoCl 4 , a close realization of the S = 1/2 transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. Overall, we find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.

1-dimensional spin chains↗