Neutron-state entanglement with overlapping paths
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11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
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Results for “Neutron state entanglement”
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Experimental evidence for the two-path description of neutron spin echo
Here, we describe an experiment that strongly supports a two-path interferometric model in which the spin-up and spin-down components of each neutron propagate coherently along spatially separated parallel paths in a typical neutron spin-echo small-angle scattering (SESANS) experiment. Specifically, we show that the usual semi-classical, single-path treatment of Larmor precession of a polarized neutron in an external magnetic field predicts a damping as a function of the spin-echo length of the SESANS signal obtained with a periodic phase grating when the transverse width of the neutron wave packet is finite. However, no such damping is observed experimentally, implying either that the Larmor model is incorrect or that the transverse extent of the wave packet is very large. In contrast, we demonstrate theoretically that a quantum-mechanical interferometric model in which the two mode-entangled (i.e., intraparticle entangled) spin states of a single neutron are separated in space when they interact with the grating accurately predicts the measured SESANS signal, which is independent of the wave packet width.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Entanglement maximization in low-energy neutron-proton scattering
The entanglement properties of neutron-proton scattering are investigated using a measure that counts the number of entangled pairs produced by the action of a scattering operator on a given initial neutron-proton state. All phase shifts relevant for scattering at laboratory energies up to 350 MeV are used. Entanglement is found to depend strongly on the initial state. Entanglement is maximized in very low energy scattering if the initial spin state is | ↑ ↓ >, but not if the initial state is | ↑ ↑ > . At such energies the Hamiltonian obeys Wigner SU(4) symmetry, and an entanglement maximum is a sign of that symmetry. At higher energies the angular dependence of entanglement is strong and the entanglement is large for many scattering angles. Furthermore, the tensor force is shown to play a significant role in producing entanglement at laboratory kinetic energies greater than about 50 MeV.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Tutorial: Extracting entanglement signatures from neutron spectroscopy
This tutorial is a pedagogical introduction to recent methods of computing quantum spin entanglement witnesses from spectroscopy, with a special focus on neutron scattering on quantum spin systems. We offer a brief introduction to the concepts and equations, define a data analysis protocol, and discuss the interpretation of three entanglement witnesses: one-tangle, two-tangle, and Quantum Fisher Information. We also discuss practical experimental considerations, and give three examples of extracting entanglement witnesses from experimental data: Copper Nitrate, KCuF 3 , and NiPS 3 .
47 OTHER INSTRUMENTATION↗
Multipartite entanglement in the one-dimensional spin- 1 2 Heisenberg antiferromagnet
Multipartite entanglement refers to the simultaneous entanglement between multiple subsystems of a many-body quantum system. While multipartite entanglement can be difficult to quantify analytically, it is known that it can be witnessed through the quantum Fisher information (QFI), a quantity that can also be related to dynamical Kubo response functions. In this work, we first show that the finite temperature QFI can generally be expressed in terms of a static structure factor of the system, plus a correction that vanishes as T→0. This implies that the static structure factor witnesses multipartite entanglement near quantum critical points at temperatures below a characteristic energy scale of the system. Therefore, in systems with a known static structure factor, we can deduce finite temperature scaling of multipartite entanglement and low temperature entanglement depth without knowledge of the full dynamical response function of the system. This is particularly useful to study 1D quantum critical systems in which sub-power-law divergences can dominate entanglement growth, where the conventional scaling theory of the QFI breaks down. Furthermore, the 1D spin- 1 2 antiferromagnetic Heisenberg model is an important example of such a system, and we show that multipartite entanglement in the Heisenberg chain diverges nontrivially as ~ln(1/T) 3/2 . We verify these predictions with calculations of the QFI using conformal field theory and matrix product state simulations. Finally, we discuss the implications of our results for experiments to probe entanglement in quantum materials, comparing to neutron scattering data in KCuF 3 , a material well described by the Heisenberg chain.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NaCo 2 (SeO 3 ) 2 (OH): competing magnetic ground states of a new sawtooth structure with 3d 7 Co 2+ ions
While certain magnetic sublattices have long been known theoretically to give rise to emergent physics via competing magnetic interactions and quantum effects, finding such configurations in real materials is often deeply challenging. Here we report the synthesis and characterization of a new such material, NaCo 2 (SeO 3 ) 2 (OH) which crystallizes with a highly frustrated sublattice of sawtooth Co 2+ chains. Single crystals of NaCo 2 (SeO 3 ) 2 (OH) were synthesized using a low-temperature hydrothermal method. X-ray single crystal structure analysis reveals that the material crystallizes in orthorhombic space group of Pnma (no. 62). Its crystal structure exhibits one-dimensional chains of corner-sharing isosceles triangles that are made of two crystallographically distinct 3d 7 Co 2+ sites (Co(1) and Co(2)). The chains run along the b-axis and are interconnected via [SeO 3 ] groups to form a three-dimensional structure mediating super-exchange interactions. The temperature dependent magnetization data show a ferromagnetic-like (FM) transition at 11 K (T 1 ) followed by an antiferromagnetic (AFM) transition at about 6 K (T 2 ). Neutron-powder diffraction measurements reveal that at T 1 = 11 K only the Co(2) site orders magnetically, forming ferromagnetic zigzag chains along the b-axis. Below T 2 = 6 K, both Co(1) and Co(2) sites order in a nearly orthogonal configuration, with Co(1) moments lying inside the plane of the sawtooth chain while Co(2) moments cant out of the plane. The canting of the magnetic moments leads to a net ferromagnetic component along b-axis, parallel to the chain direction. The ordered moments are fully compensated in the ac-plane. Inelastic neutron scattering measurements reveal crystal field excitations that are consistent with the presence of a spin–orbital entangled pseudo-spin state J eff = 1/2 for the Co 2+ ions. Low-energy spin-wave excitations are observed below the second magnetic transition. The analysis of powder excitation spectrum suggests complex exchange interactions that go beyond a Heisenberg Hamiltonian model with nearest neighbor couplings. Our results demonstrate the richness of the magnetic properties of sawtooth-type structures and encourage the study of similar structures with different oxyanion groups.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Quantum magic and multipartite entanglement in the structure of nuclei
Motivated by the Gottesman-Knill theorem, we present a detailed study of the quantum complexity of p -shell and s d -shell nuclei. Valence-space nuclear shell-model wave functions generated by the code are mapped to qubit registers using the Jordan-Wigner mapping (12 qubits for the p shell and 24 qubits for the s d shell), from which measures of the many-body entanglement ( n -tangles) and magic (nonstabilizerness) are determined. While exact evaluations of these measures are possible for nuclei with a modest number of active nucleons, Monte Carlo simulations are required for the more complex nuclei. The broadly applicable Pauli-string I ̂ Z ̂ exact (PSIZe) Markov chain Monte Carlo (MCMC) technique is introduced to accelerate the evaluation of measures of magic in deformed nuclei (with hierarchical wave functions), by factors of ≈ 8 for some nuclei. Significant multinucleon entanglement is found in the s d shell, dominated by proton-neutron configurations, along with significant measures of magic. This is evident not only for the deformed states, but also for nuclei on the path to instability via regions of shape coexistence and level inversion. These results indicate that quantum-computing resources will accelerate precision simulations of such nuclei and beyond. Published by the American Physical Society 2025
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Weak entanglement approximation for nuclear structure
The interacting shell model, a configuration-interaction method, is a venerable approach for low-lying nuclear structure calculations, but it is hampered by the exponential growth of its basis dimension as one increases the single-particle space and/or the number of active particles. Recent, quantum-information-inspired work has demonstrated that the proton and neutron sectors of a nuclear wave function are weakly entangled. Furthermore, the entanglement is smaller for nuclides away from N = Z, such as heavy, neutron-rich nuclides. Here, in this study, we implement a weak entanglement approximation to bipartite configuration-interaction wave functions, approximating low-lying levels by coupling a relatively small number of many-proton and many-neutron states. This truncation scheme, which we present in the context of past approaches, reduces the basis dimension by many orders of magnitude while preserving essential features of nuclear spectra.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Unconventional bipartite entanglement in the quantum dimer magnet Yb2Be 2 SiO 7
The quantum dimer magnet, with antiferromagnetic intradimer and interdimer Heisenberg exchange between spin-1/2 moments, is known to host an (|$\uparrow$$\downarrow$$\rangle$ - |$\downarrow$$\uparrow$$\rangle$)/$\sqrt{2}$ singlet ground state when the intradimer exchange is dominant. Rare-earth-based quantum dimer systems with strong spin-orbit coupling offer the opportunity for tuning their magnetic properties by using magnetic anisotropy as a control knob. Here, we present bulk characterization and neutron scattering measurements of the quantum dimer magnet Yb 2 Be 2 SiO 7 . We find that the Yb3+ ions can be described by an effective spin-1/2 model at low temperatures and the system does not show signs of magnetic order down to 50 mK. The magnetization, heat capacity, and neutron spectroscopy data can be well-described by an isolated dimer model with highly anisotropic exchange that stabilizes a singlet ground state with a wavefunction (|$\uparrow$$\uparrow$$\rangle$ - |$\downarrow$$\downarrow$$\rangle$)/$\sqrt{2}$ or (|$\uparrow$$\uparrow$$\rangle$ + |$\downarrow$$\downarrow$$\rangle$)/$\sqrt{2}$. Our results show that strong spin-orbit coupling can induce unusual entangled states of matter in quantum dimer magnets.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Complete field-induced spectral response of the spin-1/2 triangular-lattice antiferromagnet CsYbSe 2
Fifty years after Anderson’s resonating valence-bond proposal, the spin-1/2 triangular-lattice Heisenberg antiferromagnet (TLHAF) remains the ultimate platform to explore highly entangled quantum spin states in proximity to magnetic order. Yb-based delafossites are ideal candidate TLHAF materials, which allow experimental access to the full range of applied in-plane magnetic fields. We perform a systematic neutron scattering study of CsYbSe 2 , first proving the Heisenberg character of the interactions and quantifying the second-neighbor coupling. We then measure the complex evolution of the excitation spectrum, finding extensive continuum features near the 120°-ordered state, throughout the 1/3-magnetization plateau and beyond this up to saturation. We perform cylinder matrix-product-state (MPS) calculations to obtain an unbiased numerical benchmark for the TLHAF and spectacular agreement with the experimental spectra. The measured and calculated longitudinal spectral functions reflect the role of multi-magnon bound and scattering states. These results provide valuable insight into unconventional field-induced spin excitations in frustrated quantum materials.
36 MATERIALS SCIENCE↗
Neutron Reflectometry Reveals Diffusion in Contrast-Matched Brush Particle Bilayers
A material system for performing layer-spread experiments on brush particle bilayers is presented and used to determine the diffusion constant of brush particles in the melt state. Selective deuteration of the core and shell of organo-silica nanoparticles grafted with poly(methyl methacrylate) was used to match the scattering length density of the core and the polymer canopy layer. This subdued the scattering of particle cores (i.e., formfactor scattering) and enabled the analysis of the interdiffusion kinetics using neutron reflectivity. For low molecular grafts, i.e., grafts with a molecular weight below the entanglement limit, the interdiffusion kinetics revealed both a sub- and Fickian diffusion regime. The former was attributed to the local dynamics that was constrained by the slow-moving cores of neighboring brush particles that acted as long-lived physical cross-links. No transition to Fickian diffusion was observed for entangled systems, even at prolonged annealing times. This suggested a higher level of kinetic restraint in entangled brush particle melts as compared to, for example, star polymers with a comparable chain length for which Fickian diffusion has been reported under similar conditions.
Diffusion, Polymer Grafted Nanoparticles, Neutron ↗
Localized triplons and site stuffing in the quantum dimer magnet BiYbGeO5
Thermodynamic and muon spin relaxation measurements have recently highlighted BiYbGeO5 as a new example of a rare-earth-based quantum dimer magnet with isolated Yb3+ spin-1/2 dimers. However, direct spectroscopic evidence of the triplet excitations and measurements of the structural disorder are lacking. In this work, polycrystalline BiYbGeO5 was synthesized using conventional high-temperature solid-state methods and investigated via high-resolution neutron powder diffraction and inelastic neutron scattering. Diffraction measurements down to 58 mK reveal no signatures of magnetic order and indicate that nearly 20% of Yb3+ sites are replaced by nonmagnetic Bi3+, introducing significant structural disorder. Inelastic neutron scattering shows dispersionless triplon excitations, consistent with localized, noninteracting spin dimers. Fits to the triplet excitation spectrum with an XXZ-type anisotropic exchange give 𝐽XX=0.100(1)meV and 𝐽Z=0.202(1)meV. These findings establish BiYbGeO5 as a structurally disordered but magnetically well-isolated quantum dimer system, providing a model platform for studying the resilience of entangled spin states to site dilution.
Kapoor, Rachit [Brock University, Canada]↗
Classical signatures of quenched and thermal disorder in the dynamics of correlated spin systems
Neutron scattering is frequently used to look for evidence of features indicative of quantum-entangled phases of matter such as continua from fractionalisation or quantised excitations. However, the non-specificity of these features and difficulty of both fully quantum treatments and semiclassical models of disorder, make the diagnosis of such states problematic. Here, we demonstrate the feasibility of semiclassical treatments of disordered systems for supercells of ~10 000 spins. By examining a number of classically disordered models we show the presence of quantised excitations, broad continua and anomalous damping originating from quenched disorder or large classical degeneracies.
36 MATERIALS SCIENCE↗
Spin-textured neutron beams with orbital angular momentum
In this work, we present a rigorous theoretical framework underpinning the technique of spin-echo modulated small-angle neutron scattering (SEMSANS), and show how the technique can be extended in order to generate spin-textured neutron beams with orbital angular momentum (OAM) via birefringent neutron spin-polarization devices known as magnetic Wollaston prisms. Neutron OAM beams are mathematically characterized by a “cork-screw” phase singularity e iℓΦ about the propagation axis where ℓ is the OAM quantum number. To understand the precise relationship between the emergent OAM state and the variety of spin textures realized by various setups, we have developed a path-integral approach that in the interferometric limit makes a judicious use of magnetic Snell's law. We show that our proposed technique produces a complex two-dimensional pattern of spin-OAM entangled states which may be useful as a probe of quantum magnetic materials. We compare our path-integral approach to the well-known single-path Larmor precession model and present a pedagogical derivation of magnetic Snell's law of refraction for both massive and massless particles based on Maupertuis's action principle.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Proximate spin liquid and fractionalization in the triangular antiferromagnet KYbSe 2
The Heisenberg triangular-lattice quantum spin liquid and its phase transitions to nearby magnetic orders have received much theoretical attention, but clear experimental manifestations of these states are rare. Here we demonstrate that a spin-half delafossite material, namely, KYbSe 2 , shows close proximity to the triangular-lattice Heisenberg quantum spin liquid. Using neutron scattering, we identify a diffuse continuum with a sharp lower bound within the measured spectra. Applying entanglement witnesses to the data indicates multipartite entanglement spread between its neighbours, and an analysis of its magnetic-exchange couplings reveals close proximity to the theoretical quantum spin-liquid phase. The key features of the data are reproduced by Schwinger boson theory and tensor network calculations with a substantial next-nearest-neighbour coupling. The strength of the dynamical structure factor at the Brillouin-zone K point shows a scaling collapse down to 0.3 K, indicating the existence of a second-order quantum phase transition. Finally, comparing this with previous theoretical work suggests that the proximate phase at a larger next-nearest-neighbour coupling is a gapped $\mathbb{Z}_{2}$ spin liquid, resolving a long-debated issue. Similar content being viewed by others
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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↗
Spin liquid state in a rare-earth hyperkagome lattice
We report quantum fluctuations enhanced by frustration and subtle interplay between competing degrees of freedom offer an ideal ground to realize novel states with fractional quantum numbers in quantum materials that defy standard theoretical paradigms. Quantum spin liquid (QSL) is a highly entangled state wherein frustration-induced strong quantum fluctuations preclude symmetry-breaking phase transitions down to zero temperature without any order parameter. Experimental realizations of QSL in quantum materials with spin dimensionality greater than one is very rare. Here, we present our thermodynamic, nuclear magnetic resonance, muon spin relaxation, and inelastic neutron scattering studies of a rare-earth hyperkagome compound Li 3 Yb 3 Te 2 O 12 in which Yb 3+ ions constitute a three-dimensional spin lattice without any detectable disorder. Our comprehensive experiments evince neither signature of magnetic ordering nor spin freezing down to 38 mK that suggest the realization of dynamic liquid-like ground state in this antiferromagnet. The ground state of this material is interpreted by a low energy J eff = 1/2 degrees of freedom with short-range spin correlations. The present results demonstrate a viable basis to explore spin-orbit driven enigmatic correlated quantum states in a class of rare-earth-based three-dimensional frustrated magnets that may open avenues in theoretical and experimental search for spin liquids.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Nonlinear magnons and exchange Hamiltonians of the delafossite proximate quantum spin liquid candidates KYbSe 2 and NaYbSe 2
Quantum spin liquids (QSLs) are theoretical states of matter with long-range entanglement and exotic quasiparticles. However, they generally elude quantitative theory, rendering their underlying phases mysterious and hampering efforts to identify experimental QSL states. Here we study triangular-lattice resonating-valence-bond QSL candidate materials KYbSe 2 and NaYbSe 2 . We measure the magnon modes in their 1/3 plateau phase, where quantitative theory is tractable, using inelastic neutron scattering and fit them using nonlinear spin wave theory. We also fit the KYbSe 2 heat capacity using high-temperature series expansion. Both KYbSe 2 fits yield the same magnetic Hamiltonian to within uncertainty, confirming previous estimates and showing the Heisenberg ratio J 2 / J 1 to be an accurate model for these materials. Most importantly, comparing KYbSe 2 and NaYbSe 2 shows that the smaller A -site Na + ion has a larger J 2 / J 1 ratio. However, hydrostatic pressure applied to KYbSe 2 increases the ordering temperature (a result consistent with density functional theory calculations), indicating that pressure decreases J 2 / J 1 . In conclusion, these results show how the periodic table and hydrostatic pressure can tune the A YbSe 2 materials in a controlled way.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗