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DOE OSTI2023

Thermalization at low temperatures via weakly damped multisite baths

We study the thermalization properties of one-dimensional open quantum systems coupled to baths at their boundary. The baths are driven to their thermal states via Lindblad operators, while the system undergoes Hamiltonian dynamics. We specifically consider multisite baths and investigate the extent to which the late-time steady state resembles a Gibbs state at some controllable temperature set by the baths. We study three models: a noninteracting fermion model accessible via free-fermion technology, and two interacting models, the XZ model and the chiral clock model, which are accessible via tensor network methods. We show that, by tuning towards the weak coupling and slow relaxation limits, one can engineer low temperatures in the bulk of the system provided the bath size is big enough. Here, we use this capability to study energy transport in the XZ model at lower temperatures than previously reported. Our work paves the way for future studies of interacting open quantum systems at low temperatures.

1-dimensional spin chains↗
DOE OSTI2026

A Tensor Network-Based Quantum Algorithm for the Nonlinear 1D Burgers' Equation

In this work, we implement a tensor network-based quantum algorithm to solve unsteady, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the compressible 1-dimensional (1D) Burgers' equation as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts to solve nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. Our framework is based on matrix product states (MPSs) and matrix product operators (MPOs). For example, the velocity field is represented by MPS, whereas the linear and nonlinear spatial differential terms of the velocity field are processed by MPOs. Our primary focus herein is to verify and validate the various tensor network components of the algorithm using solutions obtained by the classical algorithms on high performance computing (HPC) architectures. We use a classical time marching method to demonstrate the functionality of the tensor network operations to model the PDE and their robustness with the time evolution of the system. Our classical simulation results demonstrate the utility of tensor network-based operations in modeling nonlinear PDEs and highlight the necessity as well as potential advantages of using quantum simulations for these techniques.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗
DOE OSTI2024

Strong Zero Modes in Integrable Quantum Circuits

It is a classic result that certain interacting integrable spin chains host robust edge modes known as strong zero modes (SZMs). In this Letter, we extend this result to the Floquet setting of local quantum circuits, focusing on a prototypical model providing an integrable Trotterization for the evolution of the XXZ Heisenberg spin chain. By exploiting the algebraic structures of integrability, we show that an exact SZM operator can be constructed for these integrable quantum circuits in certain regions of parameter space. Our construction, which recovers a well-known result by Paul Fendley in the continuous-time limit, relies on a set of commuting transfer matrices known from integrability, and allows us to easily prove important properties of the SZM, including normalizabilty. Our approach is different from previous methods and could be of independent interest even in the Hamiltonian setting. Furthermore, our predictions, which are corroborated by numerical simulations of infinite-temperature autocorrelation functions, are potentially interesting for implementations of the XXZ quantum circuit on available quantum platforms.

1-dimensional spin chains↗
DOE OSTI2025

Doping Dependence of 2-Spinon Excitations in the Doped 1D Cuprate Ba 2 ⁢CuO 3+δ

Recent photoemission experiments on the quasi-one-dimensional Ba-based cuprates suggest that doped holes experience an attractive potential not captured using the simple Hubbard model. This observation has garnered significant attention due to its potential relevance to Cooper pair formation in high-T c cuprate superconductors. To scrutinize this assertion, we examined signatures of such an attractive potential in doped 1D cuprates Ba 2 ⁢CuO 3+δ by measuring the dispersion of the 2-spinon excitations using Cu L 3 -edge resonant inelastic x-ray scattering (RIXS). Upon doping, the 2-spinon excitations appear to weaken, with a shift of the minimal position corresponding to the nesting vector of the Fermi points, q F . Notably, we find that the energy scale of the 2-spinons near the Brillouin zone boundary is substantially softened compared to that predicted by the Hubbard model in one dimension. Finally, such a discrepancy implies missing ingredients, which lends support for the presence of an additional attractive potential between holes.

1-dimensional spin chains↗
DOE OSTI2024

Pseudorapidity dependence of anisotropic flow and its decorrelations using long-range multiparticle correlations in Pb–Pb and Xe–Xe collisions

The pseudorapidity dependence of elliptic (v 2 ), triangular (v 3 ), and quadrangular (v 4 ) flow coefficients of charged particles measured in Pb–Pb collisions at a centre-of-mass energy per nucleon pair of $\sqrt{S_{NN}}$ = 5.02 TeV and in Xe–Xe collisions at $\sqrt{S_{NN}}$ = 5.44 TeV with ALICE at the LHC are presented. The measurements are performed in the pseudorapidity range − 3.5 < η < 5 for various centrality intervals using two- and multi-particle cumulants with the subevent method. The flow probability density function (p.d.f.) is studied with the ratio of flow coefficient v 2 calculated with four- and two-particle cumulant, and suggests that the variance of flow p.d.f. is independent of pseudorapidity. The decorrelation of the flow vector in the longitudinal direction is probed using two-particle correlations. The results measured with respect to different reference regions in pseudorapidity exhibit differences, argued to be a result of saturating decorrelation effect above a certain pseudorapidity separation, in contrast to previous publications which assign this observation to non-flow effects. The results are compared to 3 + 1 dimensional hydrodynamic and the AMPT transport model calculations. Neither of the models is able to simultaneously describe the pseudorapidity dependence of measurements of anisotropic flow and its fluctuations. The results presented in this work highlight shortcomings in our current understanding of initial conditions and subsequent system expansion in the longitudinal direction. Therefore, they provide input for its improvement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Towards Automated Reasoning Chains for Verification of LLM-Generated Scientific Code

With the rise of Large Language Model (LLM) generated code, including in domains like scientific computing, ensuring not only syntactical, but also mathematical correctness, has become a critical task. Traditional formal methods approaches often struggle with the ambiguity of floating-point code, and full symbolic execution is extremely costly and limited. We propose a chain-of-reasoning approach that iteratively lifts basic semantics from code into the SPIRAL system and then establishes numerical equivalency to the desired mathematical operation. Here, we leverage the ample mathematical knowledge already formalized in SPIRAL to enable the system to recognize not just different implementations of the same algorithm but fully separate approaches to solving the given problem. The chain establishes tight error bounds on the output of given code with respect to the true continuous solution it approximates, quantifying all sources of error. We demonstrate this approach by establishing the correctness of a pseudospectral solver for a simple 1-dimensional Poisson problem.

Oschatz, Quentin [Carnegie Mellon University,Pitts↗
DOE OSTI2023

Magnetic properties of the quasi-one-dimensional S = 1 spin chain antiferromagnet BaNi Te 2 O 7

We report a quasi-one-dimensional S=1 spin chain compound BaNiTe 2 O 7 . This magnetic system has been investigated by magnetic susceptibility, specific heat, and neutron powder diffraction. These results indicate that BaNiTe 2 O 7 develops a short-range magnetic correlation around T ~ 22K. With further cooling, an antiferromagnetic phase transition is observed at T N ~ 5.4K. Neutron powder diffraction revealed antiferromagnetic noncollinear order with a commensurate propagation vector k = (1/2,1,0). The refined magnetic moment size of Ni 2+ at 1.5 K is 1.84 μB , and its noncollinear spin texture is confirmed by first-principles calculations. In conclusion, inelastic neutron-scattering results and density functional theory calculations confirmed the quasi-one-dimensional nature of the spin systems.

1-dimensional spin chains↗
DOE OSTI2023

Structure and magnetic properties of Ba 9 ⁢V 3 ⁢Te 15 with ferromagnetic spin chains

Here we report a ferromagnetic compound Ba9⁢V3⁢Te15 with quasi-one-dimensional (1D) spin chains. It was synthesized at high-temperature and high-pressure conditions and systematically investigated via structural, transport, magnetic and heat capacity measurements. Ba9⁢V3⁢Te15 mainly consists of trimerized face-sharing V⁢Te6 octahedral chains running along the 𝑐 axis, which are separated by a distance of 10.184⁢(8)⁢Å, thus demonstrating a strong 1D structural character. Ba9⁢V3⁢Te15 is a semiconductor with a band gap ∼128meV and undergoes a ferromagnetic transition with 𝑇C∼3.6K. Far above 𝑇C, the short-range spin orders due to the intrachain spin coupling have developed, which leads to a negative magnetoresistance effect, the deviation of magnetic susceptibility from the Curie-Weiss law and 𝑇1/2 dependence of magnetic heat capacity. Our results reveal that Ba9⁢V3⁢Te15 provides a good opportunity to study the intrinsic properties of a system with quasi-1D ferromagnetic spin chains.

1-dimensional spin chains↗
DOE OSTI2025

$2+1$ dimensional Floquet systems and lattice fermions: Exact bulk spectral equivalence

A connection has recently been proposed between periodically driven systems known as Floquet insulators in continuous time and static fermion theories in discrete time. This connection has been established in a (1+1) ( 1 + 1 ) -dimensional free theory, where an explicit mapping between the spectra of a Floquet insulator and a discrete-time Dirac fermion theory has been formulated. Here we investigate the potential of static discrete-time theories to capture Floquet physics in higher dimensions, where so-called anomalous Floquet topological insulators can emerge that feature chiral edge states despite having bulk bands with zero Chern number. Starting from a particular model of an anomalous Floquet system, we provide an example of a static discrete-time theory whose bulk spectrum is an exact analytic match for the Floquet spectrum. The spectra with open boundary conditions in a particular strip geometry also match up to finite-size corrections. However, the models differ in several important respects. The discrete-time theory is spatially anisotropic, so that the spectra do not agree for all lattice terminations, e.g. other strip geometries or on half spaces. This difference can be attributed to the fact that the static discrete-time model is quasi-one-dimensional in nature and therefore has a different bulk-boundary correspondence than the Floquet model.

Iadecola, Thomas (ORCID:0000000251456441)↗
DOE OSTI2025

Fusion burn-propagation simulations using the collisional and radiative particle-in-cell code TRIFORCE

The ability to accurately model burn propagation in inertial confinement fusion plasmas is crucial for advancing fusion energy research. This work presents enhancements to the triforce hybrid fluid-kinetic multiphysics code, focusing on its kinetic half, which employs the particle-in-cell (PIC) method with Monte Carlo collisions (MCC). We use a moment-preserving collision model that mitigates numerical noise, particularly in spherical geometries where particle weights vary significantly. Additionally, we refine the treatment of inverse bremsstrahlung to account for electron–ion collision frequency reductions in degenerate plasmas and incorporate a blackbody radiation source to enable realistic photon injection. These improvements enable the simulation of 1-dimensional (1D) spherical fusion burn propagation in deuterium–tritium plasmas. Benchmark comparisons with the hydra radiation-hydrodynamics code confirm that triforce accurately captures the dynamics of hot-spot expansion and burn propagation, demonstrating sensitivity to ignition thresholds consistent with theoretical models. Findings show the ignition cliff to be less steep in our work compared to radiation-hydrodynamic modeling. These results highlight the role of kinetic effects in fusion ignition physics and underscore the necessity of hybrid fluid-kinetic models for advancing predictive capabilities in high-energy-density plasma systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Spontaneously Broken Noninvertible Symmetries in Transverse-Field Ising Qudit Chains

Recent developments have revealed that symmetries need not form a group, but instead can be noninvertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a noninvertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group 𝐺 (reducing to ordinary qubits when 𝐺=ℤ 2 ). We construct Ising-type transverse-field Hamiltonians with Rep⁡(𝐺) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group 𝐺 . For non-Abelian 𝐺 , the symmetry is noninvertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain—features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with nontrivial internal Hilbert spaces and fusion rules. Our Letter identifies properties of noninvertible symmetry breaking that existing quantum hardware can probe.

1-dimensional spin chains↗
DOE OSTI2024

Slow thermalization and subdiffusion in $U$(1) conserving Floquet random circuits

Random quantum circuits are paradigmatic models of minimally structured and analytically tractable chaotic dynamics. We study a family of Floquet unitary circuits with Haar random U(1) charge conserving dynamics; the minimal such model has nearest-neighbor gates acting on spin-1/2 qubits, and a single layer of even/odd gates repeated periodically in time. We find that this minimal model is not robustly thermalizing at numerically accessible system sizes, and displays slow subdiffusive dynamics for long times. We map out the thermalization dynamics in a broader parameter space of charge conserving circuits, and understand the origin of the slow dynamics in terms of proximate localized and integrable regimes in parameter space. In contrast, we find that small extensions to the minimal model are sufficient to achieve robust thermalization; these include (i) increasing the interaction range to three-site gates, (ii) increasing the local Hilbert space dimension by appending an additional unconstrained qubit to the conserved charge on each site, or (iii) using a larger Floquet period comprised of two independent layers of gates. Furthermore, our results should inform future studies of charge conserving circuits, which are relevant for a wide range of topical theoretical questions.

1-dimensional spin chains↗
DOE OSTI2023

On the relation between the subadditivity cone and the quantum entropy cone

Given a multipartite quantum system, what are the possible ways to impose mutual independence among some subsystems, and the presence of correlations among others, such that there exists a quantum state which satisfies these demands? This question and the related notion of a pattern of marginal independence (PMI) were introduced in [1], and then argued in [2] to be central in the derivation of the holographic entropy cone. Here we continue the general information theoretic analysis of the PMIs allowed by strong subadditivity (SSA) initiated in [1]. We show how the computation of these PMIs simplifies when SSA is replaced by a weaker constraint, dubbed Klein’s condition (KC), which follows from the necessary condition for the saturation of subadditivity (SA). Formulating KC in the language of partially ordered sets, we show that the set of PMIs compatible with KC forms a lattice, and we investigate several of its structural properties. One of our main results is the identification of a specific lower dimensional face of the SA cone that contains on its boundary all the extreme rays (beyond Bell pairs) that can possibly be realized by quantum states. We verify that for four or more parties, KC is strictly weaker than SSA, but nonetheless the PMIs compatible with SSA can easily be derived from the KC-compatible ones. For the special case of 1-dimensional PMIs, we conjecture that KC and SSA are in fact equivalent. To make the presentation self-contained, we review the key ingredients from lattice theory as needed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Challenges in Pulsed-Field Gradient Nuclear Magnetic Resonance on Magnetically Heterogeneous Interfaces: Sequence and Field-Dependent Apparent Diffusion Coefficients

It is well known that the internal gradient (gi) that exists within pores haunts the diffusion coefficient (D) as measured by the pulsed-field gradient (PFG) nuclear magnetic resonance (NMR). Several PFG-NMR methods developed to determine an accurate D were not successful. Then, the steady-state diffusion coefficient (Dapp,8) for the cation [C4mim]+ of [C4mim][Tf2N]; [1-butyl-3-methylimidazolium][bis(trifluoromethylsulfonyl)imde] ionic liquid confined in ordered mesoporous carbon (OMC) were determined by comparing Dapp,8 obtained from 1H PFG-NMR performed with three different stimulated echo sequences: STE, APFG, and MPFG under the two external magnetic field strength, B0 = 9.4 and 14.1 Tesla. The measured Dapp,8 which is an order of magnitude smaller than D of bulk [C4mim][Tf2N], is in good agreement between APFG and MPFG both in B0 = 9.4 and 14.1 Tesla. However, the strong gi artifact, which caused apparent diffusion coefficient (Dapp) depending strongly and weakly on B0 and temperature, respectively, in diffusion-time dependent Dapp, Dapp(?) obtained from a sequence with monopolar gradients (STE) was suppressed by using sequences employing bipolar gradients (APFG and MPFG) in the region of steady-state diffusion. But incompletely suppressed gi artifact resulting in the different behaviors of the early part of Dapp(?) between the sequences leads a ˜ 0.6 and 0.9 in MPFG and APFG, respectively, in the relationship between mean squared displacement and diffusion time: = 2Dta, where a = 0.5 and 1 for 1-dimensional single file diffusion and 3-dimensional bulk diffusion, respectively. The above observations clearly show that the diffusion behavior of ions/molecules within the pores and pore structure, such as the surface-to-volume ratio? (D?_app (?)=D_0 [1-4/(9vp) S/V v(D_0 ?)]) and tortuosity (T = D0/Dapp,8), are possible to be misunderstood, especially in the systems with a non-negligible gi. This work demonstrates that it may be necessary to test several PFG sequences under multiple external magnetic fields for the correct determination of the diffusion behavior of ions/molecules in the pores with a larger internal gradient, gi.

Han, Kee Sung↗
DOE OSTI2025

Single-Walled Zeolitic Nanotube–Poly(oxazoline) Nanocomposites as Heterogeneous Catalysts for Acid–Base Cascade Reactions

Zeolites with a unique, 1-dimensional form factor were recently discovered − zeolite nanotubes (ZNTs). Here we describe the synthesis and characterization of NaH-ZNTpoly( oxazoline) composites targeting liquid-phase acid−base cascade catalysis. NaH-ZNT, a one-dimensional zeolite analogue with mesoporosity (3−4 nm) associated with nanotubes and inherent Brønsted acid sites associated with the microporous zeolite domains, is functionalized with poly(oxazoline)-based triblock copolymers with varying molecular weights (3−17 kDa). The composites are characterized using N2 sorption, STEM, FTIR, and elemental analysis, confirming successful grafting and preservation of the zeolite nanotube structure. The composites’ catalytic performance is evaluated through separate acid and base reactions, followed by a combined cascade of a deacetalization−Knoevenagel condensation for the synthesis of chalcone compounds. High initial reaction rates are demonstrated, but modest overall cascade product formation rates are observed, attributed to interactions between Brønsted acid sites and base amine groups that occur in the polymer-grafted systems. Physical mixtures of NaH-ZNT-SH and poly(oxazoline)s, lacking covalent linkages between ZNT and the polymer, support this supposition. This work demonstrates the potential of NaH-ZNT-poly(oxazoline) composites for liquid-phase cascade catalysis for synthesizing compounds of potential medicinal interest, highlighting the benefits of the grafting-to approach as well as the need for further optimization of the catalytic performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Higher Dimensionality in the Mg–Co–B System: Synthesis and Structure of Incommensurate Composite Mg 1+ε Co 4 B 4

Guided by high-temperature in situ X-ray diffraction, the discovery and synthesis of Mg 1+ε Co 4 B 4 (ε ≈ 0.272) using a MgH 2 hydride precursor is reported, along with a detailed crystal structure description and measurement of magnetic properties. The mismatch in lattice periodicities between Mg and Co–B substructures places Mg 1+ε Co 4 B 4 in the family of incommensurate composite crystals and prompted structural refinement in a (3 + 1)-dimensional model. The structure of Mg 1+ε Co 4 B 4 (P4 2 /ncm(00γ)s00s, a = 6.75847(7) Å, c = 3.94007(8) Å, q = (0, 0, 1.2721(3))) was refined from neutron powder diffraction and high-resolution powder X-ray diffraction data and confirmed by scanning transmission electron microscopy and electron diffraction. Mg 1+ε Co 4 B 4 is isostructural to Nd 1+ε Fe 4 B 4 and several related ternary borides with 0.07 ≤ ε ≤ 0.17, with Mg occupying the rare-earth site. Satellite reflections in the electron diffraction patterns hinted at positional modulation of the transition metal–boron substructure by Mg atoms, but this could not be refined from the neutron or X-ray diffraction data. Low-temperature magnetic measurements show no indications of long-range magnetic ordering or superconductivity down to 5 K. DFT calculations confirmed the absence of a magnetically ordered ground state and the stability of a 5:4 supercell (ε = 0.25) relative to the fully commensurate structure. Neutron diffraction and synthesis from elemental Mg demonstrated that Mg 1+ε Co 4 B 4 is not a hydrogen-stabilized phase. Mg 1+ε Co 4 B 4 represents the second compound reported in the Mg–Co–B system and the first superspace symmetry model of a Nd 1+ε Fe 4 B 4 -type incommensurate composite compound refined from powder diffraction data.

chemical structure↗
DOE OSTI2023

Confinement of many-body Bethe strings

Based on the Bethe ansatz approach and inelastic neutron scattering experiments, we reveal the evolution of confinement of many-body Bethe strings in ordered regions of the quasi-one-dimensional antiferromagnet YbAlO 3 . In the antiferromagnetic phase, the spin dynamics is dominated by confined length-1 Bethe strings, whose dominancy in the high-energy branch of the excitation spectrum yields to confined length-2 Bethe strings when the material is tuned to the spin-density-wave phase. In the thermal-induced disordered region, the confinement effect disappears, and the system restores the conventional quantum integrable physics of the one-dimensional Heisenberg model. Finally, our results establish a unified picture based on a Bethe string for the spin dynamics in different magnetic phases of YbAlO 3 , and thus provide profound insight into many-body quantum magnetism.

1-dimensional spin chains↗
DOE OSTI2025

Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems

We establish a holographic duality between d -dimensional mixed-state symmetry-protected topological (mSPT) phases and ( d + 1 ) -dimensional subsystem symmetry-protected topological (SSPT) states. Specifically, we show that the reduced density matrix of the boundary layer of a ( d + 1 ) -dimensional SSPT state with subsystem symmetry S and global symmetry G corresponds to a d -dimensional mSPT phase with strong S and weak G symmetries. Conversely, we demonstrate that the wave function of an SSPT state can be constructed by replicating the density matrix of the corresponding lower-dimensional mSPT phase. This mapping links the density matrix in lower dimensions to the entanglement properties of higher-dimensional wave functions, providing an approach for analyzing nonlinear quantities and quantum information metrics in mixed-state systems. Our duality offers a new perspective for studying intrinsic mSPT phases that are unique to open quantum systems, without pure-state analogues. We show that strange correlators and twisted Rényi- N correlators can diagnose these nontrivial phases and we explore their connection to strange correlators in pure-state SSPT phases. Furthermore, we discuss several implications of this holographic duality, including a method for preparing intrinsic mSPT phases through the duality. Published by the American Physical Society 2025

Sun, Shijun (ORCID:0000000168880030)↗