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DOE OSTI2024

Classifying photonic topology using the spectral localizer and numerical K -theory

Recently, the spectral localizer framework has emerged as an efficient approach for classifying topology in photonic systems featuring local nonlinearities and radiative environments. In nonlinear systems, this framework provides rigorous definitions for concepts such as topological solitons and topological dynamics, where a system’s occupation induces a local change in its topology due to nonlinearity. For systems embedded in radiative environments that do not possess a shared bulk spectral gap, this framework enables the identification of local topology and shows that local topological protection is preserved despite the lack of a common gap. However, as the spectral localizer framework is rooted in the mathematics of C*-algebras, and not vector bundles, understanding and using this framework requires developing intuition for a somewhat different set of underlying concepts than those that appear in traditional approaches for classifying material topology. In this tutorial, we introduce the spectral localizer framework from a ground-up perspective and provide physically motivated arguments for understanding its local topological markers and associated local measure of topological protection. In doing so, we provide numerous examples of the framework’s application to a variety of topological classes, including crystalline and higher-order topology. We then show how Maxwell’s equations can be reformulated to be compatible with the spectral localizer framework, including the possibility of radiative boundary conditions. To aid in this introduction, we also provide a physics-oriented introduction to multi-operator pseudospectral methods and numerical K-theory, two mathematical concepts that form the foundation for the spectral localizer framework. Finally, we provide some mathematically oriented comments on the C*-algebraic origins of this framework, including a discussion of real C*-algebras and graded C*-algebras that are necessary for incorporating physical symmetries. Looking forward, we hope that this tutorial will serve as an approachable starting point for learning the foundations of the spectral localizer framework.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Open momentum space method for the Hofstadter butterfly and the quantized Lorentz susceptibility

Here we develop a generic k ∙ p open momentum space method for calculating the Hofstadter butterfly of both continuum (moiré) models and tight-binding models, where the quasimomentum is directly substituted by the Landau level (LL) operators. By taking a LL cutoff (and a reciprocal lattice cutoff for continuum models), one obtains the Hofstadter butterfly with in-gap spectral flows. For continuum models such as the moiré model for twisted bilayer graphene, our method gives a sparse Hamiltonian, making it much more efficient than existing methods. The spectral flows in the Hofstadter gaps can be understood as edge states on a momentum space boundary, from which one can determine the two integers (t ν , s ν ) of a gap ν satisfying the Diophantine equation. The spectral flows can also be removed to obtain a clear Hofstadter butterfly. While t ν is known as the Chern number, our theory identifies s ν as a dual Chern number for the momentum space, which corresponds to a quantized Lorentz susceptibility γ xy = eBs ν .

2-dimensional systems↗

DOE OSTI2023

Atmospheric Turbulent Intermittency Over the Arctic Sea‐Ice Surface During the MOSAiC Expedition

Turbulent motions in the Arctic stable boundary layer are characterized by intermittency, but they are rarely investigated due to limited observations, in particular over the sea‐ice surface. In the present study, we explore the characteristics of turbulent intermittency over the Arctic sea‐ice surface using data collected during the Multidisciplinary drifting Observation for the Study of Arctic Climate expedition from October 2019 to September 2020. We first develop a new algorithm, which performs well in identifying the spectral gap over the Arctic sea‐ice surface. Then the characteristics of intermittency are investigated. It is found that the strength of intermittency increases under the conditions of light surface wind speed, small surface wind speed gradient, and strong surface air temperature gradient. The momentum flux, sensible heat flux, and latent heat flux calculated by raw eddy‐covariance fluctuations are overestimated by 3%, 10%, and 24%, respectively, because submesoscale motions are included. Furthermore, the characteristics of the atmospheric boundary layer structure under various intermittency conditions reveal that strong low‐level jets are favorable to surface turbulent motions that result in weak intermittency, while strong temperature inversions above the surface layer suppress surface turbulent motions and lead to strong intermittency.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Comparison Between the f-Electron and Conduction-Electron Density of States in the Falicov-Kimball Model at Low Temperature

The spinless Falicov-Kimball model is one of the simplest models of many-body physics. While the conduction-electron density of states is temperature independent in the normal state, the f -electron density of states is strongly temperature dependent—it has an orthogonality catastrophe singularity in the metallic phase and is gapped in the insulating phase. The question we address here is whether the spectral gap is the same for both electron species as T → 0. Finally, we find strong evidence to indicate that the answer is affirmative.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Anisotropic Thermal Conductivity Oscillations in Relation to the Putative Kitaev Spin Liquid Phase of α-RuCl 3

In the presence of an external magnetic field, the Kitaev model could host either gapped topological anyons or gapless Majorana fermions. In α-RuCl 3 , the gapped and gapless cases are only separated by a 30° rotation of the in-plane magnetic field vector. The presence or absence of the spectral gap is key for understanding the thermal transport behavior in α-RuCl 3 . Here, we study the anisotropy of the oscillatory features of thermal conductivity in α-RuCl 3 . We examine the oscillatory features of thermal conductivities (κ / / a, κ / / b) with fixed external fields and find distinct behavior for the gapped (B / / a) and gapless (B / / b) scenarios. Furthermore, we track the evolution of thermal resistivity (λ α ) and its oscillatory features with the rotation of in-plane magnetic fields from B / / b to B / / a. The thermal resistivity λ(B, φ) displays distinct rotational symmetries before and after the emergence of the field-induced Kitaev spin liquid phase. These results suggest that oscillatory features of thermal conductivity in α-RuCl 3 are closely linked to the putative Kitaev spin liquid phase and its excitations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Energy spectrum and current-phase relation of a nanowire Josephson junction close to the topological transition

A semiconducting nanowire proximitized by an $\textit{s}$-wave superconductor can be tuned into a topological state by an applied magnetic field. This quantum phase transition is marked by the emergence of Majorana zero modes at the ends of the wire. The fusion of Majorana modes at a junction between two nanowires results in a 4π-periodic Josephson effect. Here, we elucidate how the 4π periodicity arises across the topological phase transition in a highly-transparent short nanowire junction. Owing to a high transmission coefficient, Majorana zero modes coming from different wires are strongly coupled, with an energy scale set by the proximity-induced, field-independent pairing potential. At the same time, the topological spectral gap—defined by competition between superconducting correlations and Zeeman splitting—becomes narrow in the vicinity of the transition point. The resulting hybridization of the fused Majorana states with the spectral continuum strongly affects the electron density of states at the junction and its Josephson energy. We study the manifestations of this hybridization in the energy spectrum and phase dependence of the Josephson current. We pinpoint the experimentally observable signatures of the topological phase transition, focusing on junctions with weak backscattering.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Nearly-frustration-free ground state preparation

Solving for quantum ground states is important for understanding the properties of quantum many-body systems, and quantum computers are potentially well-suited for solving for quantum ground states. Recent work [1] has presented a nearly optimal scheme that prepares ground states on a quantum computer for completely generic Hamiltonians, whose query complexity scales as δ − 1 , i.e. inversely with their normalized gap. Here we consider instead the ground state preparation problem restricted to a special subset of Hamiltonians, which includes those which we term "nearly-frustration-free": the class of Hamiltonians for which the ground state energy of their block-encoded and hence normalized Hamiltonian α − 1 H is within δ y of -1, where δ is the spectral gap of α − 1 H and 0 ≤ y ≤ 1 . For this subclass, we describe an algorithm whose dependence on the gap is asymptotically better, scaling as δ y / 2 − 1 , and show that this new dependence is optimal up to factors of log ⁡ δ . In addition, we give examples of physically motivated Hamiltonians which live in this subclass. Finally, we describe an extension of this method which allows the preparation of excited states both for generic Hamiltonians as well as, at a similar speedup as the ground state case, for those which are nearly frustration-free.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Avalanches and many-body resonances in many-body localized systems

Here we numerically study both the avalanche instability and many-body resonances in strongly disordered spin chains exhibiting many-body localization (MBL). Finite-size systems behave like MBL within the MBL regimes, which we divide into the asymptotic MBL phase and the finite-size MBL regime; the latter regime is, however, thermal in the limit of large systems and long times. In both Floquet and Hamiltonian models, we identify some landmarks within the MBL regimes. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition occurs much deeper in the MBL regimes than has been suggested by most previous studies. Our other landmarks involve systemwide many-body resonances: We find that the effective matrix elements producing eigenstates with systemwide many-body resonances are enormously broadly distributed. This broad distribution means that the onset of such resonances in typical samples occurs quite deep in the MBL regimes, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regimes of finite-size systems into three subregimes: (i) at strongest randomness, typical samples do not have any eigenstates that are involved in systemwide many-body resonances; (ii) there is a substantial intermediate subregime where typical samples do have such resonances but the pair of eigenstates with the minimum spectral gap does not, so the size of the minimum gap agrees with expectations from Poisson statistics; and (iii) in the weaker randomness subregime, the minimum gap is larger than predicted by Poisson level statistics because it is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain nonresonant and the system thus still appears MBL in most respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i) and the other subregimes are entirely in the thermal phase, even though they look localized in most respects, so are in the finite-size MBL regime.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Supersymmetry breaking in SYK and the black hole spectrum

The spectrum and dynamics of near-extremal black holes is strongly modified by quantum effects at low temperatures. When the extremal limit does not preserve any supersymmetry, the density of states goes to zero at extremality and no extremal black holes remain. However, when the extremal limit is supersymmetric, a large microscopic degeneracy survives and there is a gap to the first excited black hole visible from gravity. In this article we study large N quantum mechanical models where supersymmetry is explicitly broken, allowing us to interpolate between these two qualitatively different pictures. We propose and analyze deformations of N = 2 SYK models with such a pattern of (super) symmetry breaking which violate the U(1) R-symmetry. These models feature a lifting of the BPS degeneracy and a closing of the spectral gap, and we further show that the large N soft effective action is given by a modification of the N = 2 Schwarzian theory in which the U(1) R mode becomes massive.

1/N Expansion↗

DOE OSTI2024

Influence of disorder on antidot vortex Majorana states in three-dimensional topological insulators

Topological insulator/superconductor two-dimensional heterostructures are promising candidates for realizing topological superconductivity and Majorana modes. In these systems, a vortex pinned by a prefabricated antidot in the superconductor can host Majorana zero-energy modes (MZMs), which are exotic quasiparticles that may enable quantum information processing. However, a major challenge is to design devices that can manipulate the information encoded in these MZMs. One of the key factors is to create small and clean antidots, so the MZMs, localized in the vortex core, have a large gap to other excitations. If the antidot is too large or too disordered, the level spacing for the subgap vortex states may become smaller than temperature. In this paper, we numerically investigate the effects of disorder, chemical potential, and antidot size on the subgap vortex spectrum, using a two-dimensional effective model of the topological insulator surface. Our model allows us to simulate large system sizes with vortices up to 1.8 µ⁢m in diameter (with a 6 nm lattice constant). We also compare our disorder model with the transport data from existing experiments. As a result, we find that the spectral gap can exhibit a nonmonotonic behavior as a function of disorder strength, and that it can be tuned by applying a gate voltage.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Tunable Phonon Polariton Hybridization in a Van der Waals Hetero‐Bicrystal

Abstract Phonon polaritons, the hybrid quasiparticles resulting from the coupling of photons and lattice vibrations, have gained significant attention in the field of layered van der Waals heterostructures. Particular interest has been paid to hetero‐bicrystals composed of molybdenum oxide (MoO 3 ) and hexagonal boron nitride (hBN), which feature polariton dispersion tailorable via avoided polariton mode crossings. In this work, the polariton eigenmodes in MoO 3 ‐hBN hetero‐bicrystals self‐assembled on ultrasmooth gold are systematically studied using synchrotron infrared nanospectroscopy. It is experimentally demonstrated that the spectral gap in bicrystal dispersion and corresponding regimes of negative refraction can be tuned by material layer thickness, and these results are quantitatively matched with a simple analytic model. Polaritonic cavity modes and polariton propagation along “forbidden” directions are also investigated in microscale bicrystals, which arise from the finite in‐plane dimension of the synthesized MoO 3 micro‐ribbons. The findings shed light on the unique dispersion properties of polaritons in van der Waals heterostructures and pave the way for applications leveraging deeply sub‐wavelength mid‐infrared light‐matter interactions.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Transient Terahertz Oscillations During Photoinduced Polarization Topology Reconfiguration in Ferroelectric Superlattices

Terahertz resonances embedded in crystalline heterostructures could close a spectral gap between conventional electronics and photonics while opening new windows on non-equilibrium lattice dynamics. We show that femtosecond optical screening of the depolarization field in epitaxial PbTiO3/SrTiO3 superlattices launches a collective polar mode that oscillates near 1 THz and coherently spans the entire mini-Brillouin zone. Wave-vector-resolved pump–probe X-ray diffraction resolves a nearly dispersion-less oscillation at 0.87 THz and 0.94 THz at the zone boundary and zone center, respectively, persisting for ~2.5 ps, corresponding to a weakly damped resonance. Dynamical phase-field simulations reveal the origin of the mode to mesoscopic rotation of closure-domain textures during the photo-excited transition from an unscreened to a screened electrostatic state. Varying the PbTiO3 and SrTiO3 ratio tunes the mode frequency continuously from 0.9 to 1.4 THz, providing a quantitative design rule for frequency-selectable THz oscillators in ferroelectric heterostructures. By coupling nanoscale polarization reconfiguration to long-wavelength coherent dynamics, this work establishes depolarization-field engineering to topology-driven THz functionality and expanding the landscape of collective lattice dynamics.

Sri Gyan, Deepankar [Univ. of Wisconsin, Madison, ↗

DOE OSTI2020

Tauberian-Cardy formula with spin

We prove a $2$ dimensional Tauberian theorem in context of $2$ dimensional conformal field theory. The asymptotic density of states with conformal weight $(h,\bar{h})\to (\infty,\infty)$ for any arbitrary spin is derived using the theorem. We further rigorously show that the error term is controlled by the twist parameter and insensitive to spin. The sensitivity of the leading piece towards spin is discussed. We identify a universal piece in microcanonical entropy when the averaging window is large. An asymptotic spectral gap on $(h,\bar{h})$ plane, hence the asymptotic twist gap is derived. We prove an universal inequality stating that in a compact unitary $2$D CFT without any conserved current $Ag\leq \frac{\pi(c-1)r^2}{24}$ is satisfied, where $g$ is the twist gap over vacuum and $A$ is the minimal "areal gap", generalizing the minimal gap in dimension to $(h',\bar{h}')$ plane and $r=\frac{4\sqrt{3}}{\pi}\simeq 2.21$. We investigate density of states in the regime where spin is parametrically larger than twist with both going to infinity. Moreover, the large central charge regime is studied. We also probe finite twist, large spin behavior of density of states.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Detecting thermodynamic phase transition via explainable machine learning of photoemission spectroscopy

Identifying thermodynamic signatures of electronic phases, such as superconductivity, is challenging in low-dimensional materials due to strong fluctuations and low probing volume. Spectroscopic methods are often used to identify new bulk phases, but their main measurable quantity—electronic energy gaps—is no longer an effective order parameter in low-dimensional and fluctuating systems. Combining angle-resolved photoemission with a domain-adversarial neural network, we report a data-driven method to identify thermodynamic phase transitions solely based on single-particle spectra. We demonstrate 97.6% accuracy in cuprate superconductor Bi 2 Sr 2 CaCu 2 O 8+δ with strong superconducting fluctuations. This model notably compensates for the scarcity of experimental data by leveraging virtually inexhaustible simulated data. Further, its explainability reveals the crucial role of in-gap spectral weight in detecting phase fluctuations and thermodynamic transitions. Our work pinpoints the spectroscopic signatures of fluctuating orders and enables using spectroscopy for machine-learning-assisted material discovery for low-dimensional and strong coupling systems.

2D materials↗

DOE OSTI2021

Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics

Understanding the driving forces behind the nucleation of different polymorphs is of great importance for material sciences and the pharmaceutical industry. This includes understanding the reaction coordinate that governs the nucleation process and correctly calculating the relative free energies of different polymorphs. Here, we demonstrate, for the prototypical case of urea nucleation from the melt, how one can learn such a one-dimensional reaction coordinate as a function of prespecified order parameters and use it to perform efficient biased all-atom molecular dynamics simulations. The reaction coordinate is learnt as a function of the generic thermodynamic and structural order parameters using the “spectral gap optimization of order parameters (SGOOP)” approach [Tiwary, P. and Berne, B. J. Proc. Natl. Acad. Sci. U.S.A. (2016)] and is biased using well-tempered metadynamics simulations. The reaction coordinate gives insights into the role played by different structural and thermodynamics order parameters, and the biased simulations obtain accurate relative free energies for different polymorphs. This includes an accurate prediction of the approximate pressure at which urea undergoes a phase transition and one of the metastable polymorphs becomes the most stable conformation. Here, we believe the ideas demonstrated in this work will facilitate efficient sampling of nucleation in complex, generic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Dissipative ground state preparation in ab initio electronic structure theory

Dissipative engineering is a powerful tool for quantum state preparation, and has drawn significant attention in quantum algorithms and quantum many-body physics in recent years. In this work, we introduce a novel approach using the Lindblad dynamics to efficiently prepare the ground state for general ab initio electronic structure problems on quantum computers, without variational parameters. These problems often involve Hamiltonians that lack geometric locality or sparsity structures, which we address by proposing two generic types of jump operators for the Lindblad dynamics. Type-I jump operators break the particle number symmetry and should be simulated in the Fock space. Type-II jump operators preserves the particle number symmetry and can be simulated more efficiently in the full configuration interaction space. For both types of jump operators, we prove that in a simplified Hartree-Fock framework, the spectral gap of our Lindbladian is lower bounded by a universal constant. For physical observables such as energy and reduced density matrices, the convergence rate of our Lindblad dynamics with Type-I jump operators remains universal, while the convergence rate with Type-II jump operators only depends on coarse grained information such as the number of orbitals and the number of electrons. To validate our approach, we employ a Monte Carlo trajectory-based algorithm for simulating the Lindblad dynamics for full ab initio Hamiltonians, demonstrating its effectiveness on molecular systems amenable to exact wavefunction treatment.

Quantum chemistry↗

DOE OSTI2025

Upstreamness and downstreamness in input–output analysis from local and aggregate information

Abstract Ranking sectors and countries within global value chains is of paramount importance to estimate risks and forecast growth in large economies. However, this task is often non-trivial due to the lack of complete and accurate information on the flows of money and goods between sectors and countries, which are encoded in input–output (I–O) tables. In this work, we show that an accurate estimation of the role played by sectors and countries in supply chain networks can be achieved without full knowledge of the I–O tables, but only relying on local and aggregate information, e.g., the total intermediate demand per sector. Our method, based on a rank-1 approximation to the I–O table, shows consistently good performance in reconstructing rankings (i.e., upstreamness and downstreamness measures for countries and sectors) when tested on empirical data from the world input–output database. Moreover, we connect the accuracy of our approximate framework with the spectral properties of the I–O tables, which ordinarily exhibit relatively large spectral gaps. Our approach provides a fast and analytically tractable framework to rank constituents of a complex economy without the need of matrix inversions and the knowledge of finer intersectorial details.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Reaction–drift–diffusion models from master equations: application to material defects

We present a general method to produce well-conditioned continuum reaction–drift–diffusion equations directly from master equations on a discrete, periodic state space. We assume the underlying data to be kinetic Monte Carlo models (i.e. continuous-time Markov chains) produced from atomic sampling of point defects in locally periodic environments, such as perfect lattices, ordered surface structures or dislocation cores, possibly under the influence of a slowly varying external field. Our approach also applies to any discrete, periodic Markov chain. Here, the analysis identifies a previously omitted non-equilibrium drift term, present even in the absence of external forces, which can compete in magnitude with the reaction rates, thus being essential to correctly capture the kinetics. To remove fast modes which hinder time integration, we use a generalized Bloch relation to efficiently calculate the eigenspectrum of the master equation. A well conditioned continuum equation then emerges by searching for spectral gaps in the long wavelength limit, using an established kinetic clustering algorithm to define a proper reduced, Markovian state space.

36 MATERIALS SCIENCE↗