Papers

We study the variance of the free energy in the Gaussian Sherrington-Kirkpatrick model at zero external field. For every system size and inverse temperature $\beta>0$, we prove $2N^2\operatorname{Var} F_N^{\mathrm{off}}(\beta) \le \log\chi+(\beta^2-1)(\chi-1), \chi=N\mathbb{E}\langle R_{1,2}^2\rangle_\beta$, where $R_{1,2}$ is the replica overlap and $F_N^{\mathrm{off}}=N^{-1}\log Z_N^{\mathrm{off}}$ omits diagonal disorder. The proof uses an exact identity for the edges incident to one spin, Schur complements, and Gaussian disorder interpolation. At criticality the bound reduces to $2N^2\operatorname{Var} F_N^{\mathrm{off}}(1)\le\log\chi$. An explicit nonnegative integral measures its gap. A second decomposition relates this gap to a mixed cubic overlap functional. Existing moment and cavity estimates imply that its required integral is bounded. Critical susceptibility asymptotics give the sharp logarithmic upper coefficient and show that the gap converges exactly when the variance has a constant term. We extend an entropy bound throughout bounded critical temperature windows and establish overlap moment stability on a smaller interval.

Ultralong-range Rydberg molecules, formed by the interaction between a highly excited Rydberg atom and a ground-state atom, provide a unique platform for exploring quantum phenomena spanning nanometer-to-micrometer distances as well as exotic few-body interactions. The formation mechanisms and resultant physical properties differ markedly between s-wave and p-wave scattering channels. Here we report the experimental observation of node-dependent p-wave molecular signals in Rb(nS)-Rb(5S) Rydberg molecular spectra, where variations in the principal quantum number n directly reveal the shift of molecular binding energies induced by the moving nodal structure of the Rydberg electron wavefunction. This node-dependence is attributed to a cooperative effect between the local gradient of the nS-electron wavefunction and the energydependent p-wave scattering length. In addition, resolving two p-wave bound states associated with adjacent nodes highlights the remarkable sub-nanometer spatial resolution achieved in our experiment. Our findings reveal a more profound quantum control mechanism, wherein the principal quantum number acts as a switch for nodal-selective molecular bound states, and the reported method provides a sensitive spectroscopic probe of electron-atom scattering.

Artificial intelligence (AI) is transforming scientific discovery, but its effectiveness is fundamentally limited by the availability of structured scientific knowledge. Although existing databases have accelerated data-driven materials research, much of the knowledge needed for predictive modeling and inverse design remains embedded in unstructured scientific literature. We present an Autonomous Scientific Knowledge Generation Framework that transforms scientific publications into a Unified AI-Ready Scientific Knowledge Base. The framework integrates ontology-guided literature acquisition, hybrid scientific knowledge extraction, semantic harmonization, knowledge fusion, and validation within a unified workflow. Rather than treating literature retrieval, information extraction, and database construction as separate tasks, the framework progressively converts scientific publications into structured, semantically consistent, and provenance-preserving knowledge suitable for AI-driven reasoning. As a proof of concept, the framework was applied to electro-optic materials. Autonomous literature acquisition retrieved and validated about 1,000 publications from multiple scholarly repositories. A representative subset of eight publications was processed through the complete workflow, generating 29 structured scientific records that were harmonized into 7 canonical scientific records. The results demonstrate the complete transformation from scientific literature to an AI-ready scientific knowledge base while preserving quantitative measurements, operating conditions, provenance, and scientific context. The proposed framework provides a scalable, domain-independent foundation for predictive AI, generative AI, and closed-loop AI-driven scientific discovery.

For a weakly interacting Bose gas trapped by an imperfect one-dimensional artificial crystal, we study the effect of its punctual defects, i.e. vacancies, on the ground state properties of the system. In the framework of the mean field approximation, we numerically solve the corresponding Gross-Pitaevskii equation using the “Gradient Flow with Discrete Normalization” method, also known as the imaginary time method. The crystal is artificially produced by applying an external Dirac comb potential to the Bose gas where vacancies are created by randomly removing a predetermined number of deltas. We observe that as the number of randomly removed deltas increases, the ground state energy decreases exponentially from its value for the perfect crystal case until it reaches its value when the Bose gas is free. The ground state energy is reported for different magnitudes of the interaction between bosons and several system sizes which we extrapolate to infinity for the crystal with only one vacancy. Also, we observe the presence of an energy gap between the ground state energies of the perfect system and that with a vacancy, which is more noticeable for values of the particle interaction magnitude $ g \leq 0.1$, when the delta strength $P_0 = 10$. In addition, we report the boson distributions within the crystal, %inside a box with periodic boundary conditions, i.e. the probability density functions which show localization features around vacancies which disappear as $g$ increases. From the ground state energy, the chemical potential is obtained immediately.

Water isobaric heat capacity is anomalously large under ambient conditions and exhibits a sharp maximum upon supercooling. Using classical and path-integral molecular dynamics with accurate machine-learning interatomic potentials, we show that nuclear quantum effects primarily act by suppressing high-frequency vibrations, while the anomalous temperature dependence of the isobaric heat capacity originates from structural fluctuations, quantified by the second-solvent-shell intruder order parameter. A simple two-state mapping reveals an effective enthalpy scale of about 4 kJ/mol associated with the interconversion of low- and high-density-like local structures, providing a microscopic link between their population changes and the excess heat capacity from supercooled to ambient conditions.

We present an ab initio calculation of the band-to-band internal-conversion rate of the $\hbar\omega_{\rm nuc} \approx 8.35$ eV isomeric transition in $^{229}$ThO$_2$. Because the nuclear transition energy exceeds the electronic band gap of ThO$_2$, the isomer can decay nonradiatively by resonantly promoting a valence electron into the conduction band. We formulate this process as a Brillouin-zone sum over vertical interband transitions weighted by local Th-centered hyperfine matrix elements, which are evaluated directly from all-electron full-potential linearized augmented-plane-wave Bloch spinors. A finite nuclear magnetization model is included to regularize the short-range hyperfine interaction and to account for the Bohr-Weisskopf effect. After applying scissor shifts to span the experimentally reported ThO$_2$ band gaps, we find calculated internal-conversion lifetimes in the range of $1-16~\mu{\rm s}$. The lifetime increases strongly as the band gap approaches $\omega_{\rm nuc}$ because the resonant interband phase space at the nuclear transition energy is reduced. For the larger reported ThO$_2$ gaps, the calculated lifetime is comparable to the measured conversion-electron Mössbauer lifetime [Nature 648, 300 (2025)]. Our analysis implies that choosing solid-state hosts with band-gap values slightly lower than $\omega_{\rm nuc}$ can optimize solid-state nuclear clock performance with internal-conversion electron readout.

The choice of crystalline orientation and offcut angle is non-trivial for low-symmetry $\beta\text{-Ga}_2\text{O}_3$, where anisotropy impacts bulk and thin film synthesis, material properties, and power device fabrication and performance. Scalable (100)-oriented $\beta\text{-Ga}_2\text{O}_3$ wafers are desirable for electronic devices but are not typically used due to 10-30x slower growth rates compared to other orientations. Here we report molecular beam epitaxy (MBE) growth rates equal to the fast growth direction by using (100) $Ga_2O_3$ wafers with large grown-in offcuts. The offcuts (up to 13.4{\deg}) are directly grown by Edge-defined Film-fed Growth (EFG) of 2D ribbons with rotated seed crystals, avoiding material loss from crystal boule offcut methods while maintaining high crystalline quality. Chemical-mechanical polishing produces epitaxy-ready substrates, and step flow growth is observed across all offcut angles. We measure an unintentional n-type doping density of $2{\times}10^{15} cm^{-3}$, one of the lowest values reported for MBE-grown films. Planar Schottky barrier diodes on these epilayers without edge termination have an on/off ratio ~10$^5$ and an average breakdown field of 1.56 MV/cm, comparable to or exceeding similar devices fabricated on other orientations. Overall, these results illustrate the importance of both crystal face and offcut angle and validate the use of the scalable (100)-oriented $\beta\text{-Ga}_2\text{O}_3$ wafers.

Interfacial charge-transfer processes play a critical role in plasmon-enhanced spectroscopy, yet the energetic conditions governing charge-transfer resonance within molecule-metal nanocavities remain poorly understood. Here, plasmonic nanoparticle-on-mirror junctions incorporating systematically engineered biphenylthiol derivatives monolayers were used to investigate how frontier orbital alignment influences chemical enhancement mechanisms. A molecular library spanning a broad range of electronically tuned acceptor states was examined using surface-enhanced Raman scattering (SERS), vibrational sum frequency generation (vSFG) spectroscopy, and density functional theory calculations. By combining different excitation wavelengths with controlled variation of substrate composition and molecular electronic structure, the energetic relationship between plasmon-enhanced charge transfer excitation and molecular orbital alignment was quantitatively evaluated. The results reveal that charge-transfer enhancement of Raman scattering is governed by a well-defined interfacial resonance condition dependent on substrate work function and excitation energy. We further probe a subset of molecular-metal systems by nanocavity-enhanced vSFG and identify the same resonance conditions as in SERS, consistent with expectations. These findings establish an experimentally accessible framework for probing and engineering charge-transfer processes in plasmonic molecular junctions and provide mechanistic insight relevant to molecular plasmonics, charge carrier photophysics, and nanoscale interfacial spectroscopy.

Two-dimensional van der Waals heterobilayers provide an attractive platform for the development of next-generation spintronic devices. Here, first-principles calculations are performed to investigate the structural, electronic and magnetic properties of MSe2/WTe2 (M = V, Cr, Mn, Fe, and Co) van der Waals heterobilayers. The pristine WSe2/WTe2 heterobilayer in AA'-configuration is found to be energetically favorable and exhibits type-II band alignment with a band gap of 0.70 eV, and this provides an ideal platform for controlling carrier transport. Substituting W with 3d transition metal atoms, induces long-range magnetic ordering and reconstructs the spin-resolved electronic band structure. The formation of the heterointerface generates pronounced charge redistribution and an intrinsic built-in electric field, leading to interface-induced electronic reconstruction. MnSe2/WTe2 heterobilayer exhibits half-metallicity, whereas FeSe2/WTe2 heterobilayer simultaneously exhibits half-metallicity and spin-resolved type-II band alignment. Interfacial electronic reconstruction further produces a substantial perpendicular magnetic anisotropy, driving MnSe2 from an in-plane easy axis with MAE value of 1.10 meV in the isolated monolayer to a robust out-of-plane easy axis with MAE value of 20.8 meV in the heterobilayer. Among all the structures, CoSe2/WTe2 heterobilayer exhibits maximum Curie temperature (273.87 K). The combined results establish that interface engineering makes MSe2/WTe2 heterobilayers as a promising candidates for next-generation low-dimensional spintronic applications.

Molecule-surface interactions are central to many research and technological areas, spanning from heterogeneous catalysis and polymer science to electrochemistry. Of particular relevance are metallic nanogaps used in molecular electronics and near-field spectroscopy. Due to the buried nature of these double interfaces, few methods exist to monitor side-specific interactions and relative molecular orientation inside the gap. In this work, we introduce plasmon-enhanced nonlinear vibrational spectroscopy as an efficient tool to investigate surface molecular adsorption within metallic nanojunctions. By exploiting simultaneous vibrational sum- and difference-frequency generation in dual-resonant nanocavities, we resolve molecular orientation and preferential binding to one of the two gold surfaces, with few-molecule sensitivity. We also discover that the non-resonant (electronic) second-order nonlinear response is not an intrinsic property of the metal surface, but is instead governed by the molecule-surface interaction. Our findings provide a powerful analytical tool, easily implementable as an add-on to Raman spectroscopy, thanks to commercially available mid-infrared quantum cascade lasers.

X-ray diffraction (XRD) is fundamental to structural materials characterization, yet transforming a raw powder pattern into a refined crystal structure still demands considerable domain expertise. We present AGAPI-XRD, a hybrid framework integrating DiffractGPT generative structure prediction, database pattern matching against JARVIS-DFT and COD, and automated Rietveld refinement and ALIGNN-FF relaxation through a unified API at https://atomgpt.org/xrd. First, we used the AGAPI-XRD pipeline to evaluate the crystal structure of a variety of minerals in the RRUFF database that were experimentally characterized using powder x-ray diffraction. Next, we benchmarked the lattice parameter prediction fidelity of the AGAPI-XRD pipeline using a subset of the Alexandria PBE-hull dataset and the subset of RRUFF minerals that have known lattice parameters. AGAPI-XRD returns valid lattice parameters for 79.7% of the RRUFF benchmark minerals and for 94.8–98.1% of the Alexandria subset, while identifying a candidate structure for 93.8% of RRUFF minerals. For this benchmark, pattern matching delivers the highest accuracy for known phases, while DiffractGPT extends structure generation to complex materials absent from existing databases. Together, AGAPI-XRD advances accessible, end-to-end automated crystal structure determination from powder XRD data.

Vapor-deposited glass mixtures of organic semiconductors commonly serve as active layers in organic electronic devices, whose lifetime and performance are strongly influenced by the stability and structure of these mixed glasses. Here, we study the stability and anisotropic molecular packing of six co-deposited organic semiconductor glass mixtures with 50:50 weight ratio, by differential scanning calorimetry and spectroscopic ellipsometry. We find that all six binary systems exhibit high kinetic stability and significantly reduced enthalpy relative to the corresponding liquid-cooled glassy mixtures (ultrastable behavior), even for systems where the glass transition temperatures of the components differ by more than 90 K. Furthermore, we demonstrate that the birefringence of a co-deposited glass mixture, a measure of its anisotropic packing, can be predicted from the birefringence of glasses of the two pure components. These results for stability and structure are expected to be applicable to other co-deposited organic semiconductor glass mixtures, so long as the two components mix well in the glass and individually can form ultrastable glasses. Therefore, our findings are significant for designing novel electronic devices with enhanced device lifetime and increased operational efficiency.

Physical Vapor Deposition (PVD) is widely utilized for the production of organic semiconductor devices due to its ability to form thin layers with exceptional properties. Although the layers in the device usually consist of two or more components, there is limited understanding about the fundamental characteristics of such multi-component vapor-deposited glasses. Here, spectroscopic ellipsometry was employed to characterize the densities, thermal stabilities and optical properties of co-vapor deposited NPD and TPD glasses across the entire range of composition. We find that co-deposited NPD and TPD form high density glasses with enhanced thermal stability. The dependences of density and stability upon substrate temperature are correlated, and the birefringence of the co-deposited glasses is determined by the reduced substrate temperature of mixtures. Additionally, we observe that the transformation of a highly stable and dense two component glass into its supercooled liquid initiates from the free surface and propagates into the bulk at constant velocity, like single component PVD glasses. All these features are consistent with the surface equilibration mechanism.

The graphite-to-diamond transition exhibits striking variability under high-pressure, high-temperature (HPHT) conditions, producing diamond, graphitic phases, or metastable, mixed diamond-graphite nanocomposites despite similar synthesis conditions. Existing atomistic models, largely based on idealised single-crystal graphite, do not explain the persistence of partially transformed intermediate states under HPHT conditions. Here, using large-scale molecular dynamics simulations, we show that precursor grain structure governs graphite-to-diamond transformation pathways by decoupling diamond nucleation from cooperative transformation propagation. Grain boundaries first facilitate local sp$^3$ nucleation, after which diamond growth propagates within individual grains but becomes arrested at crystallographically mismatched grain boundaries. As a result, structurally heterogeneous graphite stabilizes kinetically arrested mixed sp$^2$-sp$^3$ states, whereas large or single-crystalline domains favour cooperative bulk transformation into diamond. Our findings identify structural heterogeneity as a missing control parameter alongside pressure and temperature, reframing metastable transformation products as kinetically trapped states arising from precursor microstructure rather than thermodynamic intermediates. Precursor crystallinity therefore emerges as a practical control parameter governing graphite-to-diamond transformation pathways.

We investigate the formation of loop-current ordered phases in half-filled SU($N$) two-leg fermionic ladders. Using a low-energy approach, we uncover the existence of non-perturbative duality symmetries relating four competing orders. Two of these orders correspond to loop-current ordered phases that spontaneously break the time-reversal symmetry and describe charge currents circulating in a staggered pattern either around the plaquettes or along the diagonals of the ladder. These unconventional phases are shown to be dual to conventional (charge and bond) density-wave phases through an exact density-current duality symmetry existing on the lattice. From a perturbative renormalization group approach, we find that these phases for $N>2$ are stabilized in a half-filled SU($N$) two-leg Hubbard ladder with an additional SU($N$) Hund's interaction. The effect of a small doping on these phases is also discussed.

We investigate the role of the CaCl2-type (Pnnm) phase in the high-pressure transformation of rutile TiO2, whose experimental signature has remained elusive. While analogies with other rutile-type oxides suggest such an intermediate, TiO2 typically exhibits a direct transformation to higher-coordination phases such as baddeleyite. Using an all-electron density functional framework combined with density functional perturbation theory, we show that rutile TiO2 undergoes a ferroelastic instability characterized by the development of an orthorhombic strain and a double-well energy landscape at 13.5 GPa. This instability is associated with the softening of the C11 - C12 elastic combination and the condensation of a B1g phonon mode, involving coordinated rotations of TiO6 octahedra that lower the symmetry to the Pnnm structure. Despite this clear elastic and dynamical pathway, enthalpy calculations show that the CaCl2-type phase is only weakly stabilized relative to rutile and remains energetically unfavorable compared to competing columbite and baddeleyite phases. Consequently, the Pnnm phase does not emerge as a stable high-pressure polymorph but instead exists as a transient or weakly metastable intermediate. These results demonstrate that the CaCl2-type phase represents the intrinsic ferroelastic response of rutile TiO2, yet is suppressed by thermodynamic competition, providing a consistent and unified explanation for its elusive experimental observation.

A pair of parallel polarizable planar walls at distance d is considered. The walls are symmetrically charged with a uniform surface charge density, neutralized by mobile point counterions moving between them. The case of repulsive particle images is studied in the strong-coupling (SC) regime. Of interest is the dependence of the effective inter-wall interaction (pressure), mediated by the mobile counterions, as a function of the distance d. It is shown that previous virial SC single-particle theories work well at small d when the dielectric jump is small; for intermediate and large dielectric jumps they are inadequate even in the SC region. Here, we propose a Wigner-type SC theory based on harmonic deviations of particles from their ground-state monolayer or bilayer Wigner structures formed inside the space between the dielectric walls. Our Monte-Carlo simulations are in very good agreement with the Wigner SC predictions, even down to moderate coupling constants ($\Xi > 10$).

The Cooper pair momentum in a superconductor is associated with a phase gradient of the superconducting order parameter. In general, this momentum is small compared to the Fermi momentum, which makes it challenging to measure. Josephson junctions, however, enable the creation of large phase gradients and transfer of the Cooper pair momentum to quasiparticles via Andreev reflection. In this work we demonstrate that Andreev bound states propagating along ballistic planar Josephson junctions eject into an adjacent normal region at a phase-controlled angle that scales as $\Theta \sim \sqrt{\Delta/ \mu}$, where $\Delta$ is the superconducting gap and $\mu$ is the chemical potential. This angle parametrically exceeds the conventional Cooper pair momentum scale $\Delta/ \mu$, and thus this phenomenon is sizeable even within the Andreev approximation regime $\Delta / \mu \ll 1$. Our results establish phase-controlled quasiparticle ejection as a kinematic probe of condensate momentum transfer: unlike existing probes that detect the Doppler energy shift, the signal appears as a momentum-space deflection of emitted quasiparticles.

The Casimir effect is typically governed by intrinsic material properties and lacks in situ tunability. We show that, in mesoscopic rings, both the magnitude and sign of the fermion-mediated Casimir interaction can be controlled via the Aharonov-Bohm effect. The resulting interplay between the Aharonov-Bohm phase and the Casimir interaction provides a route to engineer long-range interactions. In particular, this mechanism enables the implementation of non-Clifford SWAP$^{\alpha}$ gates between spatially separated spin qubits, thereby reducing the overhead for universal quantum computation and quantum error correction in spin-qubit architectures.

By integrating the quantum Monte Carlo technique into the similarity renormalization group (SRG), we have developed a stochastic SRG framework (SRGQMC) capable of both free-space two-body and in-medium many-body evolutions. This approach circumvents the combinatorial tensor-space explosion of many-body flow equations by mapping continuous unitary transformations onto an ensemble of signed random walkers. We benchmark the SRGQMC against deterministic free-space SRG evolutions of realistic nucleon-nucleon (NN) interactions, as well as against in-medium SRG (IMSRG) many-body calculations with the Richardson pairing model at two- and three-body levels [IMSRG(2)/(3)]. While a deterministic extension to the four-body level [IMSRG(4)] remains unfeasible due to prohibitive computational costs, we have achieved the first IMSRG(4) calculation by using the stochastic technique, demonstrating a substantial improvement toward the full configuration-interaction limit. This stochastic framework provides a practical pathway to higher-order IMSRG calculations.

Altermagnetic order gives rise to momentum-dependent spin splitting of electronic and magnonic excitations even in the absence of a net magnetization. Here, we investigate the magnetic field dependence of the spin-wave spectrum of altermagnetic $\alpha$-MnTe using inelastic neutron scattering and linear spin-wave theory. An in-plane magnetic field continuously reorients the Néel vector by overcoming the weak crystalline anisotropy, while remaining small compared with the dominant exchange scale. We find that this reorientation leaves the magnon energies and line widths essentially unchanged, but strongly modifies the measured spectral intensity through the transverse-momentum projection. Our results demonstrate a clear separation between the soft orientational degree of freedom of the antiferromagnetic order and the robust exchange-dominated chiral magnon spectrum. This combination establishes $\alpha$-MnTe as a platform for reconfigurable magnon coupling, in which external fields tune how excitations interact with polarized probes without substantially altering their frequency or coherence.

Analyzing the dynamics of physical observables in open quantum many-body systems is a fundamental but highly challenging task that has yielded very few exact results. In this work, we identify intrinsic conformal structures that restore exact solvability in $(1+1)$D conformal field theories. For $N$ Majorana fermions with linear mode jumps, the adjoint Lindbladian is triangular on reduced even Majorana monomials, yielding recursive exact Heisenberg evolution. In Wess-Zumino-Witten models admitting conformal Majorana embeddings, this hierarchy gives exact dynamics of affine-current products realized as Majorana bilinears, including regimes where the Kac-Moody current algebra alone does not close. In diagonal rational conformal field theories, Verlinde topological defect lines furnish jump operators whose primary-sector dynamics is exactly diagonal: topological-charge probabilities are conserved, while intersector coherences dephase at rates fixed by the modular $S$ matrix and nonnegative measurement strengths. These examples show that intrinsic conformal structures, such as conformal embeddings and modular data, can organize exactly solvable open conformal dynamics.

Certain 3D $U(1)$ spin liquids, such as those arising in dipolar quantum spin ice, have an emergent monopole which is the source of an emergent magnetic field that transforms under symmetries like an electric polarization. As a consequence, these monopoles carry a physical electric charge in their cores and form a plasma at low temperatures. Due to the monopole coupling to emergent gauge fields, the full system behaves as an electrical insulator for DC transport, but can display a sharp plasma resonance analogous to a metal at very low frequencies. This can serve as a clear fingerprint to detect these states in materials. We discuss the optimal conditions to observe this phenomenon in the 3D $U(1)$ spin-liquid candidate Ce$_2$Zr$_2$O$_7$.

Topological semimetals host band nodes characterized by quantized invariants that can appear in bulk responses, yet some invariants remain hidden from standard probes. In particular, band nodes can carry secondary topological charges whose transport signatures are still largely unexplored. Here we study three-dimensional nodal-line semimetals in which nodal rings carry both the Berry phase $w_1\pi$ and a $\mathbb{Z}_2$ monopole charge $w_2$. We show that magnetic quantum oscillations, usually treated as a probe of $w_1$, can directly diagnose $w_2$, with the relevant signal selected by the magnetic-field direction. For a field along the ring axis, the inner and outer extremal orbits of the toroidal Fermi surface both encircle the $w_2$-enforced thread and exhibit a topological phase shift $\nu w_2\pi$ in the $\nu$th harmonic, which is accessible through standard phase-resolved quantum-oscillation analysis. By contrast, for a field applied perpendicular to the ring axis, the relevant extremal orbit exhibits the usual $\pi$ phase shift associated with the Berry phase $w_1\pi$, independent of $w_2$. For weak doping, three-dimensional ABC-stacked graphdiyne is predicted to exhibit the proposed oscillations in a field range accessible with present-day high-field facilities.

Fractional anomalous Hall crystals (FAHCs) replicate the topological order of the fractional quantum Hall effect in the continuum without requiring any external magnetic field. They spontaneously break continuous translation symmetry like a Wigner crystal, but are distinguished by each unit cell holding a fixed fractional number of electrons. Until now, these states have been confined to theoretical speculation or engineered models, leaving open the question of whether they can plausibly emerge in actual physical systems. Here, we establish them as energetically competitive candidate states in a realistic material setting. We study rhombohedral pentalayer graphene (R5G) with variational wavefunctions that are exact zero modes of a recently proposed ideal model of R5G. We evaluate their energies using Monte Carlo, after reinstating realistic dispersion and screened Coulomb interactions. We find FAHCs to be energetically competitive with integer anomalous Hall crystals and Fermi liquids, and their stability follows a simple principle. Each crystal maps onto a parent quantum Hall liquid that fixes its interaction energy, while the kinetic energy favors crystal periods that match the finite-momentum minimum of R5G's Mexican-hat dispersion. A weak periodic potential can then selectively lower and pin the commensurate fractional crystals. This picture predicts how the integer and fractional quantum anomalous Hall stability windows evolve with twist angle and displacement field, which we compare to recent experiments. These results support a continuum-and-interactions-first route to fractional anomalous Hall states in rhombohedral graphene.

Programmable quantum simulators are beginning to access correlators of increasing complexity, ranging from four-point out-of-time-ordered correlators to even higher-order many-body correlators. The theoretical framework for interpreting such data, however, remains comparatively underdeveloped. Although a variety of higher-order correlators can be constructed straightforwardly, their physical meaning is often difficult to infer. A further complication is that different correlators are generally not independent: some may be mutually redundant, while others may encode genuinely distinct information. These features make it necessary to analyze correlators not as isolated quantities, but as a structured family. In this work, we develop a geometric framework for the collective analysis of higher-order correlator families. By representing correlators as inner products between operator words, we recast each family as a geometry in operator space. The key idea is to introduce conditioning subspaces that separate this geometry into reducible information, already explained by a chosen resolved sector, and irreducible information, encoded in the residual correlator geometry. Focusing on the latter component, we define irreducible volume profiles that quantify how broadly the unexplained part of a correlator family spreads over independent geometric directions. This perspective leads to several complementary forms of conditioning. Canonical conditioning optimally explains a correlator family. Targeted conditioning fixes the resolved sector to isolate a chosen physical feature. Krylov and cross conditioning extend the framework from a single correlator family to comparisons among correlator geometries. Our framework reveals irreducible structures hidden at the level of individual correlator values and establishes correlator geometry as a higher-level description of quantum many-body dynamics.

Whether a heat engine can approach Carnot efficiency while maintaining finite power is a fundamental question in finite-time thermodynamics. For classical Markovian heat engines with local interactions, the power-efficiency trade-off forbids an asymptotic approach to Carnot efficiency at finite power. In quantum systems, by contrast, degeneracy, symmetry, and collective jumps have been theoretically predicted to enable such an asymptotic attainment by enhancing activity. It has remained open, however, whether this mechanism can be realized in an experimentally implementable heat engine. In this Letter, we propose a superconducting-circuit heat engine that emulates the collective enhancement, thereby enabling an asymptotic approach to Carnot efficiency at finite power. This result demonstrates that, in an implementable model, such an enhanced dissipative mechanism circumvents the power-efficiency trade-off of classical Markovian engines. Our work connects abstract bounds in finite-time thermodynamics to a concrete circuit-QED platform and suggests a route toward quantum-device design based on collectively enhanced dissipative processes.

Moiré materials realize a versatile platform for exploring the physics of fractional Chern insulators (FCIs). The recently observed evolution from FCIs to an extended quantum anomalous Hall background upon lowering the electronic temperature in moiré rhombohedral graphene (mRG)8 raises a fundamental question: Is it caused by a failure to equilibrate the edge states of an FCI or by a genuine phase transition in the bulk from an FCI to a generalized anomalous Hall crystal? Here we address this question by probing quasiparticle charging in a mesoscopic mRG antidot device and by bulk resistance measurements, both of which are bulk-sensitive and free from complications from edge states. Tunneling to the mRG antidot reveals quasiparticles carrying one electron charge for both Chern states at filling factors {\nu}=1 and 2/3 at low temperatures. Temperature dependence measurements of the bulk resistance near {\nu}=2/3 further suggest a thermodynamic phase transition from an FCI to a generalized anomalous Hall crystal at temperatures below about 150mK. The results clearly exclude the edge state equilibration scenario and favor the phase transition scenario. Our work establishes mesoscopic probes as a powerful approach to uncover competing ground states in moiré materials and provides a basis for probing fractionalized excitations in FCIs.

We perform a semiclassical, large-spin S, analysis of the quantum approximate optimization algorithm (QAOA) on the Sherrington-Kirkpatrick (SK) model, using the truncated Wigner approximation. Fixing the QAOA angles to their previously determined optimal S=1/2 values, we observe a non-monotonic dependence of the final energy on the spin. At small S the semiclassics is dominated by noise, while the large-S limit is constrained by the exponential growth of the initial fluctuations. For a depth-p QAOA one achieves the optimal balance at S of order p, resulting in a convergence of the final energy to the Parisi value like log(p)/p. We find that the semiclassics slightly outperforms the true spin-1/2 QAOA, and thus suggest they both converge to the Parisi value in the same way. Finally, removing all the initial noise, and re-optimizing the parameters to account for that change, results in superior performance with 1/p convergence.

We design lattice models with tailored quantum geometry, including generalized Landau levels (LLs) satisfying the integrated trace condition and higher-Chern bands with ideal quantum geometry. Our models with $N=2$, $3$, and $4$ sublattices include a generalized Haldane model ($N=2$ honeycomb lattice model) with Gaussian-decaying hoppings realizable in twisted bilayer MoTe$_2$, and $N \geq 3$ models with exponentially decaying hoppings. Exact diagonalization reveals fractional Chern insulators in the generalized zeroth LL bands of all three models, a Moore-Read state in the generalized first LL band of the $N=4$ model, and various interaction-driven topological phases$\unicode{x2013}$including integer and fractional anomalous Hall crystals and a multicomponent Halperin state$\unicode{x2013}$in the ideal higher-Chern band of the $N=3$ model. Informed by quantum geometry, our work provides a pathway for lattice realizations of Landau-level and beyond-Landau-level physics.