Papers

Every 3-regular graph of girth at least $g$ has a cut containing at least a fraction $M_g$ of its edges, and the best rigorous bounds at large girth are $0.912\le \lim_{g\to\infty}M_g \le 0.92386$. Lower bounds on $M_g$ follow from the performance of local algorithms: on a graph of girth $g \ge 2p+2$ a depth-$p$ local algorithm sees the same tree around every edge, so its expected cut fraction on that tree bounds $M_g$ from below. We apply this strategy to the Variational Iterative Rotation Algorithm (VIRAL), a classical local algorithm, and evaluate it on the depth-$p$ tree for every even depth up to $p=32$. The resulting bounds exceed those recently obtained from the Quantum Approximate Optimization Algorithm (QAOA) for every $p\ge 4$, by $0.005$ to $0.011$, and they extend the range of girths covered from $g=36$ to $g=66$. Notably, at $g=66$ we obtain $M_{66} \ge 0.9127$ at $99.99999\%$ confidence level, which raises the asymptotic lower bound from $0.912$ to $0.9127$.

Motivated by the observation of superconductivity in twisted bilayer WSe$_2$ over an extended range of displacement fields, reaching from the correlated insulator down to zero field, we analyze the correlated electron phases of this system at hole filling $\nu = -1$ and twist angle $3.65^\circ$ using Hartree–Fock, random phase approximation, and functional renormalization group calculations. We derive a continuum model with gate-screened Coulomb interaction from first principles and compare its instabilities to those of a realistic three-orbital Wannier model with a Hubbard interaction and an artificial single-orbital Hubbard model. In both cases, we find a superconducting instability of mixed $d$-wave singlet and $p$-wave triplet character, arising adjacent to inter-valley-coherent spin-density-wave order in the phase diagram spanned by displacement field and interaction strength. Our additional analysis of the pairing mechanism points to inter-valley coherent spin fluctuations as the pairing glue. The extent of the pairing regime and the associated critical temperatures depend on the model input, and we trace differences to the interaction range entering the projected interaction. Within the continuum model, the gate-screened Coulomb interaction yields pairing down to zero displacement field, bringing theory into agreement with experiment.

Interacting fermions owe both their non-trivial correlations and their computational power to their departure from Gaussianity. Yet, quantifying that departure geometrically faces two challenges: the Gaussian manifold is non-convex, and perturbative treatments are confined to weak interactions. Here, we introduce a geometric measure of fermionic non-Gaussianity, the fidelity distance of a target state to the manifold of fermionic Gaussian states. We construct an iteration formalism to numerically access it, applicable also at strong coupling. Further, we prove a sharpened operator Jensen inequality, of interest in its own right. We use it to derive a witness that involves only two- and four-point fermionic correlators. Numerical benchmarks on the one-dimensional Fermi–Hubbard model show that the quality of the witness improves with system size and, for strong coupling, is tighter than antiflatness. Our results open a scalable route to charting non-Gaussianity of strongly-interacting fermionic quantum simulators.

Two-dimensional materials can host topological phases stabilized either by an intrinsic moiré potential or topological crystallization. Crucial to the topology of these phases is the interplay between the (self-consistently generated) potential and the spinor structure, which imbues the band-projected potential with momentum-dependence. Truncating this potential at linear-order in momentum, we obtain a three-band model that captures the low-energy band structure and Berry curvature of such topological bands. We analytically find that the Berry curvature strongly depends on momentum-dependence of the potential. Furthermore, we identify that the model can be tuned to have emergent symmetries, including $U(1)$ and anti-unitary symmetries. Emergent-symmetry breaking perturbations drive the system to regimes hosting topological flat bands, quadratic band touchings, and multiple Dirac cones. We recover many of these features when studying an un-truncated model of a $\lambda$-jellium spinor inside of a periodic potential. Our results reveal a rich interplay of spinor structure and a potential in determining the topology of the ground state.

A recent experiment reported coherent parity oscillations between minimal Kitaev chains, demonstrating a Majorana parity qubit (arXiv:2607.09511). Operations on this qubit are controlled by coupling two Kitaev chains and are intrinsically unprotected against noise in the coupling strength. Here we show how the exponential protection in the underlying chains can nevertheless be revealed through unprotected qubit operations. To this end, we develop an analytical theory of quasistatic dephasing for two coupled $N$-site Kitaev chains at the sweet spot. In Rabi experiments, protection can be resolved by adapting the operating point with chain length: depending on the coupling architecture, it appears as an exponentially increasing optimized number of coherent oscillations or as a longer coherence time. Ramsey experiments show an exponentially increasing coherence time, provided the chains can be sufficiently decoupled. Our analytical theory takes into account the non-Gaussian splitting statistics of the Kitaev chains, allowing us to quantitatively predict the scaling with chain length. Moreover, we determine how residual noise and imperfections limit the range of chain lengths over which this scaling can be observed. Our results show how qubit dynamics can be used to probe Majorana protection in experimentally realistic devices.

Structured light provides a powerful means of controlling matter while itself exhibiting nontrivial spatial topology. Here, we show that these spatial structures can be harnessed to locally engineer the topological properties of matter. In a paradigmatic example of a topological insulator with Dirac surface states driven by an optical skyrmion beam, we show that structured light spatially tailors the effective Hamiltonian, yielding position-dependent topological gaps and Dirac velocities. The resulting gap modulation can create topological and trivial regions separated by optically defined interfaces, without introducing material boundaries or chemical modifications. We further show that the geometry of these interfaces can be controlled through the spatial structure of the light, in particular its orbital angular momentum. Our results establish structured light as a route to dynamically pattern topological phases and open a broader perspective on the interplay between topology in light and matter, including the possibility of transferring topological characteristics between the two.

Designing synthesizable materials with targeted properties remains one of the central objectives in materials sciences. Ionic liquids (ILs) are well suited to this goal due to their "tunability", where physical and chemical properties can be precisely customized by modifying their molecular structure, specifically by varying the combination of cations and anions. At the same time, current data-driven property models for ionic liquids often degrade in scarce, noisy, and uneven data regimes, where measurements cover only a small fraction of chemical space and a limited range of thermodynamic conditions. This makes out-of-distribution screening brittle: even when point predictions look plausible, it is difficult to compare candidates consistently, quantify downstream implications, or trust rankings enough to guide molecular discovery. We present a property-prediction and optimal candidate selection workflow that treats data processing, deep learning modeling, and physics-based calculations as a coupled system, linking property prediction with uncertainty estimation and physics-based filtering. By tightening the link between predicted properties and the criteria used for down-selection, the workflow supports reliable out-of-distribution ranking and enables prioritization of previously untested ionic liquid candidates with favorable predicted trade-offs. We demonstrate the application of our workflow by designing novel ionic liquids for CO2 capture from flue gas, predicting their properties and selecting Pareto-optimal candidates based on CO2 solubility, IL viscosity and working capacity.

Hydrogen-rich materials offer a route to high-temperature conventional superconductivity, but often require extreme pressures. Here we report a first-principles study of NaH$_6$, identified in our large-scale hydride search and independently predicted in a subsequent high-throughput study. Several phases compete, with $R\bar{3}m$ and $Pm\bar{3}m$ dominant over broad pressure ranges. The $R\bar{3}m$ phase remains dynamically stable down to 10 GPa, where its calculated $T_\mathrm{c}$ is 34 K, rising to 99 K at 50 GPa. Cubic $Pm\bar{3}m$ becomes thermodynamically competitive at higher pressures and reaches a calculated $T_\mathrm{c}$ of 230 K at 50 GPa, decreasing only weakly upon further compression. Molecular dynamics and phonon-renormalization calculations support structural persistence over the sampled timescale and indicate relatively small anharmonic effects. Despite their high $T_\mathrm{c}$, both phases contain elongated H$_2$-like units, often considered unfavorable for high-$T_\mathrm{c}$ hydrides. Mode-resolved electron-phonon coupling links Raman-active hydrogen vibrations to superconductivity. In $R\bar{3}m$, the linewidths of these modes increase with the pressure-induced tilt of H$_2$ units relative to the threefold axis, alongside the rise in $T_\mathrm{c}$. A minimal symmetry-based model of the vibration-induced second-moment tensor of the hydrogen sublattice shows that these trends are consistent with a significant contribution from response components perpendicular to the threefold axis. NaH$_6$ thus represents an unusual molecular-like hydride in which hydrogen-sublattice reorganization may enable high-$T_\mathrm{c}$ superconductivity at comparatively moderate pressures.

We investigate how the translational motion of a compact skyrmion cluster can be converted into collective rotation through interactions with a periodic obstacle substrate. Using an effective particle model, we consider a seven-skyrmion cluster driven along a one-dimensional array of repulsive obstacle sites. For suitable obstacle spacings and interaction strengths, repeated interactions with the substrate produce coherent clockwise or counterclockwise rotation, giving rise to gear-like cluster dynamics. We characterize these states using the translational velocity, Hall angle, angular velocity, structural deformation, and a dimensionless gear ratio that relates cluster rotation to motion over the substrate periodicity. Dynamical phase diagrams identify rotating, nonrotating, wall-guided, transverse, and deformed regimes. We further show that coherent rotation persists in the overdamped limit, demonstrating that the conversion mechanism does not require an intrinsic Magnus force and may therefore extend to other driven cluster systems, including colloidal assemblies. These results provide a simple route for controlling collective rotation through structured substrates.

Electrical excitation and detection of propagating spin waves are key elements of magnonic devices. While conventional antennas consisting of non-magnetic metals such as Au or Cu excite spin waves predominantly through radio-frequency (RF) Oersted fields, antennas comprising Pt can additionally generate spin-orbit torques (SOTs) via the spin Hall effect. Recent theoretical work has proposed RF-SOT as an alternative mechanism for coherent spin-wave excitation, predicting distinct characteristics compared with conventional inductive excitation. Here, we investigate Pt antennas for the excitation of coherent spin waves in 105-nm-thick epitaxial $\text{Y}_3\text{Fe}_5\text{O}_{12}$ (YIG) films through two potential mechanisms: an oscillating Oersted field and an oscillating spin current. The raw experimental transmission spectra are strongly affected by fabrication-induced modifications to the YIG film associated with the etching process together with spatially inhomogeneous interface conditions induced by Pt. After removing these contributions, we find the remaining two wave propagation consistent with a combined excitation from Oersted fields and SOTs.

Electrical control of orbital magnetism is a central goal of orbitronics. While current-induced orbital polarization has recently been demonstrated in inversion-asymmetric systems, nonvolatile electrical control of an equilibrium orbital moment has remained elusive. Here, using x-ray absorption spectroscopy with in situ electric-field control of the FE polarization, we demonstrate non-volatile switching of the equilibrium orbital magnetization of the oxide q2DEGs formed at the LaAlO$_3$/EuTiO$_3$/Ca-STO (001) interface. X-ray linear dichroism reveals a reversible modulation, driven by the FE-polarization direction, of the Ti-3$d$ crystal-field splitting and orbital occupancy, establishing a ferroelectric-like metallic state. X-ray magnetic circular dichroism shows a polarization-controlled switching of the Eu$^{2+}$ orbital magnetic moment induced by the orbital magnetization of the q2DEG projected onto Eu-5$d$ states and detected at the Eu-$M_{4,5}$ edge through Eu-5$d$/Eu-4$f$ hybridization in the inversion-symmetry-broken interface. These results provide spectroscopic evidence of ferroelectric control of orbital magnetism in an oxide q2DEG.

High-charge Weyl semimetals (WSMs), particularly those hosting charge-three Weyl point (C-3 WPs), have attracted considerable interest owing to their unconventional topological properties and enhanced boundary phenomena. However, ideal C-3 WSMs remain rare, and the symmetry-constrained coexistence of charge-three and charge-one Weyl point (C-1 WPs) in nonmagnetic crystals remains largely unexplored. Here, we investigate a representative eight-node Weyl configuration, consisting of two C-3 WPs and six C-1 WPs with opposite chirality, corresponding to two identical $\{3,-1,-1,-1\}$ irreducible Weyl molecules. By combining topological charge conservation with space-group symmetry analysis, we systematically classify all 230 space groups and identify 12 and 23 candidate groups without and with spin–orbit coupling (SOC), respectively. First-principles calculations without SOC reveal that the boron allotropes TBR-B$_{48}$ and chiral OBD-B$_{48}$ realize this configuration, hosting hourglass-type and non-hourglass-type C-3 WPs, respectively. Surface-state calculations reveal six Fermi-arc branches at the shared projection of the charge-three pair and three at each individual projection. Reversing the structural chirality of OBD-B$_{48}$ reverses the signs of all Weyl charges, establishing a direct correspondence between crystal and momentum-space chirality. Furthermore, breaking the protecting $C_6$ symmetry in TBR-B$_{48}$ splits each C-3 WP into three C-1 WPs and reconstructs the surface Fermi arcs. Our work establishes symmetry-based guidelines for designing and searching for nonmagnetic WSMs hosting charge-three and charge-one Weyl-point coexistence.

Local coordination cores are critically important in metal-organic frameworks (MOFs) and polyoxometalates (POMs), as they govern the fundamental chemical and structural properties of these materials. Existing methods, including element-resolved persistent homology (ERPH), have limited ability to translate local coordination cores into quantitative, scalable, and interpretable information. Here, we introduce persistent Mayer homology (PMH) to enable the detection of the geometric variability invisible by classical topology. By focusing on coordination cores formed by periodic metal-centered heavy-atom, carbon, and donor channels, PMH distinguishes different arrangements of the local coordination environment, linker framework, and potential coordinating atoms. We examine explainable PMH of orders $N=3$ and $N=5$ and separately combine each with ERPH, which characterizes the multiscale organization of chemically defined element groups across the extended framework, to predict eight nitrogen- and oxygen-related adsorption and self-diffusion properties. The resulting coordination-core PMH representations consistently improve predictive performance over ERPH alone, with the third-order Mayer representation providing the strongest overall performance. These results demonstrate that the inner coordination configurations captured by PMH contain essential structural information that is not fully represented by conventional element-resolved topological descriptors. This finding provides a quantitative interpretable topological framework for understanding local coordination environments and may facilitate the rational design of MOFs and POM-based materials.

Direct and parametric driving together generate nonlinear response structures beyond conventional Duffing hysteresis, including multiple switching regions and isolated branches. Understanding how these structures are connected requires identifying the bifurcations that reorganize the response as the parametric excitation is varied. At a phase difference of 45 degrees between the direct and parametric excitations, we experimentally and analytically determine how the steady-state response changes as the parametric excitation is increased. A single resonance peak first splits into two while the response remains single valued. Two successive cusp bifurcations then create two saddle-node pairs and establish a double-hysteretic response. At the parametric-instability threshold, one saddle node of each pair is displaced towards unbounded amplitude and detuning, and an isolated-branch structure emerges above threshold. A parametric representation of the steady state distinguishes amplitude extrema from genuine saddle-node bifurcations and provides analytical conditions for these changes. Measurements on a dielectrically actuated pre-stressed SiN nanostring reproduce the predicted response and associated switching behavior. These results establish the bifurcation pathway connecting the different response structures at this phase configuration, providing a systematic basis for controlling multistability and switching in parametrically driven nonlinear resonators.

Spatial sudden death of entanglement refers to the disappearance of quantum correlations between subsystems after a certain distance called the entanglement length. Specifically, given a density matrix $\rho_{ABC}$ on a tripartite system $ABC$ with $B$ spatially separating $A$ and $C$, the entanglement length is the distance $\ell(A,C)$ after which the reduced density matrix $\rho_{AC}$, given by tracing out the $B$ subsystem, is separable. We show in the case of gapped ground states in any dimension that the entanglement length is finite on finite subsystems. Restricting to one-dimensional systems, we prove that normal matrix product states have a finite entanglement length independent of $A$ and $C$, and that a finite pure state with such uniform entanglement length has a matrix product state representation with bond dimension independent of $A$ and $C$. Consequently, in one dimension, entanglement length distinguishes matrix product states from all other pure states.

A two-dimensional electron gas in a uniform neutralizing background forms a triangular Wigner crystal at low density. In a strongly mass-asymmetric electron-hole bilayer, localized heavy holes instead provide a nonuniform positive background that supports an electron crystal at densities two orders of magnitude higher than for a homogeneous electron gas in the same material. Here we show that correlated mobile electrons can overturn the preference for triangular order, stabilizing a honeycomb electron-hole crystal. Using the powerful real-space neural-network variational Monte Carlo in the Born-Oppenheimer limit with fixed holes, we find that increasing the density drives a transition from a triangular electron-hole crystal to a honeycomb crystal, which eventually melts into itinerant electrons coexisting with the honeycomb or the triangular hole lattice at fixed interlayer separation. Relative to triangular order, honeycomb order emerges when gains in electronic kinetic energy and electron-hole attraction outweigh its higher intralayer Coulomb repulsion, a threshold never reached in the rigid point-dipole model. Moreover, the honeycomb hole lattice supports paramagnetic, antiferromagnetic, and stripe-ordered spin states. Complex polarization indicates a metal-insulator transition, while the states on the honeycomb hole lattice are consistent with a stripe-ordered Dirac semimetal and paramagnetic or antiferromagnetic Mott insulators via mapping to the half-filled Hubbard model. We further propose a BLG/hBN/WS$_2$-WSe$_2$ heterostructure as a platform for the predicted honeycomb crystal, at an experimentally feasible density $n\sim10^{11}~\text{cm}^{-2}$.

Nitrite photochemistry in atmospheric aerosols and natural waters is a major source of hydroxyl radicals and reactive nitrogen oxides. Contrary to the prevailing view that in the environment aqueous nitrite photochemistry proceeds exclusively through photoexcitation followed by homolytic bond cleavage, we show that visible light directly ionizes aqueous nitrite in individual micron-sized droplets. Although the photoionization cross section is exceptionally small, this pathway is observable at the high photon flux densities accessible in single-droplet experiments. Molecular simulations reveal that this is because photoionization absorption has an exceptionally long wavelength tail due to the large solvent reorganization energy in aqueous solutions. Kinetic modeling of an aqueous-phase reaction mechanism quantitatively accounts for the observed chemistry and predicts the formation of nitrate, hydroxyl radicals, and solvated electrons. The overlap of the predicted broad photoionization continuum with the visible solar spectrum further suggests that visible-light photoionization is an overlooked source of nitrogen oxides, solvated electrons, and oxidants in atmospheric aerosols, snowpack, and natural waters. Under dilute conditions, where dissolved oxygen is the main sink for solvated electrons, photoionization is expected to be the dominant photochemical loss pathway for nitrite.

Bosonic codes often read out their syndrome with a transmon ancilla whose computational levels $g$ and $f$ have equal parity and matched dispersive shifts: a decay $f\to e$ is then heralded and leaves the code intact, while the direct $f\to g$ is forbidden by parity. We show that the photons of the code open this decay at first order in the ancilla's decay rate. Dressing by the code mode lets the charge noise that limits the ancilla's $T_1$ drive a photon-stimulated Raman decay $|f,n\rangle\to|g,n+1\rangle$, at $(n+1)(\chi_{ge}/2g_{01})^2$ times the $f\to e$ rate for a smooth noise spectrum. When the matching is set by the detuning, the decay costs $\approx\Gamma_{fe}/\alpha$ per gate and photon, whatever the coupling strength; a deliberate mismatch or matching by a drive lowers this cost, and a qubit ancilla has no such channel. The opened decay is unheralded and flips a cat with probability $\approx 1/2$; being first order, it overtakes the second-order double decay $f\to e\to g$ as the ancilla improves. In a microscopic model of the Ocelot repetition cat code, it makes the bit-flip floor of the gates grow linearly with the cat size, by a factor 1.2-1.7 from four to ten photons, which would limit the noise bias to $\sim 10^3$. The published gate data end at four photons and do not yet test this growth.

The acoustic Faraday effect probes phonon Hall viscosity through the rotation of transverse acoustic polarization, conventionally interpreted in terms of circular birefringence. We show that magnetic order breaking rotational symmetry generates anisotropic phonon responses and elliptically polarized eigenmodes, so that Faraday rotation cannot be attributed to Hall viscosity alone. To elucidate their microscopic origin and consequences, we derive spin-phonon couplings from a generic $J$-$K$-$\Gamma$-$\Gamma'$ model with interlayer coupling, identifying transverse strain couplings for propagation along the $c$-axis arising from the interplay of Kitaev $(K)$ and $\Gamma$ interactions, along with strain-induced $g$-tensor contributions. Incorporating these couplings into our theory for the Kitaev spin-liquid candidate $\alpha$-RuCl$_3$, we find that symmetry breaking modifies the Faraday response, revealing a Hall viscosity approximately twice the value inferred assuming rotational symmetry. Our results establish a microscopic framework beyond circular birefringence, refining the connection between acoustic Faraday rotation and phonon Hall viscosity in symmetry-broken spin-orbit-coupled magnets.

Near-ideal, field-free superconducting diode behavior is demonstrated in room-temperature-grown Mo$_2$N/FePt bilayers. The response is consistent with remanent FePt stripe domains producing polarity-dependent thresholds for flux entry and vortex motion. Micromagnetic simulations reveal a periodic stray-field modulation across the stripes and asymmetric field enhancement near their ends at the bridge edges. One current polarity remains nearly dissipationless up to a sizable fraction of the estimated depairing current, whereas the opposite polarity develops dissipation at much lower current, yielding diode efficiencies up to approximately 85% in the thinner bilayer. The nonreciprocity can be continuously tuned by the in-plane magnetic preparation angle and reversibly switched by reverse-field excursions through the hysteretic reversal of the FePt layer. These results support edge-controlled flux entry and vortex motion as a route to high-efficiency superconducting diodes.

Quantum spin liquids are exotic states of matter in which strongly interacting spins remain disordered down to zero temperature and host fractionalized excitations. This has motivated an extensive search for their realization in materials. Among candidate systems, $\alpha$-RuCl$_3$ has drawn particular attention as a platform for the quantum spin liquid proposed by Kitaev, in which the low-energy excitations in applied magnetic fields are interpreted as itinerant Majorana fermions and local flux excitations. However, conflicting experimental signatures have cast doubt on whether a Kitaev quantum spin liquid-like state is really the right starting point to interpret the low-energy states in $\alpha$-RuCl$_3$, motivating a closer look at the nature of these excitations. Here we report an extensive high field study of specific heat up to 35 T on $\alpha$-RuCl$_3$. We find that the low-energy thermodynamics exhibit universal $B/T$ scaling with a single effective energy scale proportional to the applied field as long as the magnetic field is not close to the $c$-axis. This behavior persists continuously from the antiferromagnetic phase boundary to the highest fields, suggesting that the perturbative Kitaev limit, with its Majorana and flux excitations, may not be an appropriate starting point for describing the low-energy thermodynamics of $\alpha$-RuCl$_3$ for fields away from the $c$-axis.

We present first-principles calculations of the electron-hole-pair creation energy in semiconductors and dielectrics, focusing in particular on AlN, 3C-SiC, 4H-SiC, Si, and SiO2. We have employed density functional theory (DFT) to calculate the band structure, density-functional perturbation theory to obtain the phonon dispersion, and time-dependent DFT (TDDFT) to calculate the electron energy loss function (via the dielectric function). We performed full-band Monte Carlo simulations of electron thermalization for energies up to ~100 eV and calculated the average energy required to excite an electron-hole pair. We calculated pair-creation energies of approximately 12.2, 6.5, 7.3, 3.10, and 16.7 eV/pair for AlN, 3C-SiC, 4H-SiC, Si, and SiO2, respectively. These values are in good agreement with measured data, with the largest discrepancy being that of Si (about 14.9% lower than the accepted experimental value of ~3.6 eV/pair). To improve the agreement for Si, we used the GW approach and the Bethe-Salpeter equation (BSE) to calculate the quasiparticle shifts of the electronic band structure and the dielectric function, respectively. Finally, using the GW/BSE data, we calculated a creation energy of ~3.50 eV/pair. We find that the marked improvement in the accuracy of the calculated creation energy, when using the GW/BSE approach, is primarily attributable to the slight decrease in the magnitude of the electron energy-loss function when using the GW/BSE approach for energies below ~10-15 eV. Overall, it is clear that the competition between phonon emission and ionization near the intersection of the phonon scattering and ionization rates is largely responsible for determining the value of the creation energy, with the other major factor being the location and shape of the plasmon peak in the energy-loss function.

The nearly collinear configuration of highly stretched polymer chains before fracture motivates one-dimensional models. At fixed extension, stretching one bond redistributes length among the others, coupling rupture to the whole chain. In this work, I develop a framework for fracture-healing rates in periodic Morse chains, combining deterministic theories, equilibrium simulations and a quasi-deterministic approach using equilibrium fluxes and barrier-top trajectories. Constrained-partition calculations closely reproduce simulated populations and intact-state tensions. An intact-reservoir potential of mean force (PMF) supplies the first-fracture surface probability, while recrossing corrects the attempt flux without a rate-fitted prefactor. Independent rate tests identify an operational chain-length boundary for accurate two-state kinetics; failed-return durations decrease relative to population relaxation as chains grow. Kramers-Grote-Hynes (KGH), nonlinear reactive-flux and equilibrium rates show excellent agreement in this regime. KGH predicts rates away from coexistence and a chain-dependent local activation length dominated by the barrier response. Rates decrease approximately exponentially before declining more gently for longer chains: barrier growth dominates, additional fracture sites partly compensate, and transmission varies more weakly. Beyond coexistence, long chains can fracture practically irreversibly because healing becomes too rare to observe. Projected committor crossings, where the configuration-averaged probability of reaching the fractured core first is one half, lie near site-PMF maxima, although configurations at equal bond length retain different fracture probabilities. Multiple fractures remain negligible near coexistence through at least $N=50$. The framework could supply state-dependent rates to mesoscopic fracture models of polymer networks.

The field of twistronics, recently extended to twisted bilayer cuprate systems, has generated considerable interest due to the prediction of $d+id'$ states close to a $45^\circ$ twist, as suggested by multiple experimental probes. Theoretical studies of these systems using a variety of models and many-body theoretical techniques have revealed multiple competing order parameters. The large variability in experimental results and theoretical predictions demands an accurate microscopic model for these systems, in particular a more realistic description of the interlayer tunneling. In this study, we fit the in-plane hopping and compute the interlayer tunneling amplitudes by calculating the orbital overlap between $d_{x^2-y^2}$ wave functions at each site of the twisted square-lattice model. We observe sign-changing tunneling amplitudes, a strong twist-angle dependence of the direct tunneling term, and long-range tunneling amplitudes that often dominate over direct tunneling. We investigate the band structure, Fermi surfaces, and spectral functions in comparison with those obtained from the phenomenological model and find a substantial redistribution of spectral weight that modifies the competition between different superconducting ground states. We determine the phase diagram as a function of twist angle, filling, and direct tunneling strength, which is controlled by the $c$-axis distance between the monolayers, and observe a reduction in the region of time-reversal-symmetry-breaking (TRSB) $d+id'$ states compared with the phenomenological model. Finally, we investigate the Josephson critical current across the phase diagram and find strongly suppressed critical currents close to a $45^\circ$ twist, consistent with experimental observations.

What quantum mutual information adds to conventional correlation functions is often unclear. We study the spin-1/2 $J_1$-$J_2$ Heisenberg chain, using DMRG on infinite chains and periodic rings and an SU(2) decomposition of the mutual information into correlation channels. For singlet ground states the two-site mutual information is an exact function of the spin correlator, so any additional content must come from blocks. In the dimerized phase, blocks resolve bond-energy correlations in the SU(2)-scalar channel without an independent asymptotic length: singlet and triplet correlation lengths agree to about 1%. The scalar channel dominates block mutual information at large distances in the commensurate regime up to $J_2/J_1=0.40$, but falls to a few percent beyond the disorder point, which coincides numerically with the Majumdar-Ghosh point $J_2/J_1=1/2$; the structure-factor peak splits only at the Lifshitz point $J_2/J_1=0.520622(2)$. On the gapless side we compare block mutual information on rings extrapolated to infinite size with the two-interval prediction of SU(2)$_1$ conformal field theory across the Kosterlitz-Thouless point $J_2/J_1=0.241167$. There, for block lengths $l\le6$, the correction decays as $l^{-p}$ with $p=1.96$-$2.07$, and any logarithmic term is at least 60 times smaller than in the Heisenberg chain. Expanding in the marginal coupling (from level spectroscopy) the first-order coefficient is consistent with $l^{-2}$ scaling and the second-order coefficient is positive for $x\le1/4$, suggesting that the mutual information relative to the field-theory value becomes stationary at the KT point for large blocks. The scalar-channel share approaches 1/4 at small cross ratio $x$, as expected from SO(4) symmetry; under two stated assumptions its first-order response to the coupling is $(3/8)\ln x-5/8$ at small $x$, matched by the $l=4$ data within 1-3% at $x\le1/9$.

We unify known mutual-linearity relations for Markov jump processes and chemical reaction networks within a common framework based on classical finite-response theory. In a Markov jump process, an exact finite-response identity shows that all stationary probability changes share a common factor when the rates of one edge change. Eliminating this factor gives the relations between probabilities, observables, and currents, even far from equilibrium. We also explain how the same argument applies when one coefficient of a linear system changes and recovers the known relations in Laplace space and between stationary complex activities in chemical reaction networks.

Hydrodynamics as an effective field theory (EFT) has been immensely successful for predicting the behaviour of time-ordered correlation functions in the long-time, large-distance regime. In this paper, we analyse the predictions of hydrodynamics for scrambling as probed by out-of-time order correlators (OTOCs). To do so, we consider an all-derivative order generalisation of the Schwinger-Keldysh EFT of hydrodynamics extended to a four-fold time contour required to capture OTOCs. A crucial ingredient of the construction is a local SL(2,R) symmetry, which has previously been suggested as a mechanism for scrambling. We also derive this exact EFT from the microscopic formulation of the maximally chaotic low-temperature limit of the SYK lattice, thereby determining all transport coefficients for this model. As a novel application, we compute the OTOC of energy currents, find that its exponential growth saturates the chaos bound, and match it to expectations based on a shockwave (or scramblon) effective description. Our work shows that the universality of hydrodynamics degrees of freedom extends beyond traditional time-ordered correlators to more complex observables such as OTOCs.

Can the Alexander-Orbach conjecture hold on hierarchical lattices? We construct Gromov-Hausdorff-Prokhorov scaling limits of critical percolation clusters on hierarchical lattices in the chemical metric and determine the typical spectral dimensions of the associated diffusions. These dimensions are dense in $(1,2)$; however, outside a narrow region in dimension space, we prove that the Alexander-Orbach conjecture fails on every hierarchical lattice under consideration.

We report a comprehensive experimental study including density functional theory calculations detailing the magnetic ground state of the $S = 1/2$ Mo$^{5+}$ pyrophosphate, LiMoOP2O7, and its magnetic excitations. Neutron powder diffraction measurements confirm the $P2_1/n$ structural model which is comprised of a three-legged ladder of distorted Mo$^{5+}$ octahedra. Magnetometry and specific heat reveal a long-range magnetic ordering transition at $T_\textrm{N} = 3.5$~K and a field-induced transition at $\mu_{0}$H$_\textrm{c}$ = 1 T. This zero-field long-range magnetic order was determined to be a commensurate $\kappa = 0$ order with an ordered moment that is reduced from the full $S = 1/2$ magnetic moment by 30%. Through inelastic neutron scattering measurements and density functional theory calculations, we define the minimal microscopic model and resolve the spin Hamiltonian up to the seventh leading exchange parameter, resulting in a model with dominant antiferromagnetic leg interactions, weaker ferromagnetic rung interactions, and a significant interlayer ferromagnetic coupling.

Nudged elastic band (NEB) calculations of small-polaron hopping are demanding because nuclear motion is coupled to a self-consistent localized electronic state. Near the charge-transfer region, slow self-consistent-field convergence, localization switching, and competing electronic solutions complicate surrogate-assisted optimization. We develop a Gaussian-process-assisted NEB workflow for this regime and demonstrate electron small-polaron hopping in rutile TiO2 using spin-polarized density functional theory with a Hubbard U correction (DFT+U ) with SIESTA. A joint energy-force Gaussian process (GP) with a Matérn covariance model advances the elastic band, while active-atom root-mean-square and maximum-atom displacement limits constrain surrogate motion relative to evaluated configurations. Reaching these limits triggers first-principles sampling without requiring full surrogate convergence. Three independently DFT-verified 96-atom [001] calculations using 11, 13, and 15 images and different surrogate settings and GP parameterizations yield barriers of 0.1645, 0.1637, and 0.1640 eV, respectively, spanning 0.793 meV. In the 15-image calculation, repeated central-image sampling activates a separately calibrated local GP during surrogate optimization. Final full-band DFT verification gives a maximum projected NEB force of 0.0346 eV/Å. A 324-atom calculation yields a lower barrier of 0.1302 eV, indicating supercell sensitivity and demonstrating feasibility at larger GP observation dimension. The workflow combines controlled surrogate extrapolation, targeted charge-transfer-region interpolation, and independent DFT verification to obtain polaron migration pathways, emphasizing reproducible barriers and full-band force convergence.