Papers

Transition metal dichalcogenide monolayers are promising materials for electronic and photonic applications, yet the performance of chemical vapour deposition grown samples is severely limited by native sulphur vacancies that introduce mid-gap trap states, degrade carrier mobility, and elevate electrical noise. Here we investigate octanethiol passivation of sulphur vacancies in monolayer MoS2 field effect transistors, combining x-ray photoelectron spectroscopy, photoluminescence, and Raman scattering with electrical transport and optically coupled low-frequency noise spectroscopy. Thiol treatment reduces the sulphur vacancy concentration from 7% to 4%, reducing the free electron density. Electrically, it increases the device resistance 35-fold while restoring gate switching with an on/off ratio of 10^4 and improving field-effect mobility from 1 to 5 cm^2/Vs. Low frequency noise spectroscopy directly quantifies the defect suppression: the Hooge parameter alpha_H drops by more than two orders of magnitude after passivation. Gate-dependent noise confirms carrier mobility fluctuation as the dominant dark noise mechanism, while optical excitation drives a crossover to carrier number fluctuation dominated noise, reflecting preferential interaction of photogenerated carriers with residual vacancy states via generation-recombination trapping, a mechanistic distinction inaccessible to gate-bias measurements alone. Density functional theory calculations corroborate these findings, showing suppression of vacancy-induced mid-gap states by more than half and partial restoration of the intrinsic bandgap. These results establish optically coupled low-frequency noise spectroscopy as a sensitive, low-cost, and non-destructive tool for quantifying defect passivation in TMDC-based devices.

Under mild assumptions, any quantum mechanical (QM) model or quantum field theory (QFT) admits a representation in terms of an ensemble of neural networks with countably many random parameters. We investigate the features of NN-QM and NN-FT models with finitely many parameters, such as a feedforward network of width $N < \infty$. We find that, generically, such models must violate one of the properties of conventional Euclidean QFTs, such as reflection positivity or cluster decomposition. We present several complementary ways of understanding which features can and cannot be preserved at finite $N$, both in QM and in QFT.

Long timescales in brain dynamics give rise to power law correlations measured in experiments. A simple linear recurrent neural network model can reproduce this power law behavior, but the recurrent interaction strength needs to be fine tuned in order to sit at the edge of stability. We show that by adding a dynamical recurrent feedback gain to the simple linear model removes the need for fine tuning, because the gain self-organizes so that the spectrum of the effective recurrent matrix is always gapless with the top eigenvalue landing on the stability edge for any recurrent strength. As a consequence, long timescales and scale free correlations arise generically, as we demonstrate both analytically and numerically.

We find that the measurement-induced phase transition generated by deterministic global measurements, previously observed in the integrable transverse-field Ising model (TFIM), persists in non-integrable variants of the same. To address this question, we consider the TFIM with longitudinal field and the axial next-nearest-neighbor Ising (ANNNI) model. We show that both the survival probability and the bipartite entanglement entropy consistently capture a transition between area-law and volume-law entangled phases for two distinct initial states: a product state with all spins polarized along the transverse direction and a Greenberger-Horne-Zeilinger (GHZ) state. Finite-size scaling reveals a pronounced initial state dependence: for the polarized product state, the transition point follows an inverse-square-root scaling with system size in both non-integrable models, consistent with the integrable TFIM, whereas for the GHZ initial state, it deviates from this scaling and approaches zero considerably more slowly in the non-integrable models than in the integrable TFIM. These results establish the robustness of measurement-induced transitions under deterministic measurements against integrability breaking while highlighting the crucial role of the initial state in governing their scaling behavior.

Germanium hole spin qubits are a leading platform for semiconductor quantum computation due to their strong spin-orbit coupling, all-electrical operability, and absence of valley degeneracy. A central obstacle is charge noise, which couples to the qubit through the same spin-orbit interaction that enables fast electrical control. In this work, we propose a new operational mode of a three-hole quantum dot in a planar Ge/SiGe heterostructure, modeled within a four-band Luttinger-Kohn–Bir-Pikus framework: a spin-$p$-orbital (SpO) qubit encoded in the $p$-shell of the topmost hole. We characterize charge noise sweet spots in the parameter space of electrostatic confinement and magnetic field, and estimate that relaxation rates of the SpO qubit are comparable to those of spin qubits hosted in single holes. We then design and optimize an all-electrical Landau-Zener state-transfer protocol that induces logical qubit state transitions without microwave driving, and we show that the quadrupole-quadrupole Coulomb interaction between neighboring dots enables fast two-qubit entangling gates operated by adiabatic shuttling.

We develop a method for analyzing grain boundary (GB) microstructures that identifies distinct interfacial phases and the dislocation line defects separating them. Similar to bulk materials, GBs can adopt multiple distinct interfacial phases and undergo first-order phase transitions. When these phases coexist, their spatial arrangement and phase junctions constitute a GB microstructure, characterized by variations in excess properties and line defects with associated dislocation content. Despite this intrinsic heterogeneity, our ability to quantitatively characterize GB microstructures remains limited, as it requires identification of individual GB phases, phase-resolved excess properties, and the Burgers content of phase junctions, capabilities not available in existing automated methods. Here, we present an automated tool that performs interfacial microstructure mapping for planar coincidence site lattice GBs. The method identifies the spatial distribution of GB phases, quantifies phase-specific excess properties, and estimates the Burgers content of GB phase junctions. We demonstrate the approach using three representative cases: (i) quantification of mass transport during diffusion-limited GB phase transformations; (ii) identification of structurally indistinguishable phases formed by vacancy and interstitial loops; and (iii) characterization of GB microstructures containing phase nuclei. More broadly, this framework enables quantitative studies of GB evolution processes, including spinodal decomposition and coarsening with direct implications for GB deformation, creep, and migration.

Contact-resonance atomic force microscopy (CR-AFM) provides nanoscale maps of contact stiffness, dissipation, and electromechanical response, but conventional piezoacoustic excitation can obscure the cantilever resonance with actuator and sample-holder modes. Pure Brownian excitation avoids this transfer-function background, yet its small amplitude generally requires averaging that is incompatible with routine imaging. We introduce interferometric dual-AC resonance tracking (iDART), which combines quadrature-phase differential interferometry with two-frequency resonance tracking. By positioning the interferometric spot near the displacement maximum of the first contact-resonance mode, the detector noise floor is reduced below the off-resonance thermal displacement of the cantilever. Brownian spectra identify the contact mode and define the tracking frequencies, while active electrical excitation provides the signal-to-noise ratio required for pixel-resolved imaging. Simultaneous low-frequency and resonant measurements show that both electrical and photothermal drive increases contrast in the amplitude and phase channels without appreciably shifting the contact resonance. These results establish a practical route to resonance-enhanced, drive free nanomechanical imaging at conventional AFM scan rates.

The application of density functional theory to heterogeneous catalysis is hindered by the shortcomings of conventional density functional approximations. We combine machine learning with explicitly non-local physically informed descriptors and introduce an exchange-correlation functional (CIDER26SS) framework regularized for wide transferability. CIDER26SS is size-extensive, highly efficient, provides a balanced and accurate description of both molecular and solid-state systems, and is specifically well-optimized for transition metal surface chemistry. Surpassing existing conventional functionals, CIDER26SS resolves the CO/Pt puzzle, identifying the correct binding site for CO adsorption on the Pt(111) surface, along with an accurate adsorption energy, Pt lattice constant, and surface energy. Predictions agree well with the experimental values, even when all bulk and surface data for Pt are excluded from the training set. Remarkably, CIDER26SS exceeds the accuracy of semilocal approximations even for systems far outside the training domain.

Modern quantum experiments can probe many-body wavefunctions through projective measurements, providing snapshots of individual many-body configurations. A fundamental question is whether the intrinsic structure of their measurement distributions can reveal quantum dynamics beyond predefined observables. Here, we address this question at the many-body ergodicity-breaking transition using two complementary characteristics of nonequilibrium wavefunction snapshots: their binary intrinsic dimension (BID) and the topology of wavefunction networks constructed from Hamming distances. We show that the critical point is characterized by an extensive but submaximal BID, and scale-free network connectivity with highly connected hubs. These signatures distinguish the ergodic, critical, and nonergodic regimes, and provide experimentally accessible probes of ergodicity breaking from projective measurement snapshots.

Herbertsmithite is a prototypical candidate quantum spin liquid (QSL), believed to feature a long-range entangled ground state and deconfined fractionalised spinon excitations. Confirmation of these properties has been hindered by the presence of magnetic impurities (spin-1/2 Cu2+ spins substituted onto non-magnetic Zn2+ sites). Recently these impurities were reconceptualised as 'witnesses' of the QSL, inheriting long-range interactions and entanglement mediated by the QSL spinons, leading to spin glass formation amongst witnesses below 260 mK. Here we present a full theoretical account of this idea. Despite having only one free parameter (the witness-kagome spin coupling), our model captures the full range of experimental data, including: the formation of a spin glass amongst witnesses; the frequency and temperature dependence of the magnetic noise; a sharp peak in the DC magnetic susceptibility as a function of temperature; and the static neutron scattering structure factor at 2 K. Both candidate QSLs (Z2 and U(1)) give similar agreement with all data; however, our model predicts a qualitative difference between the Z2 and U(1) neutron scattering intensities below 260 mK, providing a long-sought definitive test to distinguish the two cases. We also predict phase diagrams as a function of temperature and witness concentration, finding a phase transition to different long-range ordered witness states for Z2 and U(1) at high concentration.

The heat capacity of a system quantifies how it energetically responds to changes in temperature at equilibrium. Whilst this quantity is positive and even additive for non-interacting systems, self-gravitating systems such as stars or subsystems of strongly interacting quantum systems are known to have negative or anomalous specific heat capacities. In this work, we investigate how the presence of entanglement at equilibrium can influence how an interacting system responds energetically to changes in temperature. We examine the local heat capacity of interacting quantum systems providing an analytical understanding for when anomalies occur. Most interestingly, we find a connection between local heat capacity anomalies and entanglement by deriving a separability bound based on the fluctuations of local and interaction energies. We illustrate our results with two examples (i) a nearest neighbour spin-1/2 chain and (ii) two coupled quantum harmonic oscillators. Lastly, we provide an information-theoretic formula connecting mutual information and athermality to the non-additivity of the heat capacity. Our results provide model-independent thermodynamic entanglement detection bounds and insight into the relationship between quantum correlations and the heat capacity of quantum systems.

We formulate planetary sustainability as a minimal nonequilibrium problem for coupled finite stocks and fluxes, using the operational language of closed life-support systems: inventories, flux balances, recycling efficiencies, processing capacities, reserve times and failure thresholds. Rather than asserting that waste is universally more limiting than resources, we propose a reserve-time principle: the binding constraint is whichever buffer becomes critical first. A nonlinear model coupling a regenerative resource stock, an accumulated waste stock and an activity variable exhibits a soft threshold, where waste suppresses growth while processing remains formally capable, and a hard threshold, where waste production exceeds maximal processing capacity. With immediate waste feedback, activity settles globally at the soft threshold; the hard threshold is crossed only transiently or under exogenous forcing. A resource-side threshold completes the picture. We extend the model to recycling and to multiple resource and waste classes, give a numerical example, situate the four-function description of life against the origin of life, viruses and aging, contrast the biosphere's two long-term failure modes, and relate the approach to Spaceship Earth, planetary boundaries, Limits to Growth, System Dynamics and stock-pollution economics.

All-optical tuning of van der Waals heterostructures with coherent radiation offers a promising path toward ultrafast memory and optoelectronic devices. In the first-principles framework of real-time time-dependent density functional theory, we predict the induction of a persistent, long-lived out-of-plane polarization in MoS$_2$/WSe$_2$ heterobilayers, resonantly driven by intense ultrafast pulses. While weak fields preserve the intrinsic type-II band alignment, intermediate intensities trigger a four-fold enhancement of interlayer charge transfer. By analyzing the high-harmonic generation spectrum, we identify a transition from the perturbative to the strong-field regime inducing photoinduced interfacial polarity. We additionally show that lattice strain, ubiquitously present in heterobilayers, can be used as additional knob to adjust the resonant condition without compromising the permanent dipole induction. Our findings provide a theoretical blueprint for the all-optical manipulation of polar phases in low-dimensional heterostructures at the femtosecond scale.

We study nonequilibrium signatures of tilt-induced localization in a one-dimensional Bose-Einstein condensate loaded in a shallow optical lattice. The tilt strength acts as a control parameter for the localization-delocalization crossover. We also consider the effects of repulsive interactions, which tend to delocalize the condensate. We first characterize localized and delocalized regimes through sudden quenches of the interaction strength and the external tilt. The resulting dynamics is analyzed using the survival probability and its power spectral density. Localized condensates exhibit strong memory retention, pronounced revivals, regular dynamics and a narrow spectral response, whereas delocalized condensates show suppressed recurrences, irregular dynamics and a broader distribution of spectral weight over many frequencies. We then investigate finite-rate ramps of the tilt strength across the localization threshold. Using the localization length and the Bogoliubov excitation gap, we extract the relevant critical exponents and perform Kibble-Zurek scaling analysis in the driven dynamics. Our results establish quench response and finite-rate scaling as complementary dynamical probes of localization in interacting Bose gases, with direct relevance to cold-atom experiments in tilted optical lattices.

We study the local electrostatic response of a charged superfluid in the presence of a cylindrically symmetric vortex, allowing both the particle density and the thermodynamic compressibility to vary with the radial coordinate. Starting from the electrostatic charge response obtained from the phase-only Popov action, we introduce a local-density extension and derive the regular near-axis expansion of the scalar potential. The constant, quadratic, and quartic coefficients are obtained explicitly in terms of the local screening response and of the leading nonuniform contribution to the vortex density profile. For a three-dimensional unitary Fermi equation of state, the density dependence of the compressibility generates a definite thermodynamic contribution to the quartic coefficient. The resulting decomposition separates this equation-of-state contribution from the ordinary constant-screening and charge-source terms that occur at the same order. This provides a compact analytical connection between vortex-core thermodynamics and the local electrostatic profile of a charged superfluid.

Markov chain Monte Carlo algorithms can be viewed as feedback devices that compare a proposed move with the target distribution and then accept or reject it. In this paper the Maxwell demon is identified with the acceptance module: it measures a proposed edge, stores the outcome in the accept/reject bit, and uses that bit to shape the probability current. The decision bit carries a genuine Shannon mutual information about the proposal, whereas only its directional part is converted into a cooling information flow. The relative-entropy relaxation rate obeys $v(t)=\dot{\mathcal I}_{\rm cool}(t)+\dot S(t)$, which separates useful cooling from housekeeping circulation in nonreversible chains.

When only local observables of a many-body quantum system are of interest, it is desirable to formulate a reduced description within the Hilbert space of the corresponding subsystem, with the remaining degrees of freedom traced out and acting as an environment. Assuming initially uncorrelated states and Gaussian environments, we develop a framework for reconstructing the local dynamical generator of noninteracting quantum chains, with polynomial computational complexity. As an application, we consider two representative models: a bipartitioned Kitaev chain and a Kitaev chain boundary-coupled to a fully connected free-fermion environment. In both models, strong subsystem-environment coupling leads to non-Markovian dynamics characterized by ballistic spreading of the Lindblad dissipator support within the subsystem. On the other hand, weak coupling to a fully connected environment yields predominantly boundary-localized, Markovian dissipation. Our work highlights the implications of subsystem-environment correlations on the generator of local dynamics, beyond the conventional weak-coupling approximations.

A first-principles and device-level study of the quasi-two-dimensional transition-metal chalcogenide Mo$_2$SeTe$_3$ is performed. The material is found to be a weak topological semiconductor with a finite bulk band gap and symmetry-protected Dirac surface states, indicating strong potential for next-generation low-power quantum electronic devices. An SOC-driven band inversion accompanied by an indirect semiconducting gap of approximately 0.75 eV is observed. Topological nontriviality is rigorously confirmed through Wannier charge-center evolution and $\mathbb{Z}_2$ invariant analysis, yielding weak topological indices of $(0;001)$, while iterative Green's-function surface-state calculations corroborate Dirac-cone conducting states traversing the bulk gap on symmetry-preserving surfaces. Mo$_2$SeTe$_3$ additionally exhibits exceptional dynamical and mechanical stability, pronounced optical anisotropy, high dielectric polarizability, broad infrared-to-visible optical absorption, a large static dielectric constant, and substantial birefringence, making it favorable for photonic and optoelectronic applications. Thermoelectric transport analyses further reveal enhanced carrier mobility and a competitive figure of merit under $n$-type doping near room temperature. A dual-source tunnel field-effect transistor (TFET) is implemented via TCAD simulations with nonlocal band-to-band tunneling, yielding subthreshold switching below the thermionic limit, a high ON/OFF current ratio, and enhanced tunneling efficiency driven by SOC-induced orbital hybridization and topologically enhanced interband coupling. The concurrent realization of nontrivial bulk-boundary correspondence, robust transport properties, and steep-slope switching characteristics establishes Mo$_2$SeTe$_3$ as a multifunctional quantum material platform for topological and next-generation energy-efficient nanoelectronic devices.

Unlike second-order phase transitions, a first-order transition has a stage, in which a system is trapped in a metastable state. The decay of this state leads to abundant excitations over the ground state. We present a field theory for kinetics of defects emerging during quantum annealing computations. This theory predicts several power laws for the error generation rate during quantum annealing either though or near the first-order phase transition. Sharp changes between the power exponents are predicted for continuous parameter changes. Observation of this behavior would be a signature of first-order critical points and could help identify and avoid them for better computations. The driven Lipkin-Meshkov-Glick model (LMGm) serves as the minimal model of interacting Ising spins that demonstrates this behavior.

We realise the first ultralow-field Bose-Einstein condensation of triplons in a spin-ladder magnet, uncovering a quantum critical point at only $\mu_0 H_{c1}=0.17$ T in Henmilite ($\mathrm{Ca_2Cu(OH)_4[B(OH)_4]_2}$). Unlike dimer magnets, a ladder retains extended one-dimensional correlations in its gapped parent state, making this limit strongly fluctuation dominated. Thermodynamic, magnetoelastic, $\mu$SR, and neutron-diffraction measurements overturn the previous assignment of zero-field antiferromagnetic order, establishing a quantum-disordered coupled-ladder parent state with persistent low-energy dynamics. The weak low-temperature anomaly instead marks a gap-controlled crossover from the correlated ladder regime into the activated quantum-disordered state. These measurements further reveal an exceptionally asymmetric ordered dome extending to $\mu_0 H_{c2}\simeq 8.2$ T. Quantum Monte Carlo simulations for the relevant spin Hamiltonian place Henmilite just on the gapped side of the zero-field ladder-ordering instability, naturally accounting for the strong separation between the exchange and residual-gap scales and the tiny critical field. Our findings extend ultralow-field triplon condensation beyond the dimer paradigm and establish Henmilite as a platform for controlled tuning across quantum criticality in a fluctuation-dominated spin ladder.

These notes accompany lectures given in June 2025 at the summer school Fundamental Problems in Statistical Physics XVI. They offer a short introduction to random quantum circuits as simple models for generic many-body quantum systems. They give an outline of the motivation for introducing these models, starting from ideas of random matrix theory. They also provide a sketch of calculations of some of the quantities of most physical interest, based on an average over an ensemble of systems. These quantities give insights into operator spreading, entanglement dynamics and spectral correlations.

We investigate chemical control of the electronic, optical, and topological properties of two-dimensional \ce{Si2X2Te2} (\ce{X} = \ce{B}, \ce{Al}, \ce{Ga}, and \ce{In}) monolayers using first-principles calculations. All compounds are dynamically stable semiconductors, with their vibrational and electronic properties evolving systematically upon group-III substitution. Hybrid-functional calculations including spin–orbit coupling reveal predominantly $p$-orbital band edges and increasingly pronounced relativistic effects from B to In. Most notably, the calculated $\mathbb{Z}_2$ invariant identifies \ce{Si2In2Te2} as a candidate quantum spin Hall insulator, while the B-, Al-, and Ga-based monolayers remain topologically trivial. Bethe–Salpeter calculations further show that electron–hole interactions redistribute oscillator strength near the absorption onset while preserving a weak in-plane optical anisotropy. Our results establish group-III substitution as a simple chemical route to tune the electronic structure and drive a transition from trivial to nontrivial topology in \ce{Si2X2Te2} monolayers.

Neural quantum states provide flexible variational representations of quantum many-body wave functions by combining neural-network parametrizations with Monte Carlo sampling. In this perspective, we review recent advances in their application to condensed-matter systems, focusing on frustrated quantum magnets, interacting lattice fermions, and non-equilibrium dynamics. We discuss the architectures, symmetry constraints, optimization methods, and sampling strategies underlying state-of-the-art calculations, and summarize practical guidelines for reliable simulations. We also examine the principal remaining challenges, including learning non-trivial sign and phase structures, controlling variational bias, enforcing physical symmetries, scaling optimization to large networks, and achieving stable real-time evolution. Finally, we outline promising directions in which neural quantum states may extend the reach of classical simulations of strongly correlated quantum matter.

Mid-infrared (MIR) optical conductivities in cuprate superconductors show universal features. In this study, we demonstrate that these originate from two distinct gaps: the pseudogap mediated by antiferromagnetic spin fluctuations and the Mott-Hubbard gap. The MIR spectra from these two gaps show a characteristic and distinct shape and doping dependence, and can thus be distinguished. Specifically, the Mott-Hubbard correlations, while rendering a peak in the visible spectrum for small dopings, yield a broad optical response starting in the MIR when a “waterfall” develops in the one-particle spectrum at larger dopings. The numerically and analytically determined doping-dependence of both gaps consistently reproduce experiments, and provide a unified microscopic understanding of the cuprate MIR optical conductivity.

High-entropy alloy superconductors, characterized by extreme chemical disorder and complex electronic environments, have attracted significant attention as model systems for exploring superconductivity in disordered materials. Here, we investigate a Cr-based equiatomic HEA, Cr-V-Ti-Nb-Ta, which contains a magnetic 3d element, providing an opportunity to examine the influence of magnetic elements on superconductivity in highly disordered systems. Despite expected magnetic pair-breaking, this alloy exhibits bulk type-II superconductivity with a transition temperature of $T_c = 2.33(3)$ K and a high upper critical field. Transverse-field $\mu$SR measurements reveal an s-wave superconducting gap close to the BCS value, while zero-field $\mu$SR suggests preserved time-reversal symmetry. These results establish Cr-V-Ti-Nb-Ta as a promising platform for exploring the interplay between disorder, magnetism and superconductivity in high entropy alloys.

Multicomponent liquids can phase separate upon heating, exhibiting a lower critical solution temperature (LCST). Moreover, a narrow class of materials can undergo disordering transition upon further heating, yielding closed-loop phase diagrams. Previously, it was shown that LCST or closed-loop phase behavior can appear in the models of liquids in which components are asymmetric or interaction potentials have a specifically designed attraction. Here, we show theoretically that LCST and closed-loop phase behavior can occur in a significantly wider set of models. In particular, we found that these phenomena can be exhibited by the simplest and widely used coarse-grained (CG) models of any multicomponent liquid in which species are fully symmetric and where all particles interact via an arbitrary repulsive potential. In addition, we discovered that LCST and closed-loop phase behavior in these models emerges merely due to the basic property of CG liquid models, namely, the appearance of strong monomer-monomer positional correlations at low monomer number density $\rho$. We simulated the models of fully symmetric binary blends and diblock copolymer melts where nonbonded monomers interacted via a generic T-independent purely repulsive harmonic potential. As predicted, LCST and closed-loop phase behavior emerged at $\rho$ sufficiently low to cause strong monomer-monomer correlations leading to a strong T-dependence of the effective coordination number, which, in turn, induced a nonmonotonic T-dependence of the Flory-Huggins parameter. To summarize, we discovered that the simplest fully symmetric non-associating CG models of multicomponent liquids can exhibit complex temperature response due to a mechanism stemming from the basic nature of any CG liquid model. This mechanism might contribute to the emergence of LCST and closed-loop phase behavior in many existing polymer materials.

We study the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice with ferromagnetic nearest-neighbor couplings fixed at $J_1=1$ and strong antiferromagnetic next-nearest-neighbor interactions, i.e., $J_2 \leq -1/4$. Little is known for this range of $J_2$, whereas for less negative values of $J_2$ the system orders ferromagnetically at low temperatures and appears to remain in the Ising universality class. In previous work it was shown that the model has a largely degenerate ground state, and it was conjectured that there is some kind of phase transition. We introduce a complex-valued nematic order parameter, which can differentiate between the high-temperature paramagnetic phase and the observed partially-disordered stripe phase at lower temperatures. Configurations in this phase consist of stripes of spins parallel with respect to one lattice direction, which collectively meander along the remaining two, producing partially disordered ground states. The sharp peaks in the specific heat observed in earlier work only appear when using periodic boundary conditions and are absent for free boundaries. Additionally, we reveal a striking dependence of the behavior on the aspect ratio of the considered samples. Ultimately, even a careful finite-size scaling analysis for $J_2 = -0.5$ and $J_2 = -1$ is unable to clearly discern between a crossover without any singularities and some form of continuous transition, including the possibility of an infinite-order transition of the Berezinskii-Kosterlitz-Thouless (BKT) type. For $J_2=-1/4$ we find that the system remains disordered at all temperatures and that it exhibits a finite ground-state entropy per site, for which our simulations provide the accurate asymptotic estimate $S(T=0)/N = 0.230\,960\,93(14)$ in the thermodynamic limit $N\rightarrow\infty$.

Electron-phonon coupling is usually understood in terms of electronic quasiparticles interacting with dispersive lattice vibrations. Much less is known about the complementary limit in which the relevant phonon mode is itself localized or weakly dispersive. Here we investigate this regime in the kagome compound Rb$_{2}$Ni$_{3}$S$_{4}$, which undergoes an unconventional insulating transition near $T^{*} \approx$ 260-280~K. Combining polarization-resolved Raman spectroscopy with temperature-dependent x-ray diffraction, scanning tunneling microscopy, and electrical, thermal, and magnetic measurements, we show that the transition involves electronic localization without a conventional structural or magnetic order parameter. Raman spectra reveal a giant Franck-Condon progression associated with a nearly dispersionless 333.7~cm$^{-1}$ phonon, decorated by an equally spaced comb-like fine structure with a characteristic spacing of 40.6~cm$^{-1}$. The comb spacing is insensitive to magnetic field, whereas its spectral weight is strongly field tunable. Rather than treating either hierarchy alone as pure phonon effect, we interpret their nested coexistence as evidence for a strongly coupled electron-vibrational manifold involving a localized lattice coordinate. These results identify dispersionless phonons as an active route to vibronic correlations in solids and suggest that such electron-vibrational self-trapping is closely associated with the insulating phase of Rb$_{2}$Ni$_{3}$S$_{4}$.

We construct a continuum model for a one-dimensional moiré superlattice formed by stretching one layer of AB-stacked bilayer graphene along the x direction by a factor s. Following the spirit of the Bistritzer-MacDonald model for twisted bilayer graphene, we treat the interlayer coupling as hopping between several Dirac points. At a critical stretch factor s ~ 1.018 the two bands near the Fermi level touch, forming two degeneracy points along the k_y direction. This gap closing is accompanied by a topological phase transition, in which the Chern number changes from 1 to -1, and by a sign change of the Berry-curvature dipole, which we propose can be detected through the nonlinear Hall effect. We find that uniaxial strain modulates inter-Dirac-valley coupling, which drives band gap collapse and subsequent topological number inversion. This opens a route to engineer topological transport and quantum anomalous Hall effects via strain engineering of moiré heterostructures.

The dramatic slowing down of structural relaxation in supercooled liquids is accompanied by the emergence of dynamic heterogeneity. A monotonically increasing dynamical correlation length, measured at the $\alpha$-timescale, is one of the remarkable features of this phenomenon. Here we show that this picture is incomplete: the dynamical correlation length measured in the $\beta$-relaxation regime exhibits a striking non-monotonic temperature dependence, reaching a maximum near the mode-coupling crossover temperature $T_c$ and decreasing upon further cooling, even as local dynamical fluctuations continue to intensify. This behavior suggests a crossover from spatially extended, maximally cooperative motion near $T_c$ to increasingly compact and localized relaxation events below it. We demonstrate that this evolution is quantitatively captured by stochastic beta-relaxation theory, an extension of mode-coupling theory beyond mean-field that explicitly predicts an avoided dynamical transition in finite dimensions. Our results provide the first direct spatial evidence in favor of the avoided-transition picture of the mode-coupling crossover, and establish the peak of the $\beta$-regime correlation length as a robust indicator of the mode-coupling crossover.