Papers

Matrix product state algorithms must enlarge their bond spaces as entanglement grows and compress them to control cost. We formulate basis-update and Galerkin (BUG) time integration as a sequence of canonical MPS sweeps for Hamiltonians represented as matrix product operators. We show when two natural basis updates produce the same trial space and when transporting coefficients between successive bases preserves the represented state. Under these conditions, the existing first-order error bound for uncompressed tree-tensor-network BUG also applies to the alternating-endpoint MPS schedule. We verify the uncompressed implementation against an independent six-site calculation. We then compare BUG with two-site TDVP for 16-site transverse-field Ising and Haldane-Shastry dynamics. At matched timestep and truncation settings, BUG performs fewer local exponential actions and has lower runtime. These settings do not produce equal accuracy. The runtime versus accuracy curves cross for the Ising model and are close for the Haldane-Shastry model. The comparison therefore identifies model-dependent trade-offs rather than a general advantage for either method.

We demonstrate a static, disorder-free spin chain Hamiltonian which, by tuning the coupling to an auxiliary qubit, realizes a crossover between super-ballistic, ancilla-accelerated scrambling and sub-ballistic operator confinement. Our minimal model is the mixed-field Ising chain with a spin-1/2 ancilla coupled to its longitudinal magnetization. The ancilla mediates an effective all-to-all interaction which accelerates operator spreading and entanglement growth when weakly coupled, but rapidly saturates its entanglement and projects spin chain operators into effectively frozen subspaces when the ancilla coupling is strong. We locate this crossover independently through both a divergent peak in the mutual-information saturation time near $\lambda_c N/h \approx 8$ and an exponential suppression of the late-time OTOC growth rate, $\log\alpha \propto 1/\lambda$. Through a Feshbach-Fano projection and Schrieffer-Wolff transformation, we reveal an effective hidden symmetry on the chain which confines operators on the chain for a time exponential in the coupling strength. This reconciles the fast, $\log(N)$ scrambling reported for random-unitary-circuit realizations of the star geometry with the confinement previously found in its time-independent Hamiltonian analog, showing both emerge from a single Hamiltonian family as a function of one dimensionless parameter.

Fractionalizing a quantum two-level system is usually associated with encodings based on pairs of Majorana fermions—an operational fractionalization. We show an alternative algebraic fractionalization by embedding Székely's classical “half-coin” into a non-Hermitian Krein space. The coefficients of $(q+pz)^{1/2}$ define a signed sequence and a normalized, non-Hermitian biorthogonal operator describing a biorthogonal half-qubit. We prove that two such objects fuse into an arbitrary pure qubit through the signed Vandermonde convolution that the collective $N\ge2$ vectors are null in Krein space. $L_1$ norm of the half-qubit follows in closed form, $\lVert p\rVert_1 = 2\sqrt{q}-\sqrt{q-p}$. Its $L_1$ norm increases monotonically with the bias and attains its supremum $\sqrt{2}$ precisely at the unbiased point $p=q=1/2$. Interestingly, we identify two structural results as follows. First, number parity and the $\eta$-metric generate a distinguished commuting $\mathbb Z_2\times\mathbb Z_2$ subgroup. Second, we find the $\eta$-metric obstructs any local $\eta$-self-adjoint partner of the parity, so a half-qubit carries a $\mathbb{Z}_2$ observable but no local $SU(2)$. The full Pauli algebra emerges only upon fusion. We then show that the construction survives truncation of the Fock basis: the fused qubit is exact at every cutoff, and the Vandermonde cancellation is visible in sign-weighted photon-number statistics, and can be tested using existing cavity and trapped-ion state-synthesis methods. Finally, we generalize this algebraic fractionalization to a $1/n$-qubit, which can be achieved by replacing the square root with an $n$th root.

Protontherapy precision depends on accurately knowing the stopping power of liquid water, as it is the most abundant component of soft body tissues. Difficulties when working with volatile liquids have led to a long-standing debate regarding the values of the stopping power and the mean excitation energy $I$ of liquid water. The equivalence between the stopping power of liquid water and amorphous ice per unit mass density across all clinically relevant proton energies opens the possibility to obtain a reliable estimation of the $I$-value of liquid water. In this work, we employ two complementary theoretical methodologies to assess the proton stopping power of water. The MELF-GOS (Mermin Energy Loss Function - Generalized Oscillator Strengths) approach, based on the perturbative dielectric formalism, serves as an accurate reference for sufficiently high energies, while the novel non-perturbative TDDFT-Penn (time-dependent density functional theory - Penn) method ensures accuracy for energies even below the stopping maximum. These stopping-power values were incorporated into the simulation code SEICS (Simulation of Energetic Ions and Clusters through Solids) to evaluate proton Bragg curves from $1$ to $230$ MeV. Comparisons with available precise depth-dose measurements provide critical insights that help establish the consistent value $I = 79.4$ eV for liquid water, providing robust physical grounds for improving range prediction for treatment planning.

Ultrafast spectroscopic techniques are widely used to investigate photoinduced processes, yet they remain largely blind to molecular chirality. Here we introduce a framework for simulating time-resolved electronic circular dichroism (TRCD) along an ensemble of nonadiabatic molecular dynamics, and apply it to the photoisomerization of a second-generation molecular motor[1]. While transient absorption captures the overall excited-state dynamics, it cannot distinguish the two photoproduct pathways. The TRCD response, by contrast, resolves the stereochemical branching: trajectories returning to the stable P isomer (right-handed helix) retain a distinct chiroptical band in the visible region, whereas those forming the M isomer (leftl-handed helix) become chiroptically dark as they twist through the conical intersection. This asymmetry constitutes a directly measurable signature of the stereochemical branching, offering a real-time probe of the formation of molecular chirality and concrete predictions for future TRCD experiments.

We investigate the conditions under which momentum-dependent similarity transformations preserve spectral properties of lattice Hamiltonians with open boundary conditions (OBC). While such transformations exactly preserve spectra in infinite systems, their application to finite systems introduces subtleties due to the long-range nature of the inverse transformation in real space. For general traceless $2\times 2$ Hamiltonians, we derive necessary and sufficient conditions for reduction to skew-diagonal form via constant similarity transforms, providing explicit transformation matrices for all cases. We then establish rigorous conditions for bulk spectral preservation under momentum-dependent transformations: the generalized Brillouin zone of $H$ must lie inside the smallest zero of $\det S(z)$ (the two-radius condition $r_{\mathrm{GBZ}}^{\max}<z_{\min}$), together with a spectral-stability (no critical non-Hermitian skin effect) condition on $H$. Two-sidedness of $S(z)$ governs only the modification of a finite number of boundary eigenvalues, not the bulk. Our results establish when bulk topological invariants computed in transformed coordinates reliably predict boundary physics, with implications for non-Hermitian systems, photonic crystals, and other platforms where chiral or hidden symmetries emerge only after appropriate basis changes.

The Berry phase of an isolated electronic state is evaluated for different integration paths in reciprocal space, thanks to Riemann-Bloch states providing a consistent description in the whole Brillouin zone. The relationship with the bounded position operator is investigated for the open-path Berry phase and with different form factors of the constituent Gaussian type atomic orbitals (GTOs). When the Berry phase is evaluated over a closed loop in reciprocal space, a regularisation procedure in the complex plane is adopted and additional quasi-symmetries are exploited here for the first time in order to rationalise the occurrence of non-analytical jumps as a function of the winding number or of the GTO broadening.

We show that geometric phases accumulated during adiabatic evolution can be converted into observable interference in Krylov space, leading to a geometric-phase-dependent Krylov oscillation. Adiabatic dynamics force Krylov complexity to vanish if the initial Krylov basis is an instantaneous eigenstate of the Hamiltonian; Nevertheless, we demonstrate that the Krylov complexity will be non-vanishing if the initial Krylov basis is a superposition state rather than an eigenstate. Consequently, Krylov complexity is found to depend on the difference of dynamical phases in the Krylov space, which is deeply related to the Berry connections in the original Hilbert space. In particular, for a single qubit system with constant Lanczos coefficients, Krylov complexity oscillates harmonically at a frequency given by the strength of the external field and the geometric Berry phase. Therefore, our work may provide a novel avenue to probe the geometric phase from the Krylov complexity.

We investigate the formation of mutual coherence and deterministic phase control in a multimode exciton-polariton system realized in two optically induced traps with tunable intertrap coupling. As the coupling channel between the traps is progressively opened, the mutual first-order coherence rises sharply from nearly zero to values close to unity, revealing a threshold-like crossover from weakly correlated to highly coherent dynamics. We demonstrate deterministic multimode phase control with a short spatially localized nonresonant pulse, which allows the phase relations between selected polariton condensate modes to be set while keeping their amplitudes nearly unchanged. The induced phase transformation is read out directly from time-resolved interferograms and realized for different sets of modes in both intermediate- and high-coherence regimes. Within a reduced four-mode description, the control pulse implements an effective phase operator on the coherent multimode field with a fidelity exceeding 0.995. The same approach can be extended to larger networks of coupled traps, offering a route to optical control over phase relations in increasingly complex multimode polariton states.

Kirigami, the art of cutting sheets, offers unique characteristics such as shape morphing, stretchability, and adaptability, with applications in deployable and reconfigurable structures. While Finite Element (FE) approaches are widely used to analyze kirigami structures, they are computationally intensive and prone to convergence issues. On the other hand, existing simplified and theoretical models for evaluating kirigami are typically restricted to specific designs and analytical scenarios. This paper proposes a generalized, computationally efficient reduced-order model based on the bar and hinge approach for analyzing any kirigami system. The model represents the entire kirigami structure using truss bars, bending hinges, and torsional springs, capturing both the deformation and internal forces of the system. We derive stiffness expressions for kirigami structures that experience stretching and out-of-plane bending deformations, as well as for structures that experience only in-plane stretching and rotations. The accuracy and robustness of the model are validated through comparisons with FE analysis and experimental data on both single-cut kirigami designs and more complex designs with multiple cuts. Our results demonstrate less than 5% difference in deformation predictions and achieve at least a tenfold computational speedup compared to FE simulations. Additionally, we demonstrate the model's capabilities through simulating complex scenarios, including kirigami-skinned crawlers, high-throughput property-space exploration, and in-plane kirigami-inspired metamaterials. These examples demonstrate computational capabilities that enable large-deformation structural simulations and high-throughput design exploration beyond the practical limits of conventional FE methods.

Bipartite qubit entanglement distillation is the process of converting noisy ebits into pure ebits using only local operations and classical communication. This is a core operation for quantum repeaters, enabling such crucial tasks as long-distance quantum communication and distributed quantum computing. In this work, we introduce a method for searching for entanglement distillation protocols and, using this technique, distil qubit Werner states at a higher rate than could be achieved using previously discovered protocols. In particular, we demonstrate the advantage of our new distillation strategy by improving the best-known lower bound for the two-way-assisted quantum capacity of the qubit depolarising channel across a wide range of channel parameters, making progress in one of the long-standing problems of quantum information theory.

Thermal transport in dielectric, non-magnetic crystals is mediated by quantized lattice vibrations, which drift and interact when driven out of equilibrium by a temperature gradient. This phenomenon can be described at multiple theoretical levels, ranging from fully quantum descriptions to semiclassical and mesoscopic continuum approaches. This review rigorously discusses the theoretical steps and approximations connecting these levels, bridging quantum phonon Dyson and Kadanoff-Baym equations and semiclassical Boltzmann transport formalism, and discussing the coarse-graining procedures that yield mesoscopic viscous heat equations for non-diffusive, hydrodynamic heat transport in devices. We show how the Guyer-Krumhansl and dual-phase-lag equations emerge as special linear-isotropic-band and inviscid limits of the viscous heat equations, respectively; most importantly, we demonstrate that these equations predict not only Poiseuille flow and second sound, but also more exotic effects such as negative thermal resistance, steady-state thermal backflow and vortices. We highlight how combining these frameworks with first-principles simulations connects microscopic phonon physics to observable non-diffusive heat-transport phenomena and guides their detection, amplification, and control. We recast the viscous heat equations in terms of Helmholtz and biharmonic equations solved analytically, and use this to discuss similarities and differences between the macroscopic behavior of the phonon fluid and other hydrodynamic systems, such as classical and electron fluids, focusing on compressibility, vorticity, and their influence on phonon hydrodynamics. We conclude with a roadmap to generalize the tools used to describe phonon hydrodynamics to other quasiparticles, motivating future advances in collective quantum transport phenomena in solids.

Energy and charge transfer in condensed matter systems are often described in terms of quasiparticles. The order of accuracy of the results in terms of the electron-to-nucleus mass ratio $\epsilon$, an adiabatic small parameter, is usually not known. To quantify energy transfer with controlled accuracy in $\epsilon$, we use adiabatic perturbation theory to derive a formula for the rate of change of the nuclear kinetic energy. Applying a sequence of near-identity unitary transformations decouples the electronic and nuclear degrees of freedom to higher and higher order and produces an effective Hamiltonian. In the special case that the nuclei are treated classically, the energy transfer formula reduces to the usual formula for the rate of work done on a classical particle but the mass of the particle is enhanced by the factor $M_0^{-1}(M_0+\epsilon M_1)$, where $M_1$ is a nonadiabatic correction to the bare nuclear mass tensor $M_0$. Additional quantum geometric corrections appear at higher orders. Adiabatic perturbation theory is further used to incorporate, order-by-order in $\epsilon$, nonadiabatic transitions into linear response calculations. The nonadiabatic frequency-dependent conductivity and Drude weight of an electron-ion system are calculated.

We analyze the dynamics of two harmonic oscillators with nonlinear, non-Hermitian coupling between them. Specifically, we consider a synthetic antiferromagnet composed of two ferromagnetic layers with antiferromagnetic interactions between the two layers, leading to the emergence of two oscillation modes of the combined system. We analyze the response of this system to external driving fields. We determine the allowed steady states under various driving conditions. We then analyze the dynamics of small deviations away from the different steady states, which reveals the normal modes that can be probed using spectroscopic techniques in experiment. As expected, the nonlinear system exhibits multistability, in which multiple steady states can exist for the same driving conditions. We find that the dynamical response can be drastically different depending on which one of the two modes is driven and on the strength of the driving. Specifically, we can obtain level-repulsion or level-attraction patterns in the spectrum. In addition to the rich variety of spectra, we find that some steady states exhibit normal modes that contain multiple frequencies. Our results explain recent experiments on synthetic antiferromagnets and provide guidance for designing experiments that can explore previously unseen phenomena in these systems.

Free-space quantum communication provides a flexible complement to fiber-based quantum networks, but its point-to-point capacity is fundamentally limited by diffraction, atmospheric extinction and beam wandering induced by turbulence. In this work, we study the end-to-end performance of large-scale free-space quantum networks connecting randomly distributed fixed or mobile users, modelled as Waxman random graphs. We derive the mean network capacity, edge consumption and connectivity phase transitions for both single-path and multi-path (flooding) routing. We also study router-centered star networks, deriving the full distribution of end-to-end capacities as a function of the router's coverage radius. We then consider how performance may be improved by reinforcing free-space networks with a small number of optimally placed fiber-based backbone nodes. We prove that any optimal backbone configuration must correspond to a capacity-maximizing Voronoi tessellation of the network region, and show that this can be efficiently approximated by a centroidal Voronoi tessellation via Lloyd's algorithm, with backbone nodes connected according to a Delaunay triangulation. Numerical results show that even a modest number of backbone nodes substantially improves end-to-end capacity and reduces edge consumption for both mobile and fixed users.

Real-to-complex spectral transitions mark the onset of amplification in non-Hermitian systems, but their thresholds are often treated as model-specific quantities. Here we develop a general, non-perturbative activated-mode principle that governs the real-to-complex threshold across broad classes of non-Hermitian systems. A central insight is that only a small Hilbert subspace is “activated" at the transition onset, which can be variationally determined through the competition between spectral detuning and mode-level projected non-Hermitian couplings. The result is a closed-form exceptional-activation condition for arbitrarily large “disturbances", rather than a perturbative estimate. We apply our framework to three contrasting illustrative problems, establishing (i) a closed-form threshold for critical non-Hermitian skin amplification at all system sizes; (ii) a new link between impurity tunneling threshold and exceptional point switching; and (iii) activation channel switching without underlying topological phase transition. Overall, our findings recast real-to-complex transitions as generic mode-selection problems independent of any specific symmetry.

Automated measurement of condensed-matter experiments requires instrument-control, data-acquisition, and user-interface threads to access shared, naturally hierarchical state concurrently. Coarse-grained locking can delay acquisition and cause sample loss, whereas fine-grained locking requires deadlock-prone lock ordering across instruments. Instead, we describe the lock-free software transactional memory (STM) that has been at the core of an open-source measurement platform for 16 years, in nuclear magnetic resonance experiments and, more recently, in optically detected magnetic resonance experiments. The STM organizes this state as a tree and provides atomic subtree updates and consistent subtree snapshots. After initial bundling, an unchanged subtree snapshot is acquired in $O(1)$ time through a custom lock-free atomic shared pointer. Within each bounded TLA+ configuration, TLC exhaustively checks the state space, establishing the safety and livelock-freedom properties specified for that configuration. Bounded executions of the atomic shared-pointer implementation are separately checked under the C11 weak-memory model. The same Snapshot and Transaction interfaces are exposed to Python scripting and AI-assisted automation.

The anomalous Hall effect (AHE) is a hallmark transport phenomenon in ferromagnets arising from relativistic spin-orbit interaction. Here, we report an unexpected sign reversal of the AHE in Ru/[Co/Ni]$_N$ multilayers controlled by the stacking sequence of the Ru layer. When Ru is placed beneath, rather than atop, the Co/Ni multilayers, the anomalous Hall signal switches from positive to negative. By systematically varying the multilayer repeat number N and combining transport measurements with first-principles calculations, we show that this reversal originates from in-plane tensile strain imposed by the Ru underlayer, which reshapes the electronic structure and redistributes Berry curvature near the Fermi level. Our findings establish interfacial strain as an effective knob for tuning Berry-curvature-driven transport and suggest a pathway toward strain-controlled topological transport phenomena in magnetic multilayers.

The electromagnetic response of metallic films is commonly analyzed in terahertz spectroscopy by assuming unit relative magnetic permeability. In this work we show that this assumption introduces significant distortions in the electrodynamic retrieval of highly conductive films. Aluminum and copper films, 10 nm thick, were investigated by terahertz time-domain spectroscopy in both transmission and reflection configurations. By applying a self consistent retrieval method that independently determines the complex permittivity and permeability, we show that the Drude-type dielectric response is systematically accompanied by a permeability that strongly departs from unity. This deviation is intrinsically linked to the reactive impedance of the films, which clarifies the light induced onset of large screening currents within a transversally confined geometry. A phenomenological interpretation based on the Faraday Neumann Lenz mechanism and a lumped-element model of the film impedance accounts for the observed trends. These results indicate that the common assumption $\tilde{\mu}=1$ in non-magnetic Drude films can lead to an incomplete or biased electrodynamic characterization in the terahertz regime.

Although considered a niche technique, muon spectroscopy provides a unique and complementary insight into a range of different materials from hard condensed matter to biological samples and everything in between. In matter, the muon has a mass of $\frac{1}{9}~m_p$ or $207~m_e$, and is a local probe of quantum states that can provide a focus on the bulk properties of materials. While often interpreted in a classical framework, the muon is itself a quantum particle and it is increasingly common for researchers to take account of this when thinking about muon spectroscopy experiments. In this perspective, we focus on the power of using this quantum treatment of muon spectroscopy, which is a key future direction for the technique.

Angle-resolved photoemission spectroscopy (ARPES) can measure electrons' energy vs momentum relations in solids via photoelectric effect. This pedagogical paper experimental results from this technique as a tool for visualizing the Fermi gas model in quantum statistical mechanics. This model is an important starting point for understanding more complex electronic behaviors in real metals.

We establish a global, worst-case non-identifiability theorem for periodically driven finite-dimensional quantum systems. On the unrestricted smooth periodic Hamiltonian class, we show that the period-averaged Fubini-Study metric component of a fixed initial state cannot, in general, be reconstructed from exact one-period propagators indexed by every starting time and external parameter. Thus, even complete starting-time-resolved endpoint data are insufficient to determine this intra-period geometric quantity. The obstruction is characterized exactly. The starting-time-indexed endpoint data determine the conjugation path of the monodromy, but not its particular unitary lift. On each fixed-monodromy slice, the observational fibres are precisely the right orbits generated by smooth parameter-dependent based loops taking values in the pointwise centralizer of the monodromy. The Fubini-Study functional is not invariant under this fibre action and therefore does not factor through the endpoint observation map. An explicit real-analytic two-level witness demonstrates the obstruction within a commuting, one-generator Hamiltonian family, so neither non-Abelian time ordering nor Floquet-logarithm ambiguity is required. A continuous family of Hamiltonians produces identical starting-time-indexed one-period endpoint data while yielding different, and on the unrestricted class arbitrarily separated, period-averaged Fubini-Study geometry. Non-identifiability persists under any prescribed uniform bound on the parameter derivative of the Hamiltonian. The result is a deterministic global statement, not a claim of generic non-identifiability or experimental impossibility. It identifies a precise information gap between complete one-period endpoint data and full intra-period dynamics: the missing information is the unitary lift of the observed monodromy path rather than ordinary scalar phase freedom.

The direct-sum evaluation of Madelung constants is complicated by the conditional convergence of lattice sums, which gives rise to a shape-dependent boundary term. In this work, we present, for the first time, a closed-form analytic expression for this boundary term that is valid for arbitrary crystal geometries. For general triclinic lattices, this boundary term maps exactly onto the electrostatic potential generated by a set of uniformly charged parallelograms. In addition, we demonstrate that the residual finite-size correction for a crystal of characteristic size $p$ decays as $(2p+1)^{-2}$. Building on these results, we develop a robust direct-sum method for the accurate computation of Madelung constants in arbitrary triclinic lattices and validate its effectiveness through explicit calculations on representative Bravais lattices.

We develop a microscopic theory of the long-range electron-hole exchange interaction in charged excitons (trions) confined in semiconductor quantum dots. While the ground-state singlet trion remains degenerate in the spin component of unpaired charge carrier by time-reversal symmetry, excited trion states exhibit a rich fine structure resulting from the interplay of electron-electron and electron-hole exchange interactions. We derive the effective long-range exchange Hamiltonian for both the spin-$3/2$ heavy-hole and a simple spin-$1/2$ valence band models. The long-range exchange interaction mixes singlet and triplet trion configurations, giving rise to anisotropic fine-structure splittings and related polarization-dependent optical spectra determined by the quantum-dot shape. Analytical expressions are obtained for the long-range exchange parameters. The developed theory establishes a unified microscopic description of the fine structure of excited trions in semiconductor quantum dots and provides a framework for interpreting polarization-resolved optical spectroscopy of charged excitonic complexes.

Majorana zero modes have emerged as one of the most promising platforms for topological quantum computation, since their non-Abelian braiding statistics allow quantum information to be encoded nonlocally and manipulated through braiding operations that are, in principle, protected against local perturbations. In practice, however, a braid is only as robust as its physical implementation: finite-time operation, residual couplings, and environmental noise can all convert local excitations into logical errors during the exchange process. Here, we address this question through a microscopic comparison of two representative braiding architectures, a nanowire trijunction and a quantum-dot-assisted setup, simulating the full time-dependent Bogoliubov–de Gennes dynamics under both noiseless and noisy conditions. We show that the dot-assisted architecture consistently achieves a lower error over a shorter timescale than the trijunction, owing to its more localized exchange mechanism. This advantage persists in the presence of noise, and a spatially resolved analysis further reveals that, in the dot-assisted geometry, fast noise localized on the dot produces a smaller error than equivalent noise on the wires, whereas slow, quasi-static noise on the dot becomes the dominant limitation. Taken together, these findings link the different error contributions directly to device geometry, pointing to concrete design principles for noise-resilient Majorana-based quantum gates.

CheMLFlow is an open-source platform for building and executing end-to-end, high-throughput, and agentic workflows for scientific and technological applications. CheMLFlow targets a common bottleneck in scientific machine learning development, where researchers often need to assemble data acquisition, curation, representation, model training, validation, screening, interpretation, and reporting into a reproducible pipeline, even when their primary research contribution concerns only one stage. CheMLFlow provides modular workflow components, ready-to-run reference pipelines, standardized artifacts, and evaluation outputs that reduce orchestration overhead and support benchmarking across methods and datasets. The platform is designed to be extensible, reproducible, and automation friendly, with pluggable representations and models, deterministic splits, explicit run artifacts, batch execution, and report generation. As scientific software increasingly moves toward agent assisted experimentation, CheMLFlow's configuration driven workflows and structured outputs also provide a practical interface for coding agents to help users construct experiments, inspect results, and summarize findings under human supervision. This article describes the system architecture, core workflows, and benchmarks that reach literature performance for quantum mechanical, physicochemical and bioactivity property prediction, and use cases involving time series datasets demonstrating applications beyond molecular chemistry datasets.

We study Gibbs states projected onto the symmetric sector of contractible one-form symmetries. In a three-dimensional cluster-model interpolation, this projection stabilizes symmetry-protected topological and projected-paramagnetic phases, both sharply distinct from thermal disorder. A flux-twisted membrane invariant distinguishes these three phases by the values $-1,+1,0$, respectively. These values are exact on the endpoint, self-dual, zero-temperature, and infinite-temperature lines; elsewhere their quantization requires positive spatial-sheet, winding-line, and interface tensions. Quantum Monte Carlo supports the quantization through tension diagnostics and direct finite-size estimates.

The electronic structure, lattice dynamics, bonding, elastic response, and anisotropic thermoelectric transport properties of tetragonal GeS$_2$ and GeSe$_2$ were investigated using density functional theory, density functional perturbation theory, Wannier interpolation, and scattering-aware Boltzmann transport. The relaxed structures are mechanically and dynamically stable within the calculated harmonic description. The HSE03/Wannier band gaps are 2.48 eV for GeS$_2$ and 1.23 eV for GeSe$_2$, while substitution of S by Se lowers the upper phonon frequency from approximately 13.6 to 10.3 THz. The phonon Boltzmann transport calculations reveal pronounced lattice-transport anisotropy. Within the relaxation-time approximation, the 300 K in-plane and cross-plane lattice thermal conductivities are 26.86 and 1.19 W m$^{-1}$ K$^{-1}$ for GeS$_2$, and 18.74 and 1.52 W m$^{-1}$ K$^{-1}$ for GeSe$_2$, respectively. At 800 K, these values decrease to 10.22 and 0.46 W m$^{-1}$ K$^{-1}$ for GeS$_2$, and 7.25 and 0.58 W m$^{-1}$ K$^{-1}$ for GeSe$_2$. Frequency-resolved analysis shows that low-frequency phonons carry most of the heat, whereas the small cross-plane values reflect restricted out-of-plane phonon transport. Combining the ShengBTE RTA lattice tensors with AMSET electronic coefficients gives $zT=0.257$ for n-type cross-plane GeS$_2$ at 800 K and $10^{19}$ cm$^{-3}$. The corresponding PBE-AMSET estimate for GeSe$_2$ is $zT=0.066$ for p-type cross-plane transport at 800 K and $3\times10^{20}$ cm$^{-3}$. LOBSTER analysis identifies mixed covalent–ionic Ge–X bonding, with Ge–S bonds having a larger stabilizing ICOHP magnitude than Ge–Se bonds ($-5.27$ versus $-4.74$ eV per bond). These results identify tetragonal GeX$_2$ compounds as strongly anisotropic thermoelectrics with moderate calculated $zT$ values whose cross-plane response benefits from suppressed lattice heat transport.

We study the topological properties and phase diagram of the triangular Hofstadter model with staggered flux in adjacent triangles in this work. This lattice can be used to describe the low energy physics of the twisted bilayer transition metal dichalcogenides (TMD) in a certain range of the electric displacement field between the two layers. We show that the Hofstadter spectrum of this model is generally asymmetric except at specific staggered flux $3\phi= \pi/2 \mod {\pi}$ due to an additional P symmetry at such $\phi$. Breaking the translation symmetry by dimerization lifts the P symmetry and results in rich topological phases in the system. The dimerized model with different rational external magnetic flux ${\Phi}_B = 2\pi p/q$ has phase diagram with the following common features. For even q, the dimerized model generally has three gapped regimes. The one with small dimerization has finite Chern number and the other two have zero Chern number. For odd q, the model is gapped with zero Chern number at any finite dimerization. For both q even and odd, the two regimes with zero Chern number can be further characterized by the inversion symmetry of the parametrized one-dimensional chains of the system at \phi = 0 \mod \pi/3$, and one regime is topologically non-trivial and the other is trivial. Our results may be tested in twisted bilayer TMD with weak interaction or cold atom systems in optical lattice or photonic crystals achieved in recent experiments.

Spectral transitions in non-Hermitian lattices often arise from the competition between non-reciprocal skin accumulation and inter-component hybridization. In short-range systems formed by two coupled chains, this competition conventionally leads to the logarithmic critical-length law $N_c\sim\ln D$, where $D$ is the transverse separation between the chains. Here we show that long-range hoppings fundamentally reorganizes this critical behavior, producing a hierarchy of distinct scaling laws. When only the hybridization couplings are power-law decaying with exponent $\alpha$, the onset becomes algebraic, $N_c\sim D^{\alpha/3}$. When the hoppings within each chain are themselves also power-law decaying, in addition to the hybridization couplings, the system enters a scale-covariant regime for $\alpha<2$, in which the criticality threshold equation depends only on the system aspect ratio $N_c/D$. At $\alpha=2$ and beyond, this regime is followed by a marginal logarithmically corrected and algebraically corrected regimes, respectively. We identify two new non-local mechanisms that enable this unconventional critical hierarchy: a nonanalytic band-edge dispersion from long-range intra-chain hoppings, and parity-mixing hybridization induced by non-reciprocity. Our results show that nonlocality systematically removes the physical length scales i.e. skin depth underlying conventional critical non-Hermitian skin behavior, offering a platform-independent framework testable in programmable topoelectrical circuits, photonic lattices and digital quantum simulators.