Papers

Recently, Suetsugu $\textit{at al.}$ reported microscopic signatures of an imaginary charge density wave (iCDW) and TRSB in CsV$_3$Sb$_5$ at $T^* \approx 120$ K, attributing nuclear quadrupole resonance (NQR) linewidths and asymmetric Zeeman-perturbed NQR (Zp-NQR) lineshapes to chiral loop currents in [arXiv:2605.05101; https://doi.org/10.1038/s41567-026-03339-8]. In this Comment, we demonstrate that these observations are not evidence of exotic physics but are instead fully explained by crystalline mosaicity and pre-transitional CDW fluctuations. Through exact diagonalization of the full nuclear-spin Hamiltonian, we show that the observed asymmetric lineshapes arise naturally from an angular mosaic spread in the Zp-NQR regime, completely reproducing the data without the need for internal magnetic fields. Furthermore, we reveal that the reported emergent local field ($h_{\text{loc}}$) is an artifact resulting from unjustified and unreported fitting constraints, and the use of an approximate perturbative model. Strikingly, we point out that this local-field model required for the proposed iCDW produces features that are absent in the data. Addressing the recent Reply by Suetsugu $\textit{at al.}$ [arXiv:2608.24927v1], we show that these core issues remain unresolved: the linewidth follows a standard Curie-Weiss law with no phase transition at $T^*$, and their definition of mosaicity overlooks well-documented strain-mediated lattice distortions. Most critically, when the full Hamiltonian is solved exactly and the artificial fitting constraints are removed, the inferred loop-current signature vanishes ($h_{\text{loc}} \to 0$). We therefore conclude that the claim of an iCDW state in in Ref. [arXiv:2605.05101; https://doi.org/10.1038/s41567-026-03339-8] is unsupported by the data, arising instead from incomplete spectral simulations and inadequate theoretical modeling.

Microscopic disorder in a coherent conductor is encoded in the magnitude of the transmitted current and in the energy- and channel-resolved structure of the scattering response. We develop a conductance-balanced learning framework for identifying microscopic disorder mechanisms from coherent quantum-transport spectra. Using armchair graphene nanoribbons as controlled multichannel tight-binding waveguides, we generate ensembles in which distinct disorder classes occupy the same intervals of integrated transmission, removing the dominant shortcut associated with average conductance. Within this constrained setting, we compare scalar transmission spectra with transmission-eigenvalue spectra, and use supervised classification, scale-normalizing controls, plateau-resolved tests, and principal-component analysis to identify the spectral structures that remain informative. The learned distinctions persist after normalization of the conductance envelope and are strongest in multichannel energy windows, where mode mixing and channel redistribution shape the scattering response. Principal components provide interpretable transport coordinates whose loadings identify the energy and eigenchannel sectors responsible for the dominant spectral deformations. The results establish a controlled AI-assisted protocol for learning disorder signatures from nonlinear quantum-scattering data.

Chiral molecular structure can couple to electron spin, leading to unexpected spin polarization effects. This Chirality-Induced Spin Selectivity (CISS) was first reported for DNA molecules adsorbed on gold but its microscopic origin remains unclear. We demonstrated though simulation that the exchange arising from electron-electron Coulomb interactions within the self-consistent mean field (Hartree–Fock) approximation can yield significant ($\sim 2\%$) spin polarisation for $3$-methylcyclohexanone adsorbed on Cu(111) amplifying a much smaller ($\sim 0.0014\%$) initial bias, consistent with experiment. Symmetry considerations ensure the result is physically meaningful, while its ab-initio nature ensures all parameters are physically realistic. This amplification is connected to existing studies on spin-symmetry breaking in Hartree–Fock, providing a new pathway for understanding the magnitude of CISS as an emergent phenomenon of interacting electrons.

The localization transition of the sub-Ohmic spin-boson model generates boson bath correlations that are, at low frequencies, analytically inaccessible to standard coherent-state-polaron variational ansatzes. In this paper, we introduce a “squeezed polaron” wavefunction incorporating generic Gaussian boson-boson correlations induced by the spin impurity. This gives the correct critical power-law scaling of bath observables near the localization transition together with a systematically improved ground state energy and a more accurate determination of the critical coupling. Our wavefunction captures the correct mean-field nature of the transition in the deep sub-Ohmic region. It also displays non-mean-field critical exponents in the shallow sub-Ohmic regime. Using the squeezed polaron as a starting point, we derive scattering phase shifts for bosons, and show how they encode the emergent energy scale that vanishes at the localization transition.

We present an efficient and scalable computational framework for pseudopotential Kohn-Sham density functional theory (KS-DFT) calculations using an enriched finite element (EFE) basis. The EFE basis is formed by augmenting the classical finite element (CFE) basis with compact atom-centered functions, which we term enrichment functions. The key idea is to combine the completeness of a finite element basis with the efficiency of an atom-centered basis. We orthogonalize the enrichment functions with respect to the underlying CFE basis to simultaneously improve the conditioning of the EFE basis and the efficiency of evaluating the inverse of the overlap matrix. To efficiently solve the Kohn-Sham eigenvalue problem, we employ a residual-based Chebyshev subspace iteration approach that is tolerant to approximations in the evaluation of the inverse of the overlap matrix. We demonstrate the accuracy of the framework as compared to the widely available DFT packages. For benchmark non-periodic calculations, ranging up to 39,083 electrons, the EFE basis offers a $5-7\times$ reduction in degrees of freedom over the CFE basis. As a result of this, EFE achieves a $5-9\times$ reduction in computational cost over the CFE basis. The EFE basis also provides a $4-5\times$ reduction in the required memory compared to the CFE basis, thus allowing for optimal utilization of computational resources. Finally, we demonstrate that the EFE basis affords good parallel scalability. Overall, the EFE basis offers a systematically convergent, fast, scalable, resource-efficient basis for pseudopotential DFT calculations.

Electrons trapped above the surface of superfluid helium are a disorder-free platform for investigating the formation and dynamics of low-dimensional Wigner crystals. A characteristic nonlinear transport feature of this electronic solid suspended above the helium surface is the Bragg-Cherenkov effect, in which the mobility of the smoothly moving crystal is limited by the coherent emission of helium surface waves (ripplons). The effect has been understood in the conventional Cherenkov setting in which the crystal moves at a constant speed. Here we report on transport measurements of electrons on helium confined in a microchannel geometry to investigate the non-equilibrium response of the Wigner solid when it is subjected to a high-frequency driving field. Surprisingly, the experiments reveal a strongly nonlinear transport response of the confined Wigner solid at frequencies nearly an order of magnitude larger than the ripplon frequencies contributing to the conventional Bragg-Cherenkov effect. We relate this observation to the coupling of the Wigner solid to ripplons with higher-order Bragg vectors, which gives rise to a dynamical friction that provides a mechanism for the observed high-frequency pinning.

The production of large-scale entangled states is one of the main goals of next-generation quantum technologies, with an immediate potential for applications in the context of entanglement-assisted quantum sensing. A very promising platform to achieve this goal is offered by ultracold spinor gases, made of atoms with a large internal spin sensitive to magnetic fields. Here we show that the native spin-changing collisions in a spinor Bose-Einstein condensate, combined with an arbitrary quadratic Zeeman shift, can generate scalable spin squeezing in the collective spin of the ensemble, following the universal paradigm of the celebrated one-axis-twisting model. Squeezing dynamics is driven by the quadratic Zeeman shift when this shift is small; and by the spin-changing collisions for large shifts, in the form of stroboscopic squeezing. Turning off the Zeeman shift freezes out the collective-spin dynamics, so that the ensuing collective spin dynamics can be uniquely governed by an external field to be sensed. Our theoretical results pave the way for the use of spinor Bose gases with a large spin in fundamental studies of entanglement, as well as in advanced metrological applications.

We train a neural-network Maxwell's demon to extract work from a model of an underdamped micromechanical cantilever subject to thermal noise. The demon, which periodically adjusts the position of a harmonic trap, is trained to maximize the power extracted under steady-state operation. When the demon is given the cantilever position and trap position as inputs it learns a refined version of an existing hand-designed protocol, yielding a substantial improvement in performance. When the demon receives the oscillator velocity as input it discovers a qualitatively different strategy that extracts substantially more work, close to the theoretical power bound. Analysis of the protocol shows that it implements cold damping: the trap position is displaced approximately linearly with velocity, producing an effective increase of the oscillator's damping coefficient and a reduction of its effective temperature. Thus a neural-network Maxwell's demon rediscovers a well-known cooling strategy from optomechanics, revealing a simple physical mechanism underlying near-optimal work extraction from thermal fluctuations in an underdamped system.

We have synthesized layered superconducting LiNbO$_2$ crystals through a bulk phase transformation from LiNbO$_3$ single crystals via CaH$_2$ reduction. As the Nb valence is reduced from 5+ to 3+, the material undergoes a structural transformation to the resulting product, LiNbO$_2$, which is accompanied by metallic behavior and a superconducting transition, Tc onset, as high as 14.4 K. Secondary ion mass spectroscopy (SIMS) and X-ray photoelectron spectroscopy (XPS) show that the resulting phase is hole-doped through de-lithiation during the reduction. Magnetization and AC susceptibility measurements from a tunnel diode resonator confirm the bulk nature of superconductivity with a superconducting volume fraction of approximately 77% and an upper critical field approaching 26 T. Our study demonstrates extreme hydride reduction as an effective method to induce phase transformations with non-topotactic pathways and can be used to synthesize bulk materials with exotic properties.

The Microscopic Dynamical Entropy (MDE) introduced in Ref. [1] describes irreversible relaxation of selected variables x within a finite closed Hamiltonian system of fixed total energy E. Here we extend the framework to arbitrary total-energy distributions and time-dependent Hamiltonians. This allows work interactions with external agents or protocols, crucial in stochastic and classical thermodynamics, and driven systems more generally, to be addressed directly. The central step is to reduce the full microscopic description in terms of selected variables x and unmonitored variables y to one in terms of the selected variables and the instantaneous total energy (x,E). The unmonitored degrees of freedom y in Y enter through their conditional phase-space volume (CPV) $\Omega_Y(x,E,t)$. This construction allows work and heat to be defined directly for finite Hamiltonian composites, including cases where Y is so small that its temperature is not well defined. We demonstrate monotonic MDE growth, corresponding to the macroscopic second law, under mixing and time-scale separation even for driven systems with arbitrary energy distributions. At trajectory level, we derive detailed and integral fluctuation relations for the MDE, generalising standard large-bath results. We verify these numerically in a driven few-particle Hamiltonian system, showing the emergence of stochastic thermodynamics for collective coordinates, such as the centre-of-mass position, even in closed systems with only ten or twenty degrees of freedom. Physically, these fluctuation relations connect irreversibility to the change in the number of unmonitored microstates compatible with initial and final data for the observed coordinates. Together, our results provide a finite-system Hamiltonian foundation for the emergence of classical and stochastic thermodynamics and extend their applicability to surprisingly small heat baths.

We show fast mixing of Glauber dynamics for certain quadratic Gibbs measures with large external fields. The main ingredient is an overlap condition that allows us to control correlation matrices uniformly over all pinnings, by controlling norms of small submatrices of the interaction matrix. Using stochastic localization, we then obtain a lower bound on the spectral gap and, consequently, polynomial-time mixing of Glauber dynamics. As a direct application, we consider the Sherrington-Kirkpatrick model, whose interaction matrix is a scaled GOE matrix. For this model, we show that for any fixed finite inverse temperature $\beta$, there exists a strength of external field $\theta$, not depending on the size of the system, for which Glauber dynamics mixes in polynomial time (with high probability on the draw of the interaction matrix).

We present a comprehensive computational study of driven quantum dot arrays in a square lattice configuration, subject to an external magnetic field and coupled to a cylindrical far-infrared photon cavity. The driving is introduced through a harmonic modulation of the full electron-photon interaction, therefore including both paramagnetic and diamagnetic contributions. The electron-electron Coulomb interactions are treated within density functional theory, while the electron-photon coupling is modeled using a many-body configuration interaction approach at each iteration of the density functional. By exploiting the unique properties of the cylindrical TE$_{011}$ cavity mode, we demonstrate selective enhancement of diamagnetic two-photon transitions. Our results reveal that the effectiveness of harmonic modulation of the electron-photon interaction is strongly dependent on both the driving frequency and the electron occupation number per dot. When the driving frequency approaches twice the cavity photon frequency, the system exhibits resonant behavior characterized by efficient photon pumping, occupation of higher-order photon replicas, and activation of collective radial Coulomb breathing modes. These findings establish a controllable mechanism for manipulating photon states in coupled quantum dot-cavity systems and provide insights into the interplay among harmonic modulation, photonic excitations, magnetic confinement, and many-body electron correlations in dimensionally reduced nanostructures.

Drying of nanowire-laden elongated droplets is a ubiquitous process in printed electronics fabrication, where the resulting deposition pattern critically determines device performance by controlling nanowire alignment, connectivity, and percolating charge-transport pathways. However, the physical understanding of evaporation-driven deposition is still largely derived from studies of spherical droplets on homogeneous substrates. This gap limits the ability to predict and control deposit morphology in realistic printing scenarios. Here, we use mesoscale lattice Boltzmann simulations to investigate the drying of nanowire-laden elongated droplets on wettability-patterned substrates, focusing on the effects of droplet geometry, nanowire interactions, and nanowire length. The elongated droplet geometry is found to intrinsically induce distinct axial and transverse inhomogeneities in the final deposit. Increasing the effective attraction between nanowires, which mimics changes in surface chemistry or solvent conditions, can improve electrical connectivity but also promotes clustering and local ordering, reducing structural uniformity. In contrast, increasing nanowire length yields a dual benefit by improving long-range connectivity while simultaneously enhancing deposit homogeneity. Our findings provide design guidance for balancing electrical transport and structural uniformity in evaporation-driven printed electronics.

Chiral phonons are attractive for spintronics applications, however, their zero-field generation in conventional antiferromagnets is forbidden by combined parity and time-reversal ($\mathcal{PT}$) symmetry. Here we demonstrate the emergence of chiral phonons in $\mathcal{PT}$-breaking altermagnetic systems at zero field arising from relativistic magnon-phonon coupling. Focusing on the prototypical altermagnet CrSb, we utilize first-principles methods to calculate the hybridized magnon-polarons across the complete Brillouin zone. We show that this coupling imprints an altermagnetic $g$-wave symmetry directly onto the phonon angular momentum. Furthermore, we demonstrate anomalous spin and phonon angular momentum Nernst responses arising from finite Berry curvatures. These findings establish that chiral lattice dynamics can arise in compensated magnetic ground states without requiring external fields, positioning bulk altermagnets as material candidates for zero-field spin caloritronics and chiral phononics.

We introduce a Microscopic Dynamical Entropy (MDE) for Hamiltonian systems, defined with respect to a chosen partition of degrees of freedom into a system X and its environment Y. The construction is based on the conditional phase-space volume (CPV), or conditional Boltzmann entropy, associated with the unmonitored degrees of freedom Y. The MDE is a microscopically defined entropy functional of the marginal distribution $\rho_X(t)$, obtained by discarding conditional microscopic information associated with Y from the Gibbs entropy of the joint XY system, while retaining exact Hamiltonian dynamics. This construction clarifies the microscopic origin of thermal entropy. The dependence of MDE solely on $\rho_X(t)$ is consistent with the thermodynamic assumption that the entropy increment of a heat bath Y depends on its heat content and temperature, not on details of its probability distribution. Indeed, the MDE recovers dS = dQ/T connecting entropy increments to heat flow between system and environment. More generally, it provides a consistent description of irreversible relaxation under exact Hamiltonian dynamics, while permitting transient entropy decreases in small systems and in spin-echo type protocols. Under time-scale separation between X and Y, the MDE becomes strictly monotonic in time, recovering the familiar structure of irreversible thermodynamics. The MDE can foreshadow thermodynamics even in a small isolated Hamiltonian system, if X is a well chosen subset of its degrees of freedom. An example is the centre of mass of interacting particles confined to a box. Even for as few as N=10 particles, the MDE increases during relaxation towards a maximum at equilibrium, with increasing monotonicity at larger N. Taken together, our results show that the MDE offers a microscopic interpretation of nonequilibrium thermal entropy and its time dependence within exact Hamiltonian dynamics.

The low-frequency dielectric response of liquid water is commonly described by a dominant Debye relaxation together with additional faster contributions whose microscopic origin remains debated. Here we show that the dielectric function of water between 0.14 and 1.21 THz can be represented by a collective Debye relaxation plus a Drude-Smith term constrained to the zero-dc-conductivity limit. The Drude-Smith spectral weight increases upon heating pure H2O from 20 C to 50 C and decreases upon isotopic substitution (D2O at 20 C vs. H2O at 20 C). Molecular dynamics simulations including nuclear quantum effects show correlated changes in the population of water molecules with unequal numbers of donated and accepted hydrogen-bonds. Ab-initio-based spectra calculations further indicate that the ~0.1-1 THz response contains both nuclear-motion and explicit electronic-polarisation/charge-redistribution contributions. We therefore interpret the excess low-frequency THz response as a localised, mixed nuclear-electronic dielectric response correlated with transient donor-acceptor imbalance in the hydrogen-bond network.

The topological charge and its density are related to the spin vorticity, while the spin vorticity is a part of full vorticity of the medium. The full vorticity is related to an integral of motion called the hydrodynamic helicity. Relation between two integrals of motion (the topological charge and the hydrodynamic helicity) is traced. The role of the spin-current model of the electric polarization formation due to the specific spin distribution in the helicity conservation is demonstrated. The reverse spin-current model is suggested to demonstrate the contribution of the polarization in the spin evolution equation, its importance for the helicity conservation is shown as well. Spin-field model of the electric polarization is the second model for the electric polarization (the deformation, firstly) formation due to the specific spin distribution, which appears from the same principles, but it has nonstationary origin. Moreover, the reverse spin-current model gives a mechanism for the spin structure formation due to the electric polarization in the system. It also appears as the requirement for the conservation of the helicity and the topological charge.

Majorana zero modes are the hallmark of topological superconductivity. In one-dimensional systems, these zero modes are usually introduced in the context of gapped, mean-field models that do not conserve particle number, such as the Kitaev chain. By non-locally encoding a conventional fermion across spatially separated Majorana zero modes, these systems become inherently immune to local decoherence. In this work, we show that signatures of Majorana edge physics persist in a number-conserving, gapless Luttinger liquid of spinless fermions with short-range attractive interactions. We identify the two-point correlator as a sharp diagnostic, revealing an edge-to-edge revival whose sign depends on the fermion-number parity. This revival is robust in the thermodynamic limit, and persists in the excited states of the system and at different fillings. A simple particle-hole ansatz for the ground state of the system with an odd number of fermions captures the physics of the system for a wide range of interaction strengths, interpolating between the free-fermion limit and the strongly interacting Majorana regime. Finally, we propose a concrete protocol to realize this model with ultracold dipolar molecules or atoms in an optical lattice, and to detect the revival via beam-splitter interferometry, opening an experimental route to Majorana physics beyond the conventional gapped-superconductor paradigm.

The Al-V alloy system contains a number of phases including several with complex structures and at least two exhibiting sites of partial occupation. Through electronic density functional theory-based total energy calculations combined with methods of statistical mechanics, we examine the relative stability of phases at finite temperatures. We construct composition-continuous free energy models for the V-rich solid solution and for one of the complex intermetallic phases. In the V-rich region, we identify three ground states that transform to the solid solution at elevated temperatures. We also suggest that \phase{Al}{V_3} takes the Al15 structure as an intermediate-temperature phase stabilized by anharmonic vibrational free energy.

While the anomalous Hall effect was proposed as a transport fingerprint of altermagnets, it originates from the spin-orbit coupling-induced net magnetization, corresponding to a distinct magnetic phase termed spin-orbit magnetism. However, the microscopic mechanism enabling spin-orbit magnets to yield a prominent anomalous Hall response despite a vanishingly small net magnetization remains elusive. Here, by employing oriented spin group theory and spin-orbit-coupling tensor expansion, we systematically disentangle the perturbative behaviors of orbital and spin magnetizations with respect to spin-orbit coupling in altermagnets. Remarkably, we find that only if the opposite-spin sublattices are connected through a fourfold rotation, the orbital and spin magnetizations exhibit distinct perturbative orders. In these altermagnets, we further discover a coaxial Hall effect characterized by the induced spin and orbital magnetizations aligning parallel to the Néel vector, which we further demonstrate by first-principles calculations in the altermagnet KV$_{2}$Se$_{2}$O. This effect holds great promise for achieving deterministic switching of the Néel order under weak external fields. Our work provides a systematic symmetry approach to identify potential altermagnetic candidates combining a large anomalous Hall effect with minimal net magnetization, paving the way for high-performance, stray-field-free spintronic applications.

Density functional theory (DFT) often is the method of choice for simulating the electronic properties of extended solids and surfaces from first principles due to a favorable compromise between accuracy and computational cost. In the field of heterogeneous catalysis, DFT is indispensable for deriving mechanistic insights and understanding trends in surface reactivity. The accuracy of DFT for surface reaction energetics depends strongly on the exchange-correlation (XC) approximation. We show here that optimization of such XC functionals for surface binding energies can lead to a worse description of surface reaction barriers, unless important physical exact conditions are fulfilled.

The unavoidable dissipation of heat in electronic nanostructures is a crucial problem, specially when their operation requires low temperatures. It demands finding devices able to control and redirect the excess heat, ideally without perturbing the electrostatic environment. We propose three-terminal junctions working either as thermal routers or as thermal single-pole double-throw switches controlled by a single external knob. Two models are discussed based on resonant tunneling energy filters and different couplings to the heat source: (i) Phase-coherent contact via a scanning tip modulates the relative amount of the two output currents via position-dependent quantum interference; (ii) Coupling via a gate voltage tunable filter selectively switches one of the currents in the presence of dephasing. In the later case, we find that the heat flow using ideal filtering is bounded by fourth the open conductor current.

Twisted bilayer graphene reconstructs from weak breathing corrugation to large common bending near the magic angle, but the origin of this collective crossover has remained unclear. Here we show that the crossover is a soft-mode condensation of layer-symmetric $A_1$ moiré flexural phonons: these modes soften on the breathing branch, lose stiffness near the magic angle, and freeze into the bending morphology. We call this mechanism Moiré Phonon Condensation (MPC). At $\theta=1.08^\circ$, it is extremely surprising that displacements of all 11164 atoms in the moiré supercell, with a maximum atomic position shift of 2.30 Angstrom, is captured by only two $A_1$ phonon modes at more than $99.5\%$ spectral weight. A first-harmonic continuum theory identifies a dimensionless control parameter of the phenomenon, showing that as the twist approaches the magic angle, the growing moiré length scale amplifies a smooth stress-bending competition until the flexural stiffness changes sign. Mode-resolved tight-binding calculations further show that the condensed phonon coordinates are electronically active. This work identifies MPC as a twist-controlled structural order parameter for moiré reconstruction.

We investigate how magnetic fluctuations influence spin-orbit torque in ultrathin-film magnetic heterostructures whose Curie temperature $T_C$ is suppressed by confinement. Above $T_C$, the damping-like contribution to spin-orbit field is significantly enhanced while the field-like contribution is suppressed, with the two contributions exhibiting opposite field dependencies. We show that these behaviors are consistent with fluctuation driven mixing between the longitudinal and transverse interfacial spin conductances, which enhances absorption of transversely polarized spin current by the ferromagnet. This mechanism can be activated below $T_C$ by engineering the microscopic magnetic state and by harnessing spin current-generated short-wavelength magnons, suggesting a spintronic analog of heat-assisted magnetic recording.

We consider how the presence of conserved charges affects memory in a classical stochastic process, the symmetric exclusion process, with an observer constantly measuring a single site. We find that the observer's measurement record becomes Markovian (i.e., loses memory) on a timescale that depends on their knowledge of the global charge, namely the total particle number. In particular, when the global charge is unknown a priori, the observer's time series Markovianizes on a timescale constrained by their ability to learn it from their measurement record. Augmenting the observer's record with bulk measurements drives a charge-learnability transition between charge-fuzzy and -sharp phases. We show that the memory timescale tracks the learnability timescale, diverging in the fuzzy phase and remaining finite in the sharp phase.

Temperature plays a crucial role in solid-state materials synthesis, but there is currently no mechanistic theory to explain or predict which temperature is best to conduct a solid-state reaction. Reactions between powder precursors are conventionally assumed to be slow diffusion-limited processes; however, recent in situ experiments show that solid-state reactions can complete in minutes above a critical onset temperature. Here, we present evidence that a transient liquid phase forms above the metastable eutectic temperature, and that this non-equilibrium liquid serves as a fast diffusion medium to intermix precursors and initiate a solid-state reaction. This thermodynamic principle is agnostic to the structure or chemistry of the reactants, and can be applied towards the synthesis and manufacturing of a wide range of complex materials.

Quantum circuits under sufficiently weak monitoring purify on a timescale $T_P$ exponentially long in the system size. This slowness underlies a universal purification dynamics, whose quantitative description has so far required the replica trick, with a delicate analytic continuation. We show that monitored Clifford circuits on $L$ qudits of prime dimension $q$ bypass this construction entirely: in the scaling limit at fixed $x = t/T_P(L)$, purification reduces to the Markovian decay of the density-matrix rank, an exactly solvable death process descending from infinity. We compute the full scaling functions in compact form: all Rényi entropies collapse onto a universal curve $\langle S(x) \rangle$. Exact stabilizer simulations at $q=2,3,5$ confirm the predictions, with no fitting parameter for the global model and $T_P$ as the only fitted scale for local brick-wall circuits. Also, the replica problem amounts to a tilted version of the same Markov process, in agreement with exact computations from the Clifford commutant. Finally, the quantization of the rank leaves two hallmarks that distinguish Clifford dynamics from generic monitored circuits: the entropy fluctuations saturate at short scaled times $x\to0$ to an $O(1)$ variance, instead of vanishing, and observables develop a temporal modulation periodic in $\log_q x$, which cannot be captured by the replica approach.

We evaluate the utility of the spin-zero manifold of an exchange-coupled array of $N$ spins for tasks in quantum computation and quantum simulation. Since pairs of electrons can be readily initialized into a product state of singlets in semiconducting quantum dot arrays, the full spin-zero manifold is available with exchange-only control, providing a Hilbert space of approximate dimension $2^N/(N/2)^{3/2}$, asymptotically close to the $2^N$ dimension of the full spin Hilbert space. Leveraging the spin-zero manifold enables larger computational space in a given array compared to traditional exchange-only control, in which spin arrays are organized into modular units of $n$ spins comprising $N/n$ encoded qubits, limiting to the exponentially smaller Hilbert dimension $2^{N/n}$. Here we focus on benchmarking metrics for this resource utilization by generalizing cross-entropy benchmarking, mirror benchmarking, and out-of-time-ordered correlators to this system. We show that operating in the spin-zero manifold can accelerate the realization of computational quantum advantage applications in semiconductor-based spin qubits.

Accurate knowledge of the on-chip temperature is essential for understanding and optimizing the performance of superconducting qubits, yet direct thermometry at millikelvin temperatures remains challenging. While qubits themselves are sensitive to the temperature of their environment, other factors may affect the qubits` effective temperature, and using them as thermometers with any accuracy requires specialized measurement protocols and qubit designs, limiting their practicality for routine diagnostics and adding complex infrastructure to any hardware testing apparatus. Here we demonstrate a complementary on-chip thermometry method based on superconducting Dayem bridges that are integrated on the same chip as transmon qubits. By extracting the critical current of the Dayem bridge from I-V measurements, we obtain a local, quantitative measure of the chip temperature without the need for microwave calibration or qubit-specific control sequences. To demonstrate the utility of the Dayem bridges as thermometers, we fabricate them in-situ with qubits on the same chip, calibrate the Dayem bridge critical current as a function of temperature, and characterize its resolution and stability at cryogenic temperatures. We additionally perform simultaneous measurements of the Dayem bridge thermometer and qubit excited-state population, and show agreement over the relevant temperature range, validating the method against established qubit thermometry. Furthermore, we correlate the independently measured chip temperature with qubit energy relaxation and dephasing times, demonstrating the utility of this approach for diagnosing temperature-dependent decoherence mechanisms. These results establish integrated Dayem bridges as a simple, non-invasive, and scalable tool for cryogenic hardware development, and on chip thermometry in superconducting quantum circuits.

Wilson loop operators in Chern-Simons theory have revealed profound links between quantum field theory, the fractional quantum Hall effect, topology, conformal field theory, and string theory. In Chern-Simons theories with charge conjugation symmetry, we construct a new class of observables: codimension-two monodromy defects around which fields return to themselves up to charge conjugation. Whereas Wilson loops are labeled by integrable representations of an untwisted affine Lie algebra, monodromy defects are labeled by those of the corresponding twisted affine algebra. The modular and fusion data of these two algebras determine the exact correlation functions of Wilson lines and monodromy defects, which together furnish a $\mathbb{Z}_2$-crossed braided tensor category. The spectrum of line defects in Chern-Simons theory thus gives a physical realization of every algebra in Kac's classification of affine Lie algebras: untwisted for Wilson loops, twisted for monodromy defects. We also determine the exact 't Hooft expansion of monodromy defects in $SU(N)_k$ Chern-Simons theory and identify their holographic duals in topological string theory. The insertion of the lightest monodromy defect has a striking effect: it replaces the resolved conifold background of the Gopakumar-Vafa duality by a specific orientifold of the resolved conifold, transmuting the dual theory of oriented strings into one of unoriented strings. Each excited monodromy defect is then realized as a collection of branes in the orientifold background, with the brane content determined by the representation of the twisted affine algebra that labels the defect.