Papers

Controlling valley degrees of freedom with mechanical strain is a promising approach for solid-state information processing. Current theoretical literature routinely predicts strain-tuned valley splitting at the microscopic level but rarely evaluates whether these quantum predictions remain statistically recoverable in realistic macroscopic devices. This manuscript establishes a fully classical, partial differential equation-constrained multiscale inverse framework for quantifying the device-level identifiability of predicted strain-tunable valley effects in two-dimensional magnetic heterostructures, demonstrated here for a molybdenum disulfide and chromium tribromide heterostructure. First-principles structural relaxations confirm a chiral $C_3$ point-group symmetry which mathematically reduces the relevant exchange-strain coupling tensor to a single scalar. A partial differential equation-constrained adjoint-state architecture successfully bridges continuum elastodynamics to valley-resolved anomalous Hall transport. Density functional theory yields a coupling estimate of $\eta \approx -0.07$ meV whose 95% confidence interval is consistent with zero. Evaluating this specific coupling magnitude against established thermal noise and velocity saturation limits defines a safe operating window bounded between 262.0 and 22,337.6 V/cm. Rather than asserting a confirmed nonzero material property this bounded operational window functions as a precise diagnostic threshold. Deploying this rigorous statistical identifiability framework provides a necessary mathematical filter to determine the true experimental viability of theoretically predicted two-dimensional materials before complex physical fabrication.

Molecular hydrogen is predominantly formed on dust-grain surfaces in the interstellar medium, where relative gas-dust motion can arise in dynamically active environments. While the dependence of H$_2$ formation on grain temperature and surface properties is well studied, the impact of gas-dust drift has received little attention. We investigate how gas-dust drift modifies H$_2$ formation, focusing on the competition between the drift-enhanced H-atom collision rate and reduced sticking at higher impact energies. We use an event-driven kinetic Monte Carlo model that follows individual H atoms on spherical silicate and carbonaceous grains, including adsorption, surface migration, thermal desorption, and Langmuir-Hinshelwood (LH) and Eley-Rideal (ER) reactions. Drift is described by a shifted Maxwellian velocity distribution, and we compare constant and impact-energy-dependent sticking probabilities. Drift produces increasingly anisotropic distributions of adsorbed H and H$_2$ formation across the grain surface. Assuming constant sticking, increasing drift enhances H$_2$ formation through the higher collision rate, with efficiencies up to $\epsilon=0.3-0.4$. With energy-dependent sticking, strong drift instead suppresses formation on both materials, reducing efficiencies to $\epsilon=0.01-0.03$. Carbonaceous grains remain efficient to higher dust temperatures than silicate grains. ER reactions dominate over most of the investigated parameter space and become increasingly important at strong drift as the reduced surface population suppresses LH reactions. Thus, enhanced collision rates under gas-dust drift do not necessarily increase H$_2$ formation. Models of dynamically active environments should account for both relative gas-dust velocities and their effects on sticking.

The experimental observation of the fractional quantum anomalous Hall effect in rhombohedral graphene multilayers has raised questions about the nature of the fractional Chern insulator (FCI) states and the role of the moiré potential. In this Letter we develop a composite fermion (CF) description and discuss how moiré modulation and Coulomb interactions stabilize the FCI ground states. Under a flux-attachment transformation and mean-field approximation, the CF spectrum forms Landau levels that are further split by the moiré potential. At moiré filling fractions in the Jain sequence, an integer number of CF bands are occupied, resulting in an incompressible ground state with fractionally quantized Hall response. Remarkably, when the attached flux opposes the Berry curvature of the conduction band of rhombohedral graphene, the CF Landau levels are widely spaced in energy and delocalized across layers, leading to a reduced density of states that helps protect the CF mean-field state and amplifying effects of the moiré potential acting on the layer away from the doped electrons. Interactions between CFs further enlarge the moiré-induced band gap and stabilize the FCI ground state. Our work sheds light on the nature of the FCI states in rhombohedral graphene and provides a new theoretical framework for further studies.

Designing expressive quantum circuits for the variational quantum eigensolver (VQE) is a central challenge in simulating interacting many-body systems. Even symmetry-preserving (SP) circuits need not access the full many-body symmetry sector. We demonstrate this explicitly for the spin-$1/2$ XXZ and Hubbard models, where Hamiltonian-inspired nearest-neighbor (NN) SP circuits generate restricted dynamical Lie algebras (DLAs). While these restricted manifolds can accurately represent the ground state near the free-fermion limits, $J_z=0$ for XXZ and $U=0$ for Hubbard, interactions expose inaccessible many-body directions and severely limit VQE performance even at large circuit depth. Remarkably, a minimal modification of the generator connectivity can reconstruct the full orthogonal DLA within all relevant symmetry sectors studied in this work. For XXZ model, the addition of only one SP next-to-NN single-excitation connection triggers this dramatic reconstruction, whereas the Hubbard case requires a SP correlated double-excitation;–showing that the relevant connectivity can extend from the spatial lattice to many-body configuration space. This reconstruction enlarges the tangent space and accessibility of the energy-lowering Hamiltonian direction, leading to near-unit ground-state fidelity in VQE simulations. Our results establish a direct link between generator connectivity and variational accessibility and suggest a broader circuit-design principle: identify minimal symmetry-preserving generators that enlarge the accessible many-body space rather than increasing circuit depth alone. This perspective may have broader relevance for quantum many-body simulation at the interface of condensed-matter physics and quantum computing.

One-dimensional SM-SC hybrid nanowires with Rashba spin-orbit coupling and applied Zeeman field can support Majorana zero modes (MZMs) at the ends of the wire. In finite-length systems, residual wave-function overlap between the end modes produces an energy splitting. In a two-sided tetron qubit, composed of a pair of parallel Majorana wires coupled by a trivial SC backbone in the middle, this splitting limits the parity lifetime associated with Majorana pairs involving both wires and the coherence of the qubit, adversely affecting measurement-based braiding and readout operations. Here, we propose a one-sided tetron made of four parallel Majorana wires connected at a common end by an SC backbone. In the topological phase, the free wire ends host four MZMs that define the topological qubit, while the Majoranas localized near the opposite ends hybridize through the backbone and acquire finite energy. To study the basic hybridization mechanism, we consider a simpler two-wire subsystem, i.e., half of a one-sided tetron, which we call a doublon. In a doublon, the backbone, or bridge, strongly hybridizes the two Majorana modes at the connected end and shifts them away from zero energy, while the modes at the free ends form a near-zero energy fermion. We show that the splitting of the surviving MZM pair can fall by about two orders of magnitude compared to the splitting energies in a two-sided tetron, thereby dramatically increasing the parity lifetimes. Thus, the one-sided tetron ensures a suppression of the Majorana overlap comparable to doubling the length of the corresponding two-sided tetron.

In a (1+1)-dimensional QFT with non-invertible symmetry, the fusion rules of topological lines are often the most accessible data, yet they do not fully determine whether the symmetry is anomaly-free, i.e. whether it admits trivially gapped phases. Such phases are characterized by fiber functors of the corresponding fusion category. Building on Tannaka duality, we extract fiber functors from the fusion ring alone by solving simultaneously for monoidal structure maps and tensor automorphisms. This allows us to find categorifications admitting a fiber functor without solving the pentagon equations directly. We test this procedure on the known Tambara–Yamagami ring of $\mathbb{Z}_2\times\mathbb{Z}_2$. Our main result concerns the rank-11 fusion ring shared by the representation categories of the two extraspecial groups of order 27, which has a multiplicity 3 channel and is relevant to self-triality. In both cases we find more than one fiber functor, i.e. several non-invertible SPT phases. We use the explicit data of these fiber functors to derive the $F$-symbols of the two representation categories in a compact form depending on a non-degenerate alternating bicharacter and an invertible object $\epsilon$. Using the reconstructed data, we compute the anomalous algebra on the interface between two different SPT phases.

The Heisenberg antiferromagnet on the fcc lattice is a canonical example of frustration. The fcc lattice is but one of an infinite number of close-packed structures, all of which have the same frustration-inducing local geometry. In this letter, we demonstrate a hidden symmetry that relates classical magnets on all close-packed lattices. This symmetry derives from a similar property in tight binding models that may explain the disordered low-temperature structures of lithium and sodium metals. In magnets, the symmetry holds when couplings are restricted to nearest ($J_1$) and next-nearest neighbours ($J_2$). It guarantees that all close-packed lattices are equivalent at the Luttinger-Tisza level. For any given values of $J_1$ and $J_2$, they have the same ground-state energy. Their ground state momenta are identical when projected onto the stacking plane. We construct a unified phase diagram as a function of $J_1$ and $J_2$ couplings for Heisenberg, XY and Ising magnets on any close-packed lattice. In each phase, the ground-state degeneracy is the same on all close-packed lattices, even after accounting for multi-Q spirals. This phase diagram can be easily adapted to any magnet composed of stacked triangular layers with similar couplings. Fluctuations above the classical ground state(s) are not related by any symmetry. This suggests that close-packed structures can show interesting differences in order-by-disorder selection.

We study magnets composed of molecules with atoms interacting via $SU(N)$-invariant two-body interactions. Atoms carry states transforming in generically different irreducible representations of $SU(N)$, and the interaction strength between atoms depends on the specific atoms involved. We derive the thermodynamics of these magnets in the mean-field approach, and find that they can exhibit mixed ferro-antiferromagnetic behavior. We present a full analysis of the simplest nontrivial case of molecules consisting of two atoms in the spin-$j$ representation of $SU(2)$, which generalizes conventional magnetic systems, and derive its phase structure and transitions.

Floquet topological order (FTO) extends topology beyond equilibrium, giving rise to phenomena, such as the dynamical transmutation of anyons. Here, we realize $\mathbb{Z}_N$ FTO in a generalized Kitaev honeycomb model with clock degrees of freedom using a three-step periodic drive. The driven system admits an emergent description in terms of constrained parafermions coupled to conserved $\mathbb{Z}_N$ gauge fields. At the boundary, the drive generates chiral parafermionic Floquet edge modes. We resolve their propagation through correlation functions, characterize their fractional quantum-information transport through the radical chiral unitary index, and use their dynamics to probe exchange statistics. In the bulk, we explore the dynamical anyon transmutation with a non-equilibrium loop order parameter. At a Floquet sweet spot, where the drive becomes Clifford, these phenomena can be accessed using stabilizer simulations. Short-time matrix-product-state simulations away from this point show that the chiral edge response persists at accessible times. Our results establish $\mathbb{Z}_N$ Kitaev models as a setting for exploring intrinsically non-equilibrium topological phenomena on qudit-based quantum processors.

Motivated by the recent observation of spatially modulated screening in different paramagnetic heavy-fermion materials, we propose a theoretical mechanism for the emergence of such hybridization waves in frustrated Kondo lattices with no magnetic order. By applying a parton mean-field theory and a perturbative calculation to a minimal Kondo-Heisenberg lattice model, we demonstrate that a heavy Fermi liquid can naturally develop hybridization waves when it approaches a quantum phase transition where Kondo screening breaks down and the local magnetic moments form a Dirac spin liquid. We relate the strength of this mechanism to a kinematic condition on the electronic and spinon band structures and show that the spatial periodicity of the hybridization wave is set by a momentum $\vec{Q}$ connecting the nodes in the dispersion of the Dirac spinons to low-energy portions of the electronic band structure.

Exponentially small spectral gaps are the central obstacle to adiabatic quantum annealing, yet whether such bottlenecks demand correspondingly complex entanglement remains unclear. We show that gap scaling and entanglement complexity need not be linked. Conventional first-order transitions combine exponentially small gaps with bounded $O(1)$ bipartite Schmidt rank, even though the critical states retain global multipartite correlations, while continuous transitions combine polynomially closing gaps with logarithmically growing entanglement. We show that each pairing can also be inverted: in a known first-order transition in a staggered-field antiferromagnetic Ising chain the gap closes polynomially despite bounded Schmidt rank, while we construct a mirror-twin manifold model whose gap closes exponentially even as its entanglement entropy grows logarithmically with system size. We derive bounds connecting Schmidt rank to Hamming-space geometry, and identify manifold density and connectivity as the ingredients that determine which combination occurs. These results show that entanglement complexity alone cannot characterize annealing difficulty, and point toward a broader search for quantum resources that capture the geometry of state evolution in Hilbert space.

We construct a family of chaotic brickwork quantum circuits exhibiting superdiffusive transport with dynamical exponent $z=3/2$ in the full Kardar–Parisi–Zhang (KPZ) universality class. This is enabled by the equilibrium current associated with a inhomogeneous conserved density having a nontrivial dependence on the chemical potential. Using nonlinear fluctuating hydrodynamics, we derive the propagation velocity, broadening scale, and universal scaling form of the charge correlation function from microscopic equilibrium properties. Tensor-network simulations of a two-site spin-$1$ (qutrit) circuit reproduce these parameter-free predictions, including the full stationary KPZ profile. We further construct a three-site spin-$\frac12$ (qubit) circuit, where transport varies from diffusive to superdiffusive with the chemical potential, while long-lived coherent quasiparticles delay the convergence of the profile to the KPZ scaling form. Our results establish that KPZ superdiffusion in quantum systems is not restricted to fine-tuned integrable models.

Direct-write pattering, using chemical vapor deposition through a nozzle, enables localized film growth using high-purity precursors standard to the electronics industry. Yet, achieving sub 100 $\mu\mathrm{m}$ feature control has been limited by nozzle design and unquantified precursor surface diffusion. Here, we report a direct-write chemical vapor deposition platform that employs a 10 $\mu\mathrm{m}$ tip diameter glass micro-nozzle mounted on a scanning stage above a heated substrate in ultra-high vacuum. Using this approach, we demonstrate the continuous single-pass writing of 500 $\mathrm{nm}$ thick metallic aluminum lines with a 30 $\mu\mathrm{m}$ linewidth on titanium nitride-coated silicon. This capability enables maskless, localized growth under systematically varied deposition conditions on a single substrate. To analyze the resulting deposit profiles, we introduce a transport framework coupling Knudsen gas emission from the micro-nozzle with surface diffusion to extract the effective precursor diffusion length, $L_d$. $L_d$ captures the combined impact of precursor surface mobility, residence time, substrate temperature ($165^{\circ}\mathrm{C}$ to $205^{\circ}\mathrm{C}$), growth duration, and nozzle height, contracting from 17.4 $\mu\mathrm{m}$ down to 3.2 $\mu\mathrm{m}$ at elevated temperatures. These results establish $L_d$ as a quantitative parameter for evaluating laterally confined chemical vapor growth and predicting feature resolution limits. This approach provides a practical methodology to measure and quantify precursor surface transport in localized film synthesis.

Nonreciprocal mechanical response is usually associated with built-in directional couplings, structural chirality, or external driving. Whether an achiral active body can instead generate and reverse such directionality through its own motion remains less clear. Here we show that spontaneous rotation makes an active elastic ring with reciprocal passive interactions mechanically nonreciprocal. Off-center elastic forces reorient propulsion, coupling deformation back to motion. Reversing the rotation reverses the antisymmetric response, while a compensating control preserves finite directionality but strongly suppresses the near-Hopf resonance. Approaching Hopf, the selected response grows inversely with distance to onset and becomes a self-sustained traveling deformation above threshold. Thus nonreciprocity is selected by the dynamical state, while active feedback controls its critical amplification.

Braiding and fusing anyons are fundamental to topological quantum computation, yet existing circuit protocols often employ ancillas and measurements. We determine the minimal circuit resources for performing such anyon operations in quantum double models of generic finite groups. Our approach braids anyons through a sequential unitary circuit without ancillas. Intuitively, this is obtained by deforming the underlying graph on which the anyons live. More generally, we introduce graph rewiring, a diagrammatic calculus that assigns a geometric interpretation to individual two-qudit gates and tracks their action on stabilizers. For fusion, we prove a general no-go theorem excluding purely unitary protocols for fusing unknown anyon types without introducing ancillas. Remarkably, we show such "input-agnostic" fusion is enabled by simply using a qudit reset. Hence, contrary to folklore, ancilla resources are not needed to braid or fuse non-Abelian anyons (non-Abelions). This work has implications in experimental efforts in error correction: our fusion protocol highlights reset as an underutilized primitive for error correction without the spacetime-overhead of ancillas and measurements.

The Sachdev-Ye-Kitaev model is a strongly interacting fermionic system that has been well-studied in condensed matter and high energy physics. It is highly quantum: Gaussian states are far from the thermal state (Hastings and O'Donnell, STOC'22) and representing the thermal state requires large polynomial-size quantum circuits (Anschuetz et al., QIP'25). Very recently, it was nonetheless proven that classical algorithms can estimate local thermal expectations at sufficiently high temperature in quasipolynomial time (Zlokapa, FOCS'26). We show that classical algorithms can in fact estimate local observables at all constant temperatures in polynomial time. Our techniques also extend straightforwardly to classical systems: we resolve an open question about computing thermal expectations of a classical spin glass up to its phase transition (Bencs et al., STOC'26). Our proof develops a fully rigorous quantum cavity method. Due to the success of the classical cavity method in optimization, sampling, inference and learning, we expect the quantum cavity method to find further applications of independent interest. As an example, we give a quantum algorithm that learns SYK Hamiltonians from the Gibbs state at any constant temperature with polynomial time and sample complexity.

We propose a four-level scheme for generating a uniform imaginary magnetic field for ultracold atoms using Raman coupling and state-dependent particle losses. Eliminating two lossy auxiliary states and subsequently projecting onto one of the two remaining Raman-dressed atomic states, we find that the atomic motion is affected by an imaginary vector potential which is engineered to have a constant curl corresponding to a spatially uniform imaginary synthetic magnetic field. We analytically derive the Gaussian wavepacket dynamics for atoms in such a synthetic magnetic field and study the width-dependent transport, unlike motion in a uniform real magnetic field. We find numerical agreement between the two-level non-Hermitian Hamiltonian and the adiabatic projection description, confirming the applicability of the latter adiabatic approach.

Fault-tolerant quantum computation typically relies on a fixed set of logical primitives, while realizing other desired operations can require substantial resources. We introduce irrep surface codes (ISCs), two-dimensional topological quantum error-correcting codes engineered to transversally implement a prescribed set of logical gates. The engineered gates only need to satisfy two conditions: (i) they generate a finite group, which, up to global phases, is forced by the Eastin-Knill theorem, and (ii) they are irreducible, meaning that any operator commuting with the set of gates must be proportional to the identity. This accommodates arbitrary finite groups of diagonal gates and arbitrary reversible classical gates, since each can be embedded into a larger irreducible finite group of gates. It also enables logical gates outside every finite level of the Clifford hierarchy. To incorporate these operations into surface-code computations, we further develop lattice-surgery protocols to transfer the encoded information between surface codes and ISCs obeying either of two sufficient conditions. Together, these results establish a systematic method for tailoring topological codes to desired logical operations and integrating them into conventional computations.

RuO$_2$ is a multi-orbital Fermi liquid for which an array of complementary experimental measurements has recently become available, making it a stringent testbed for quantitative many-body electronic structure theory. Using realistic dynamical mean-field calculations, we compute the spectroscopic and transport properties of RuO$_2$ in the paramagnetic state. We identify RuO$_2$ as a moderately correlated Fermi liquid and obtain (semi-)quantitative agreement with experiment for its optical conductivity, electrical resistivity, and thermopower. This broad agreement across complementary observables establishes a “precision” many-body description of RuO$_2$ and allows remaining discrepancies to be identified as meaningful tests of the theory. In particular, the calculated electronic thermal resistivity significantly undershoots the experimentally inferred low-temperature thermal resistivity, raising an important puzzle concerning the relative relaxation of charge and heat currents in the Fermi liquid regime. We explore low-temperature electron-phonon scattering as a possible mechanism for resolving this discrepancy, while a fully quantitative description remains an open problem. More broadly, our results demonstrate the power of combining precision DFT+DMFT calculations with complementary experimental probes to build and critically test quantitative descriptions of correlated quantum materials.

We study the emergent randomness in projected ensembles generated by dual-unitary circuits. Specifically, we consider evolution by solvable dual-unitary brickwork circuits followed by measurements on part of the system, which induce an ensemble of states on the unmeasured subsystem. Previous work has established that this projected ensemble of states forms a quantum state design in the limit where the bath size is large, but the rate of convergence at finite bath size has not been rigorously established. Under three inverse-polynomial assumptions, local permutation mixing, a bound on recurrent backward motion, and contraction at the measured boundary, we fill this gap and prove that a bath of polynomial size suffices to form approximate $k$-designs. In establishing our results, we develop a microscopic transport interpretation of emergent randomness in the projected ensemble, in which deviations from local permutation operators appear as defects, and make connections with the theory of quantum walks.

We report a comprehensive investigation of the magnetic, electrical, and thermodynamic properties of single crystalline Tb6Ti4Al43, in which Tb atoms form a distorted kagome lattice embedded within a complex Ti-Al framework. Tb6Ti4Al43 exhibits pronounced magnetic anisotropy and antiferromagnetic ordering at approximately 19 K. For magnetic field applied along the c-axis, a strong metamagnetic switching is observed, accompanied by a clear asymmetric hysteresis at low temperatures, while for field applied along the ab plane, a spin-flop transition is observed. The effect of field induced magnetic states is strongly reflected in magnetotransport measurements, giving rise to pronounced anomalies in magnetoresistance and an anomalous Hall contribution. A significant intrinsic contribution to the anomalous Hall conductivity is observed, highlighting the Berry curvature effects arising from the system's momentum-space topology. Our results highlight the interplay of spin, charge, and lattice degrees of freedom in Tb6Ti4Al43 and establish this distorted kagome antiferromagnet as a promising platform for field-tunable multifunctional behaviour, including electrically readable magnetic switching, spin manipulation, and magneto-mechanical functionalities.

A spiking neuron is a dynamical system exhibiting a limit cycle (a spike) when subject to sufficiently excitatory input. Famous neuroscience experiments by Bryant and Segundo as well as Mainen and Sejnowski revealed that the spike times of some biological neurons are more reliable when subject to time-varying stimuli compared to constant ones. Provided with an industrial physics-based transient noise SPICE simulation framework compatible with foundry transistor compact models, we have demonstrated similar behaviours for a CMOS analog spiking neuron designed for neuromorphic computing hardware platforms. Under constant excitation current, the neuron operates in oscillatory regime and the empirical periods (interspike intervals) suffer from accumulated phase noise (jitter) during successive cycles, mainly due to the thermal noise of transistors. A time-varying input is reported to be capable of triggering output spikes according to a controlled statetransition mechanism, thereby significantly reducing the spike time jitter in the excitability regime. The physical limitation of the oscillatory or rate-coding regime in terms of reliabilitydissipation tradeoff is further evidenced by a stochastic thermodynamic uncertainty relation, a theorem that applies to general overdamped dissipative stochastic dynamical systems.

A recurring design principle in modern optimizers is to decouple update magnitude from the raw gradient norm, yet its consequences for learning-curve and resource scaling remain unclear. We isolate this mechanism by studying normalized SGD in a random-feature model with power-law teacher and data covariance. Fixed-norm updates induce an effective learning rate that grows as gradients shrink. We derive a dynamical mean-field theory (DMFT) describing the joint dependence of the loss on training time, model width and batch size. Normalization initially accelerates SGD, mapping the power-law exponent $r_{\rm SGD}<1$ to $2r_{\rm SGD}/(1-r_{\rm SGD})$, with exponential convergence at $r_{\rm SGD}=1$ and formal finite-time convergence for $r_{\rm SGD}>1$. At finite step size, however, the same feedback ultimately breaks the acceleration and leads to marginal stability. The late-time theory yields width-limited, edge-of-stochastic-stability (EoSS), and deterministic edge-of-stability (EoS) regimes. These phases determine when larger batches or wider models reduce serial training time at comparable compute. We quantify in which of these phases increased batch size or width can compensate the excess compute use per step by fewer optimization steps to target loss. Linearized ResNet experiments on CIFAR-5M support the predicted acceleration, breakdown, and resource-scaling trends. Together, these results connect normalization-induced acceleration, EoS effects, and width–batch allocation within a solvable theory.

In this paper, we theoretically study the electron and hole $g$-factors in inorganic lead-halide perovskites for the reference cubic phase. We employ an 18-band $k \cdot p$ model and determine its parameters using target band structures obtained from DFT calculations. We use the linear response theory to calculate the $g$-factors and investigate their dependence on external strain. We then perform real-space calculations of the electron and hole $g$-factors in perovskite nanocrystals. We show that the bulk $g$-factors can be tuned over a wide range by external strain. In some cases, strain can be used to tune the $g$-factor through zero. By contrast, the carrier $g$-factors in CsPb$X_3$ nanocrystals are considerably less sensitive to strain due to quantum confinement.

We develop an operational approach to strong-to-weak spontaneous symmetry breaking (sw-SSB) of a non-Abelian symmetry group G. We formulate it as the decoding task of distinguishing two strongly symmetric states that differ by a pair of inserted irreps, after both are corrupted by strongly symmetric decoherence. For finite G, this task is dual to distinguishing logical states of the quantum double D(G) under pure-charge noise. We derive a hierarchy of statistical mechanics models describing optimal decoding from the fusion outcomes measured on successively larger nested regions. As for maximum-likelihood decoders of Abelian codes the measured irreps act as quenched disorder obeying a Nishimori-like condition. Strikingly, because local irreps do not determine how they fuse globally, the strong $G\times G$ symmetry is realized only nonlocally, and irreps trivially charged under Z(G) (the center of G) can hide inside noise-generated ones. As a result, the strong symmetry spontaneously breaks down to Z(G), times the weak symmetry. The only transition at nonzero error rate is then an ordering of the center, whose threshold cannot decrease as the hierarchy is ascended. This conclusion holds at any finite level of the hierarchy for non-nilpotent groups. We confirm these predictions with tensor-network calculations for $S_3$ and SU(2). At the first level, the $S_3$ model, whose center is trivial, shows no transition, and the fidelity correlations of all irreps provably decay to non-zero values. The SU(2) model exhibits a $Z_2$ transition consistent with the Nishimori-Ising universality class, where the fidelity correlations of spin-$1/2$ irreps become long-range. The threshold rises from the first to the second level of the hierarchy by $16\%$. Our results provide a systematic framework for studying non-Abelian sw-SSB and for constructing decoders for non Abelian topological codes.

The Hohenberg-Mermin-Wagner theorem motivates the expectation that continuous symmetries remain unbroken in one-dimensional quantum ground states. Here, contrary to this expectation, we demonstrate the spontaneous breaking of U(1) spin-rotation symmetry and the emergence of an interacting quantum critical point in lattice spin-$1/2$ and spin-$1$ chains. Using subsystem Binder scaling, we locate the critical point and determine the correlation-length critical exponent as $\nu = 0.60 \pm 0.02$, distinct from the Gaussian value $0.5$ but consistent with the perturbative renormalization-group prediction. We further analyze the finite-size scaling of the lowest neutral excitation gap and obtain the dynamical critical exponent $z=1.986 \pm 0.005$. The result $z < 2$ is incompatible with microscopic realizations of this critical theory by frustration-free models, implying a mechanism for continuous symmetry breaking in one-dimensional quantum ground states distinct from frustration freeness.

We report the growth and physical properties of HoCo$_2$ thin films on Si substrate by pulsed laser deposition. Well-defined Kiessig fringes in the x-ray reflectivity data yield a film thickness of $35 \pm 1$~nm and demonstrate smooth film surface and interface profiles. Atomic force microscopy confirms the high morphological quality of the films, revealing subnanometer surface roughness of $\sim$170~pm. Two independently prepared films exhibit a reproducible ferrimagnetic transition at $T_{\mathrm{C}}=77\pm3$~K, demonstrating retention of the characteristic magnetic ordering of bulk HoCo$_2$. However, the absence of resolvable thermal hysteresis indicates a predominantly continuous, second-order like transition in the films, in contrast to the first-order transition of bulk HoCo$_2$. At 5~K, the films exhibit clear magnetic hysteresis with a coercive field of $\sim$600~Oe, substantially larger than the negligible coercivity of bulk HoCo$_2$. X-ray photoelectron spectroscopy reveals comparable Ho $4d$ and Co $2p$ core-level line shapes and broadly similar valence-band spectra for the bulk and film, indicating preservation of the essential local electronic environment and occupied electronic structure.

We investigate the real-time dynamics of the Riesz gas (RG), a paradigmatic system of particles with power-law interactions that encapsulates several many-body interacting classical systems. While the equilibrium properties of the system have been extensively studied the connection between microscopic dynamics, macroscopic evolution and thermalization has remained largely unexplored. Combining extensive large-scale Newtonian simulations with a hydrodynamic framework formulated in terms of three coarse grained fields – density, velocity, and temperature – we establish a direct and quantitative correspondence between the two descriptions. The hydrodynamic theory incorporates two phenomenological transport coefficients, the bulk viscosity $\xi$ and thermal conductivity $\kappa$, which encode dissipative effects at a macroscopic level. By analyzing representative classes of initial conditions, such as dome-like and Newton-cradle-type profiles, we find excellent agreement between microscopic and hydrodynamic evolution over a broad range of timescales, starting from relatively early all the way up to times at which steady state is attained. Notably, this agreement persists across a substantial window of $\xi$ and $\kappa$, demonstrating the robustness of the emergent hydrodynamic description. Our results provide a systematic validation of hydrodynamics in the RG and establish a concrete bridge between Newtonian dynamics and continuum theories in systems with power-law interactions, starting from first principles.

The magnetic properties of Sm-based intermetallics are governed by a delicate interplay between localized $4f$ states, exchange interactions, and valence fluctuations, yet the role of dynamical $4f$ correlations remains poorly understood. Here we investigate the electronic structure and magnetic anisotropy of SmCo$_5$ and SmCu$_5$ using self-consistent DFT+$U$(ED), which explicitly treats dynamical fluctuations of the Sm $4f$ shell. We find that SmCo$_5$ exhibits pronounced Sm$^{2+}$–Sm$^{3+}$ valence fluctuations, with the $4f$ ground state dominated by $f^5$ and $f^6$ configurations. The resulting dynamical $4f$ correlations yield near compensation of the Sm spin and orbital moments and provide a quantitative description of the electronic structure, magnetic moments, and large uniaxial magnetic anisotropy of SmCo$_5$. Upon replacing Co with Cu, the balance shifts toward the $f^6$ configuration, with substantial changes in the Sm spin and orbital moments. In SmCu$_5$, this evolution of the $4f$ configuration is accompanied by a pronounced reduction of both the total magnetic moment and magnetic anisotropy. These results demonstrate that dynamical $4f$ valence fluctuations are essential for understanding the contrasting magnetic properties of SmCo$_5$ and SmCu$_5$ and provide a microscopic framework for describing magnetic anisotropy upon Co to Cu substitution in Sm(Co,Cu)$_5$.

What makes one quantum process more complex than another? We adopt an operational approach inspired by classical complexity science, which characterises structure through the memory required for causal generation. We develop a fully-quantum extension of computational mechanics for quantum space series: Correlated sequences of quantum outputs that do not return to interact with their generator. For stationary, memoryful quantum space series admitting finite-dimensional, primitive causal models, we show that any memory-minimal causal generator can be chosen to produce outputs isometrically, without a discarded environment. The resulting canonical matrix product state representation uniquely determines the irreducible memory required for generation. In particular, the minimum memory entropy is exactly the entanglement entropy across the past-future bipartition, giving entanglement a direct operational interpretation as irreducible memory for causal generation. The same structure determines the minimum memory dimension through the corresponding Schmidt rank. Within this class, we further show that the fundamental entropy rate vanishes, that causal generation is symmetric under time reversal, and that all memoryful processes possess infinite quantum Markov order with respect to arbitrary sharp measurements. These results establish an operational framework for quantifying intrinsic quantum structure, revealing deep connections between causal generation, complexity, memory, entropy, and entanglement.