Papers

We study at zero temperature a microscopic quantum spin-1 model on the fuzzy sphere that realizes the $O(2)$ Wilson-Fisher conformal field theory (CFT) in $(2+1)$-dimensional spacetime at a quantum critical point. Here, we use the fuzzy-sphere regularization as it preserves the full spatial $SO(3)$ rotational symmetry of the CFT, enabling the state-operator correspondence that maps energy eigenstates directly to CFT operators. Using exact diagonalization (ED) and matrix product state (MPS) techniques combined with conformal perturbation theory (CPT), we extract conformal data including scaling dimensions and operator product expansion (OPE) coefficients. We identify 48 primary operators and their descendants, organized by the conserved $O(2)$ charge $S^{z}$ and spatial angular momentum $L$. Our numerical results for the scaling dimensions of the lowest primary operators show good agreement with conformal bootstrap predictions. We verify predictions from the large charge expansion, which provides systematic predictions for operators carrying large $U(1)$ charge, connecting the Goldstone mode physics in the ordered phase to phonon primaries at the critical point.

Realization of unconventional odd-parity magnets usually requires noncollinear spin textures of the underlying lattice. We propose a different concept of $p$-wave magnetism that originates from an orbital texture induced by loop currents. The resulting $p$-wave orbital magnetism is protected by the combined translation and time-reversal symmetry, with even-parity components arising when the symmetry is broken. Our proposal is exemplified by a two-dimensional (2D) lattice model whose energy spectrum contains Dirac points and which is characterized by a nontrivial topology controlled by the magnitude of the loop currents. Since the odd-parity magnetism precludes macroscopic magnetization, we suggest measuring it via orbital Hall conductivity. Our work establishes orbital degrees of freedom as an additional platform for unconventional $p$-wave magnetism beyond noncollinear spin textures, as well as makes a step forward to bridging odd-parity magnetism and topology.

High temperature is usually expected to destroy order: as the Gibbs state approaches the infinite-temperature limit, it becomes an equal-weight ensemble over all states and the system is generically disordered. Recent works showed that entropic order can violate this expectation through coupling to bosons in classical lattice models and quantum field theories, where the ordered states have higher entropy. Here we present new analytic methods for constructing quantum lattice models that exhibit entropic orders. In particular, we construct quantum lattice models with continuous symmetry breaking at high temperature in 1+1 dimensions and clarify how entropic order can evade the Hohenberg-Mermin-Wagner theorems. We also construct high-temperature entropic $p+ip$ chiral topological superconducting states in 2+1 dimensions with temperature-independent anyon correlation functions. In addition, we obtain a broad family of high-temperature entropic non-chiral topological orders. We show that the entropic topological orders have strong higher form symmetries at high temperature unlike the conventional topological orders, and the symmetry is spontaneously broken. These results follow from two general constructions that couple a given lattice model with a low-temperature ordered phase either to ordered bosons or, for local commuting-projector Hamiltonians, to more general bosonic degrees of freedom.

Quantum interference of electrons in disordered conductors is a sensitive probe of the internal structure of quasiparticles, revealing universal signatures of symmetry through weak localization (WL) and weak antilocalization (WAL). While these phenomena are well understood for the conventional Schrödinger and Dirac-Weyl fermions, their fate in the broader class of multifold chiral fermions remains largely unexplored. We develop a unified framework for semiclassical transport and quantum interference in three-dimensional disordered fermions with an arbitrary pseudospin $s$. Starting from a general short-range matrix disorder $\mathcal{M}$, we derive compact expressions for elastic lifetimes and ladder vertex corrections for arbitrary pseudospin with multiband effects, and then show that in the scalar-disorder limit while the Drude conductivity is strongly pseudospin and helicity dependent, in contrast, the leading quantum interference correction exhibits a striking universality: its magnitude remains identical to that of conventional diffusive metals and Weyl fermions, while its sign is determined solely by the parity of $2s$, placing half-integer pseudospins in the symplectic class (WAL) and integer pseudospins in the orthogonal class (WL). We also analyze the role of interband and intervalley scattering for $s=3/2$. By solving the resulting coupled Bethe-Salpeter equations, we demonstrate that channel mixing suppresses WAL and drives a crossover toward localization. Our results establish a general theory of localization across the full pseudospin hierarchy, revealing an interplay between internal geometry, symmetry class, and transport universality.

Axis-Dependent Conduction Polarity (ADCP) refers to the phenomenon in which electrical transport within a single material is p-type along one crystallographic direction and n-type along the perpendicular direction. This behavior enables a variety of thermoelectric applications that do not require a heterojunction between two different materials. In this work, we investigate ADCP theoretically and derive a set of generic and quantitative criteria for identifying and predicting materials that exhibit ADCP. Specifically, by analyzing the thermopower for generic metals, semimetals, and semiconductors, we obtain transparent inequalities that are both necessary and sufficient for the emergence of ADCP. Moreover, we review known ADCP materials and verify that their band-structure characteristics and relaxation parameters are consistent with the inequalities derived here.

We introduce a generalized Hatsugai-Kohmoto multi-orbital model and study its phase diagram and physical properties in the additional presence of perturbations that lift any extensive ground-state degeneracies. The unperturbed, exactly solvable model already displays a rich set of spectral functions, including regimes reminiscent of unconventional magnets. We map the first-order study of additional spatially local multi-orbital Hubbard interactions to a Heisenberg model in momentum space, which leads to symmetry-breaking instabilities already at weak coupling. Interestingly, translational-symmetry breaking orders, such as antiferromagnetism, are excluded. Instead, in addition to ferromagnetism, unconventional $p$-wave and $d$-wave magnets occur, characterized by spin order on the bonds of the underlying square lattice. Adding another type of momentum-space interaction, which still allows to solve the model exactly, is shown to stabilize a non-degenerate singlet ground state that retains the spin splitting characteristic of unconventional magnets. We discuss its impact on the spin structure factor. Taken together, our findings show that Hatsugai-Kohmoto-like models provide a rich playground for unconventional magnetism.

The SYK model has played an important role in recent developments in many-body quantum chaos. We study a spatially local generalisation of it: the SYK lattice. Starting from the nonlinear action of pseudo-Goldstone bosons that dominate its dynamics at low temperatures, in the long wavelength limit we reorganise this action as the effective field theory for fluctuating hydrodynamics, thereby showing how the hydrodynamic degrees of freedom embed into the microscopic description of the model. We compute the hydrodynamic effective action to high orders in the derivative expansion and determine all the corresponding transport coefficients. Hence this work derives hydrodynamics from the microscopic description of a strongly coupled quantum many-body system.

Hybrid systems where a quantum material strongly couples to a nonlocal cavity photon mode have emerged as a new frontier for controlling and probing quantum correlations, yet the structure and scaling of light-matter entanglement produced by the nonlocal coupling remains poorly understood. We address this problem through an exactly solvable framework based on reinterpreting the Power–Zienau–Woolley (PZW) transformation as a light-matter quantum circuit that couples the photonic position quadrature $X \sim a + a^\dagger$ to the many-body dipole $\mathcal{P}$ of a one-dimensional quantum chain. We derive a closed-form expression for the reduced density matrix valid at all coupling strengths, in which off-diagonal elements between matter states of unequal dipole are suppressed by a Gaussian factor encoding the full weak-to-ultrastrong coupling crossover. At weak coupling, the reduced density matrix takes a Lindbladian form with $\mathcal{P}$ as the jump operator, and the entanglement entropy is controlled by the dipole variance. At ultrastrong coupling, the density matrix becomes exactly block-diagonal in dipole sectors, reflecting an emergent dipole symmetry dynamically imposed by the photon field, with entanglement entropy given exactly by the Shannon entropy of the dipole-sector weight distribution. Applying this framework to a half-filled Su–Schrieffer–Heeger chain, we show that, at strong coupling, both the light-matter entanglement and the spatial entanglement of the photon-dressed matter state scale logarithmically with system size, $S_\infty \sim \frac{\alpha}{2}\log L$, robust across the SSH phase diagram. The logarithm originates from the photon resolving a single collective coordinate $\mathcal{P}$ whose fluctuations grow as $L^{\alpha/2}$, a distinct mechanism from the logarithmic entanglement of critical one-dimensional systems.

Modelling fracture behavior of the shape memory alloy (SMA) that interacts with martensitic transformation and the associated elastocaloric effect (eCE) still remains challenging. Herein, a thermo-mechanically coupled phase-filed fracture model considering elastocaloric effect of SMA is proposed to simulate the cracking process coupled with the non-isothermal martensitic transformation and the associated eCE. In the phase-field model, both the thermal strain induced by eCE and the eigen strain induced by the phase transition are considered. An empirical degradation function is adopted to describe the thermal conductivity decreasing with the fracture order parameter. The model is validated with the finite element method and tensile fracture properties of Mn-Cu SMA are simulated. It is found that the martensite variant nucleates at the stress concentration where the crack initiates, and commonly spreads with an angle of 45 degree. The thermal expansion strain caused by the eCE could strengthen the critical load capacity. A large kinetic parameter for phase transition and the large orientation angle could enhance the strength and temperature change of eCE while the deformation capacity is reduced. The phase-field model demonstrates its ability in the thermal-mechanically coupled toughening of SMA. It also provides a possible fracture-resistance strategy by the utilization of eCE for elastocaloric devices.

By employing a combined method of density functional theory and dynamical mean field theory (DFT+DMFT) we investigate the effect of electronic correlations on the magnetic and superconducting properties of the iron-based parent compound LaFeAsO. We find that the static non-local susceptibility $\chi({\bf q})$ and the dynamical spin structure factor $S({\mathbf q},\omega)$ exhibit a peak at the in-plane wave vector ${\mathbf Q}=(\pi,\pi)$, which is strongly enhanced upon inclusion of dynamical vertex corrections in the ladder approximation, leading to magnetic instability. Considering the eigenfunctions of the Bethe-Salpeter equation with the vertex, obtained within the second order perturbation theory, as well as the ladder approach containing dynamic interaction vertices, in agreement with earlier weak-coupling-based studies of LaFeAsO, we obtain a close competition between $d$-wave and $s_{\pm}$ order parameters, dominating in the second-order and ladder approach, respectively. We argue that the dominating $s_{\pm}$ instability in the ladder DFT+DMFT approach is related to the reduced degree of magnetic frustration by itinerant degrees of freedom due to only partially formed local magnetic moments. Our study shows that dynamic correlation effects do not change the type of the leading superconducting instability in LaFeAsO.

We use variational exact diagonalization (VED) to calculate the two-electron removal spectral weight for the Hubbard-Holstein model, starting from the ground-state with two electrons on a one-dimensional chain. We argue that this spectral weight provides a valuable proxy for the intensity of 2eARPES processes. Our results show that when contrasted to the presumably larger signal due to two electrons ejected from two different pairs, the presumably weaker signal due to two electrons ejected from the same pair (i) is segregated in energy, appearing at a lower binding energy, and (ii) has a very characteristic momentum dependence, with a different symmetry than that of the signal corresponding to two electrons emitted from two different pairs. We verify that these fingerprints appear for pairs with different symmetries, and prove that they arise as a direct consequence of momentum and energy conservation, therefore they are generic for any model with electron-boson coupling that can lead to formation of electron pairs. Experimental observation of these fingerprints will confirm the existence of pairs. Moreover, the momentum dependence map allows one to distinguish whether the pairs are coherent (superconducting) or not. Finally, we argue that these considerations generalize to finite but low electron concentrations, finite temperatures and higher dimensions.

Preparing correlated quantum states is essential for emerging technologies, but remains challenging in many-body systems. Here we propose a dissipative protocol that engineers nonreciprocal, energy-selective transitions to steer dipolar quantum systems toward desired many-body states. This is realized by introducing two types of controllable dissipative auxiliary atoms that act as nonreciprocal excitation and de-excitation channels, respectively, enabling a directional walk in Hilbert space. This approach enables stabilization of states across the many-body spectrum, not limited to the ground state and requiring no a priori knowledge of the Hamiltonian. Our approach is designed for neutral atoms in dipolar Rydberg arrays, but applies broadly to setups with similar capabilities, providing a flexible and scalable framework for state preparation in programmable platforms.

Nonreciprocity, a hallmark of nonequilibrium systems, can generate dynamics not possible near thermodynamic equilibrium, including oscillatory and rotating patterns. The onset of temporal oscillations is often evident in linearized dynamics, where nonreciprocity appears as complex eigenvalues of an asymmetric Jacobian. Here, we show that the topology of open, thermodynamically-consistent chemical reaction networks can result in oscillatory instabilities near nonequilibrium steady states. These instabilities arise from chemostat-induced breaking of Onsager reciprocity, while the local equilibrium hypothesis preserves the variational structure of the dissipative part of the dynamics. Numerical results confirm that such nonreciprocity in reaction-diffusion systems produces oscillatory dynamics that nevertheless minimize a free energy.

We analytically investigate the diffusive motion inferred from experimental observations of active particles driven by quantum vortices on the surface of superfluid helium. We first study the dynamical behavior of an active particle subject to a viscoelastic memory effect characterized by a power-law kernel. We then analyze the dynamics of an active particle under a uniform vortex force, thermal noise, and viscous dissipation subject to a power-law kernel. Next, by including a harmonic confining force, we obtain analytical solutions for the joint probability density in two distinct time regimes.

The orbital degree of freedom in rare-earth nickelates is typically inactive across the temperature-driven metal-insulator transition, where the system develops two inequivalent Ni sites associated with Ni-O bond disproportionation and breathing-mode distortions of NiO$_6$ octahedra. Here, we show that orbital polarization can be induced by optical excitation with linearly polarized light. Using an interacting multiband tight-binding model combined with real-time simulations of coupled electron-ion-spin dynamics, we find that photoinduced $d$-$d$ transitions reduce the local magnetic moments at Ni sites and effectively suppress Hund's coupling $J$ in the excited state. Importantly, these transitions can be made strongly orbital-selective by tuning the light polarization, leading to an imbalance in $e_g$ orbital occupancies. The resulting nonequilibrium state, characterized by reduced effective $J$ and unequal orbital populations, becomes unstable toward Jahn-Teller (JT) distortions, driving structural relaxation along coherently excited JT modes. Our results demonstrate that polarization-controlled optical excitation provides a pathway to access hidden nonthermal phases with emergent orbital order, enabling coherent control of coupled charge, spin, and lattice degrees of freedom on ultrafast timescales.

The spiked Wigner ensemble is a prototypical model for high-dimensional inference. We study the spectral properties of an inhomogeneous rank-one spiked Wigner model in which the variance of each entry of the noise matrix is itself a random variable. In the high-dimensional limit, we derive exact equations for the spectral edges, the outlier eigenvalue, and the distribution of the components of the outlier eigenvector. These equations determine the BBP transition line that separates the gapped phase, where the signal is detectable, from the gapless phase. In the gapped regime, the distribution of the outlier eigenvector provides a natural estimator of the spike. We solve the equations for a noise matrix whose variances are generated from a truncated power-law distribution. In this case, the BBP transition line is non-monotonic, showing that an inhomogeneous noise can enhance signal detectability.

Excess pore pressure in granular–fluid mixtures can transiently suppress frictional contacts and dramatically enhance flow mobility, yet its evolution is commonly modeled using constant effective diffusivities. Here we show that the apparent diffusivity is not intrinsic but emerges from the coupling between pore-pressure diffusion and granular compaction. Starting from two-phase mass conservation for a deformable, gas-saturated granular assembly, we derive an evolution equation for excess pore pressure that captures deformation of the granular skeleton. In the thin-flow, small-excess-pressure limit, this reduces to a one-dimensional diffusion–compaction equation with a time-dependent source term controlled by porosity changes. A modal analysis yields a reduced basal equation that separates diffusive drainage from compaction-driven forcing and identifies the corresponding timescales. This framework introduces a dimensionless source-to-diffusion ratio, $\Psi_0$, which governs the competition between these processes and collapses effective diffusivities obtained from high-resolution two-fluid simulations over nearly two orders of magnitude in bed height. This scaling implies that the apparent diffusivity, and thus flow mobility, is not intrinsic but depends on flow thickness through the competition between diffusion and compaction. Incorporating this physics into a depth-averaged model demonstrates that the resulting closure reproduces the thickness dependence of pore-pressure decay and runout observed in experiments. These results provide a physically grounded description of pore-pressure evolution in granular–fluid flows and clarify how diffusion–compaction coupling controls their mobility.

Rydberg atom arrays are powerful platforms for studying quantum many-body systems. We consider the Rydberg-Ising Hamiltonian in a ring geometry and numerically study ensembles of states generated by random global pulse sequences subject to hardware constraints and fixed evolution times. We compare the statistical properties of such states with those of Haar-random states within the relevant lattice symmetry sector. In the strong-interaction regime (short interatomic distance), the dynamics is governed by an effective blockade that restricts Hilbert-space exploration and limits entanglement growth. In this regime, level-spacing statistics of the entanglement spectrum are close to random-matrix predictions, while the distribution of measurement probabilities deviates from Porter-Thomas behavior. For weaker interactions (larger interatomic distance), the system approaches Haar-like statistics at long times, as reflected in entanglement entropy, entanglement-spectrum statistics, and the distribution of measurement probabilities. At intermediate interactions, this behavior is observed on experimentally relevant timescales. Motivated by this observation, we investigate whether individual target states can be efficiently prepared using quantum optimal control in this regime. Employing target states drawn from an ensemble with a broad entropy distribution, we observe high fidelities (infidelities between 10^-5 and 3 x 10^-2 for nine spins). Within this ensemble, the fidelity decreases with the entanglement entropy of the target state, indicating that highly entangled targets are more difficult to prepare under the considered finite-time control constraints.

We show that a three-dimensional superconductor with a non-Abelian SU(2) order parameter can support an extended resistive regime a Bose metal, in which transport is carried by bosonic electron-Majorana bound states - separating a uniform superconductor from a pair-density-wave (PDW) phase. The setting is a solvable Kondo lattice model introduced previously by the present authors, in which Kondo screening of a Yao-Lee $\mathbb{Z}_2$ spin liquid generates an order parameter with SU(2), rather than conventional U(1), symmetry, containing both superconducting and spin-density-wave components. Two effects cooperate to make fluctuations anomalously strong in three dimensions: the vanishing of the quadratic superconducting stiffness near the Lifshitz point where the optimal pairing momentum shifts from zero to finite $Q$, and the enlarged SU(2) order-parameter manifold. Building on our prior result that doping away from half-filling drives amplitude-modulated PDW order via finite-momentum electron-Majorana condensation, we analyze the fluctuation-dominated regime above that phase using a nonlinear sigma model. We find that the order-parameter propagator develops a ring of soft modes throughout the disordered phase, and that the resulting resistivity scales approximately as $R \sim T^3$ in three dimensions.

Alterelectricity is a compensated ferroic state in which quadrupolar electronic order reshapes low-energy electronic structure without producing a net polarization. Here we show that a moiré superlattice can turn such order into a controllable phase. Within a Bloch-periodic two-orbital theory, the slowly varying interlayer registry is coarse-grained into an effective moiré field acting on a self-consistent two-component alterelectric quadrupole. The resulting phase develops above a strongly filling-dependent instability threshold and crosses over from a weakly selected regime into a robust axial-dominated ground state, while the diagonal-dominated branch remains only a weak competitor. A registry-phase sweep supplies an explicit continuous path through internal quadrupole space, demonstrating that the moiré superlattice does more than stabilize alterelectricity: it steers its internal orientation. This orientational selection is encoded directly in the redistribution of low-energy spectral weight across the moiré Brillouin zone. These results identify moiré superlattices as a generic route to controllable alterelectric order and to programmable anisotropic electronic functionality.

We study the convex hull of planar Brownian motion run until the exit time from the unit disk. Our primary objectives are to compute the expected perimeter and expected area of this convex hull, thereby complementing recent results on the convex hull of reflecting Brownian motion in confined geometries. We reduce the problem of computing the expected perimeter to computing the expected value of the Brownian motion's maximum horizontal displacement at the exit time, and then recast this maximum in terms of harmonic measure in a domain we call the truncated disk. The problem of computing the expected area is reduced to computing the expected value of the difference of squares of the Brownian motion's maximum horizontal displacement at the exit time, and the value of the vertical displacement at the time this maximum horizontal displacement is achieved. In particular, we obtain exact expressions for both the expected perimeter and the expected area. We conclude with further results on the expected areas of two related hulls of the Brownian path run until exiting the disk, namely, the star hull and topological hull.

In recent years, the dynamics of interacting quantum systems far from equilibrium have attracted significant research interest. Driven by rapid progress in quantum simulators, various non-equilibrium phenomena have now been realized experimentally. In this work, we use the time-evolving block decimation (TEBD) method to investigate the dynamics of an anisotropic spin-1 Heisenberg chain for a wide range of experimentally accessible initial states. By adjusting the parameter $J_q$ that controls the quadrupolar interaction strength, we can tune the system from a non-integrable SU(2) Heisenberg model to an integrable SU(3) Heisenberg model. We examine the local magnetization, entanglement entropy, and spin correlations, and characterize their dependence on $J_q$. We identify a new conserved quantity at the SU(3) symmetric point and provide a theoretical framework to explain our numerical observations in terms of the number of accessible states permitted by this conservation law. Our results provide a route to realize a rich array of non-equilibrium behavior in spin-1 lattice models, which can be engineered in several experimental platforms such as ultracold atoms in optical lattices.

Methane (CH4) and nitrous oxide (N2O) are potent greenhouse gases that represent substantial chemical energy. Conversion of these abundant waste gases to high-value chemicals typically requires high temperatures up to 1000 C, producing substantial CO2 emissions and limited selectivity toward desirable multi-carbon products. Here we demonstrate a plasmonic photocatalyst that enables CH4 and N2O conversion under ambient conditions to form C2 and C3 hydrocarbons. By systematically tuning AuPd alloys on TiO2, we identify an optimal composition (AuPd0.05) where Au enhances light harvesting and Pd enables selective C-H activation and C-C coupling. Under visible-light illumination, this catalyst produces C2H4, C2H6, C3H6, and C3H8 with ~80% selectivity while suppressing CO2 formation. In-situ spectroscopy and hot-carrier calculations show that plasmon-generated carriers redistribute interfacial hydroxyl intermediates, shifting the hydrophilic center to suppress overoxidation. Ab-initio calculations further reveal the reduction in C-C coupling barriers from 2.7 eV to 0.7 eV under illumination. Our work illustrates how engineering interfacial electronic and adsorbate dynamics enables selective multicarbon formation.

We investigate the kinetics of particle aggregation within the framework of the Smoluchowski coagulation equation, extending it to account for electrostatic interactions among charged clusters. Using a stochastic Monte Carlo implementation, we examine how different charge distributions and net system charge affect cluster growth dynamics. Electrostatic interactions are incorporated directly into the classical Brownian collision kernel, yielding charge-dependent modifications of the collision rates that may either enhance or suppress aggregation depending on the signs and magnitudes of the interacting charges. Our simulations reveal distinct regimes of growth: at intermediate times, charge heterogeneity accelerates or delays aggregation depending on the initial underlying charge distribution, while at long times the system tends toward quasi–stationary states whose properties depend on the net charge. Comparisons between Gaussian and Cauchy–Lorentz initial charge statistics highlight the role of heavy-tailed distributions in promoting faster cluster growth. These findings contribute to a unified understanding of coagulation kinetics in charged particulate systems, with potential implications for aerosol and astrophysical coagulation processes, volcanic ash aggregation, and clustering in industrial fluidized granular beds.

Activated transitions have rates that are often exponentially small in system size. Extracting the associated activation barriers is challenging in practice, especially in the deeply metastable regimes and in the presence of disorder. Here, we use transition path sampling to evaluate transition probabilities between ferromagnetic states in the Ising model on finite sparse random graphs, which are perhaps the simplest example of a disordered system with metastable states. To interpret the transient onset of the transition probability curve, we introduce a minimal three-state kinetic description that highlights the role of intermediate configurations. We validate the method on the heterogeneous Zachary Karate Club network, where distinct dynamical regimes emerge as temperature varies. We then apply the method to random regular graphs and Erdős-Rényi graphs, showing that sample-to-sample fluctuations are weak in the former but that quenched topological disorder induces sizable instance variability in the latter. For Erdős-Rényi graphs, we introduce an instance-dependent temperature rescaling that restores a consistent finite-size scaling of dynamical rates and enables a direct comparison with the corresponding static free-energy barrier.

The discovery of superconductivity with Tc ~ 80 K in the nickelate Ruddlesden-Popper bilayer La3Ni2O7 at high pressure has opened a new platform for unconventional superconductivity, followed by the subsequent observation of superconductivity in trilayer La4Ni3O10, also at high pressure. Remarkably, ambient-pressure superconductivity was also observed recently in La3Ni2O7 ultra-thin films when grown on substrates that provide compressive strain. This discovery significantly extends the type of experimental techniques that can be used in nickelates, previously limited due to the high-pressure constraint. Discussing the similarities and differences among these nickel oxides will provide new insights into understanding the mechanism of high-Tc superconductivity in correlated electron systems. In this paper, we review the experimental and theoretical progress on RuddlesdenPopper nickelates, with emphasis on thin films, and discuss future perspectives and research directions.

Altermagnets combine vanishing net magnetization with nonrelativistic, momentum-dependent spin splitting, offering a new paradigm for spintronics. Spin-crystal symmetry coupling, namely spin-lattice locking, is the defining mechanism of altermagnetism, enforcing opposite spin sublattices in real space and spin-momentum-locked electronic structure in reciprocal space. Direct atomic-scale visualization of spin-lattice locking therefore constitutes a decisive benchmark of the altermagnetic state, yet such evidence has remained elusive despite extensive efforts. Here we show that the electronic states in RbV2Se2O exhibit a d-wave-like spin texture at the sublattice level, providing the first atomic-scale evidence of spin-lattice locking with a predominantly c-axis spin orientation. By employing an in-situ, field-switchable spin-polarized Cr tip, we realize spin-contrast mapping of quasiparticle interference at identical energies, overcoming a long-standing experimental barrier in altermagnets. The resulting interference patterns exhibit pronounced spin-dependent modulations, establishing spin scattering locking and spin momentum locking as the real and reciprocal space manifestations. Unexpectedly, we uncover that the spin-selective scattering response is organized by a long-period stripe modulation, giving rise to a previously unidentified form of spin-texture locking, spin-stripe locking. We attribute this behavior to the emergence of a spin-density-wave moiré pattern. Together, these results establish a unified picture of quadruple spin-texture locking phenomena in a d-wave altermagnet, and position altermagnets as a versatile platform for exploring many-body interactions among intertwined degrees of freedom, including spin, lattice, momentum, moiré potential and valley.

Altermagnets are an emergent class of materials combining features of ferro- and antiferro-magnetic materials. They have spin-separated bands normally associated with ferromagnets, but a vanishing net magnetization. Moreover the symmetries giving rise to $d$-wave altermagnetism can provide them with a particular anisotropic, quadrupolar (i.e. with equal and opposite values when strained in perpendicular directions) piezomagnetism. Observing that the same symmetries provide a natural place to look for hyberbolic wave dispersion, this raises the question which properties are intrinsically linked to magnetism and which are determined by the symmetry. Here, we disentangle these concepts by introducing an alternative to altermagnets, based on electric polarization. These alterelectrics display quadrupolar piezoelectricity and a hyperbolic dispersion, which we demonstrate conceptually within a simplified model as well as a first-principles material realization. We furthermore establish that a counterpart of the spin-separated bands is formed by surface modes which allow for surface dependent anisotropic electronic transport analogous to the spintronic applications proposed for altermagnets.

Refractory multi-principal element alloys (RMPEAs) represent a novel class of alloys characterized by an extensive compositional design space and the potential for exceptional mechanical performance under extreme conditions. While accurate phase stability prediction is essential for their robust design, existing machine learning approaches rely on deterministic mappings from composition-derived features to phase labels, neglecting the uncertainty inherent in such predictions. In this study, we present a deep learning framework based on Mixture Density Networks (MDNs) to predict phase fractions in RMPEAs and quantify the associated aleatoric uncertainty across a wide temperature range. By training separate models for up to six constituent phases of RMPEAs using CALPHAD derived data, our approach achieves high predictive accuracy while capturing the probabilistic nature of phase formation. To address epistemic uncertainty arising from incomplete knowledge of the most informative features, we perform a perturbation-based feature importance analysis and identify a minimally sufficient input set that maintains both predictive performance and uncertainty calibration. Finally, we propose an uncertainty-based active learning strategy to discover novel RMPEAs with the target phase incorporating previously unseen elements, while investigating the exploration-exploitation trade-off in model-guided discovery. Our uncertainty-aware framework has the potential to accelerate and improve the reliability of discovering novel high-performance alloys and is broadly applicable.

We consider the collisional evolution towards equilibrium of a spatially homogeneous and isotropic phonon gas of a three-dimensional superfluid with a concave acoustic excitation branch, at a non-zero but arbitrarily low temperature $T$. Three-phonon collisions $1\phi\leftrightarrow 2\phi$ are forbidden by conservation of energy-momentum. Four-phonon collisions $2\phi\to 2\phi$ of Landau and Khalatnikov lead, after a time $\propto T^{-7}$, only to a partial thermal equilibrium, a Bose law of non-zero chemical potential for the phonons, because they conserve the total number of phonons. Relaxation towards complete thermochemical equilibrium is therefore ensured by the much slower five-phonon collisions $2\phi\leftrightarrow 3\phi$ of Khalatnikov, in a time $\propto T^{-9}$. Using kinetic equations on the occupation numbers of the phonon modes and explicitly calculating the $2\phi\to 3\phi$ collisional amplitude with quantum hydrodynamics at low temperature, we determine the corresponding evolution of the fugacity $z_\phi$ of the phonon gas from the non-degenerate regime $z_\phi=0^+$ to complete equilibrium $z_\phi=1^-$. Using the conservation of total energy, we find that the fugacity varies with a non-integer power law $\propto t^{4/5}$ at short times and an exponential law at long times; the speed of change of entropy, always positive, is asymptotically proportional to the square of the speed of change of fugacity, $(\mathrm{d}/\mathrm{d}t)S_\phi\propto[(\mathrm{d}/\mathrm{d}t)z_\phi]^2$, as Landau predicted for an arbitrarily slow adiabatic transformation. Our results bring to a close the study initiated by Khalatnikov in 1950 and could be experimentally verified in a gas of cold spin-1/2 fermionic atoms in the sector of the BEC-BCS crossover where the acoustic branch has a concave start, or in superfluid liquid helium-4 at sufficiently high pressure.