Non-Hermitian systems exhibit anomalous scaling, a striking departure from conventional bulk laws, rooted in the non-Hermitian skin effect (NHSE). Here, we experimentally uncover this scaling and demonstrate its active control in a temporal photonic lattice. By tracking the real-time evolution of all eigenstates as system size varies, we directly observe scaling-driven spectral reshaping and eigenstate localization, revealing phenomena absent in Hermitian or NHSE-free lattices. In a Su-Schrieffer-Heeger lattice, scaling alone can trigger a non-Hermitian topological phase transition, with edge modes remaining protected. Crucially, Kerr interactions open the frontier of nonlinear non-Hermitian physics: weak nonlinearity accelerates or decelerates anomalous scaling, while strong nonlinearity suppresses it entirely. These results establish the first experimental platform for linear and nonlinear anomalous scaling engineering, paving the way for compact non-Hermitian devices and exploration of nonlinear and many-body non-Hermitian phenomena.

Though highly impacting our lives, rotating turbulent flows are not well understood. These anisotropic three-dimensional fluctuating flows are governed by different nonlinear processes, each of which can be dominant in a different range of parameters. More than 20 years ago, Galtier used weak wave turbulence theory (WTT) to derive explicit predictions for the energy spectrum of rotating turbulence. The spectrum is an outcome of forward energy transfer by inertial waves, the linear modes of rotating fluid systems. This spectrum has not yet been observed in the presence of significant quasi-two-dimensional geostrophic modes. In this Letter, we show that the predicted WTT field spectra do exist in steady rotating turbulence, alongside with the more energetic quasi-two-dimensional turbulent field. By removing the 2D component from the steady state velocity field, we show that the residual three-dimensional field consists of inertial waves and agrees with WTT spectra predictions. Our analysis examines the dependence of the energy spectrum on all four relevant parameters and provides limits within which WTT predictions hold. These results provide a solid basis for new theoretical and experimental works focused on the coexistence of the quasi-2D field and the inertial waves field and on their interactions.

Chiral superconductivity is a novel superconducting phase characterized by order parameters that break time-reversal symmetry, endowing the state with a definite handedness. Unlike conventional superconductors, the Cooper pairs in a chiral superconductor carry nonzero orbital angular momentum. Through coupling with an external magnetic field, the finite angular momentum of the Cooper pair modulates the temperature-magnetic field phase boundary in a distinctive way, which could serve as an experimental signature of the chiral superconducting state. Here we demonstrate that the chiral signature can be detected in mesoscopic superconducting rings of $\beta \text{−}{\mathrm{Bi}}_2\mathrm{Pd}$, manifesting as a linear-in-field modulation of the critical temperature in the Little-Parks effect. Our findings establish a new experimental method for detecting chiral superconductivity.

Spin density waves (SDWs) represent a fundamental paradigm of spatially modulated order in condensed matter systems, yet their electrical and mechanical analogs—polarization and strain density waves (PDWs and StDWs)—have remained elusive as equilibrium phases. Here, we introduce a general, symmetry-driven strategy to unlock static PDWs and StDWs in perovskites ${\mathrm{SrTiO}}_3$ and ${\mathrm{SrMnO}}_3$. Using first-principles calculations, we uncover a previously overlooked soft antiferrodistortive tilt gradient mode at small-$q$ wave vector in the phonon dispersion of their presumed $Ima2$ ground state under moderate tensile strain. Group-theory analysis reveals that a hard polar-acoustic phonon, which intrinsically carries PDWs and StDWs, is improperly destabilized by a trilinear coupling with this modulated tilt mode and an inherently uniform tilt mode. This interaction drives a structural transition from the $Ima2$ phase to a novel lower-energy $Pmn{2}_1$ phase that hosts long-range-ordered PDWs and StDWs. Strikingly, the engineered StDWs in ${\mathrm{SrMnO}}_3$ activate an electrically tunable SDW via the flexomagnetic effect. These discoveries fundamentally revise the strain-phase diagrams of prototypical perovskites and establish a unified phonon engineering framework that links modulated phonon instabilities to targeted density-wave order, offering new pathways for designing advanced electromechanical and magnetoelectric functionalities.

We investigate the microscopic properties of the kagome compound ${\mathrm{Cs}}_2{\mathrm{Cu}}_3{\mathrm{SnF}}_{12}$ using ${}^{63,65}\mathrm{Cu}$ nuclear quadrupolar resonance. Analysis of the local hyperfine fields below the Néel temperature $T_{\mathrm{N}}=20\mathrm{K}$ indicates a spin structure consistent with $P{2}_1/n$ symmetry of negative vector chirality. Measurements of the spin-lattice relaxation rate $T_1^{-1}$ reveal signatures of a gapless ground state and two-dimensional Berezinskii-Kosterlitz-Thouless–type correlations above $T_{\mathrm{N}}$, extending over a broad temperature range of approximately 130 K in zero magnetic field. Within the same temperature range, the observed increase in the nuclear quadrupolar resonance linewidth is consistent with short-range chiral order recently identified by neutron scattering. Our results establish ${\mathrm{Cs}}_2{\mathrm{Cu}}_3{\mathrm{SnF}}_{12}$ as a unique quantum kagome system exhibiting Berezinskii-Kosterlitz-Thouless behavior.

Recent studies have revealed that the quantum geometry of electronic bands determines the electromagnetic properties of noninteracting insulators and semimetals. However, the role of quantum geometry in the optical responses of interacting electron systems remains largely unexplored. Here, we examine the interplay between Coulomb interactions and Bloch-band quantum geometry in clean metals. We demonstrate that the low-frequency optical conductivity of a correlated metal encodes the structure of Bloch wave functions at the Fermi surface. This response originates from integrating out highly off-resonant interband scattering processes enabled by Coulomb interactions. The resulting quantum-geometric contribution appears generically in multiband systems but becomes the dominant effect in the optical conductivity for a parabolic band. We consider a dilute correlated metal near a topological band inversion and show that the doping dependence of optical absorption can measure how the orbital character of Bloch wave functions changes at the Fermi surface. Our results illustrate how the confluence of quantum geometry and Coulomb interactions can enable optical processes and enrich the physics of Fermi liquids.

Topological superconductors are believed to host exotic quasiparticle excitations known as Majorana zero modes (MZMs), with much of the evidence based on BCS mean-field theory. The direct application of mean-field arguments is tenuous in finite, isolated systems relevant in some experiments. Here, we develop a new correlation-based method for identifying MZMs in interacting, number-conserving systems. Using the density matrix renormalization group, we study fermion number-conserving models with long-range interactions, which under periodic boundary conditions exhibit robust topological and nontopological superconductivity, tuned by the strength of interaction [Ortiz et al., Phys. Rev. Lett. 113, 267002 (2014)]. We find evidence that, on the topological side, Majorana edge modes appear in open chains, manifesting as the vanishing of the energy splitting between odd- and even-parity ground states with increasing system size. Additionally, off-diagonal two-point correlation functions show nonlocal, parity-dependent edge effects. These correlations reveal the spatial structure of Majorana modes in the many-body wave function. We show that the correlation diagnostic applies broadly, including to short-range interacting models, where topological superconductivity is more fragile due to the absence of a bulk excitation gap.

We investigate the equilibrium properties of a quantum Brownian particle moving in a periodic potential, specifically addressing the nature of the dissipation-driven Schmid transition in the Ohmic regime. By employing world-line Monte Carlo in the path-integral formalism and introducing a specific binary order parameter, we demonstrate that the transition belongs to the Berezinskii-Kosterlitz-Thouless universality class. This classification is substantiated through finite-size scaling analysis that reveals the characteristic logarithmic decay of the correlation functions associated with the order parameter at the critical point. Quantum phase transition turns out to be extremely fragile: it disappears in both over- and sub-Ohmic dissipation regimes. Crucially, we find that the presence of the periodic potential does not alter the localization properties in the sub-Ohmic and super-Ohmic regimes, where the system exhibits the same qualitative behavior as the free quantum Brownian particle. These findings highlight that the emergence of critical behavior is strictly governed by the low-frequency form of the environmental spectral function, which determines the long-range temporal decay of the dissipative kernel.

An in-principle exact working equation to compute electronic affinity and ionization Fukui functions is derived within the $N$-centered (Nc) ensemble extension of density functional theory (DFT). It circumvents the kernel derivative discontinuity problem of DFT for fractional electron numbers, whose contribution is recovered through weight derivatives of the ensemble density functional potential. Thus, it allows for the design of alternative and effective approximations, such as the weight-dependent scaling of regular functionals or the interpolation between known limits of Nc ensembles.

In Hopfield-type associative memory models, memories are stored in the connectivity matrix and can be retrieved subsequently thanks to the collective dynamics of the network. In these models, the retrieval of a particular memory can be hampered by overlaps between the network state and other memories, termed “spurious overlaps” since these overlaps collectively introduce noise in the retrieval process. In classic models, spurious overlaps increase the variance of synaptic inputs but do not affect the mean. We show here that, in models equipped with a learning rule inferred from neurobiological data, spurious overlaps collectively reduce the mean synaptic inputs to neurons, and that this mean reduction causes in turn an increase in storage capacity through a sparsening of network activity. Our Letter demonstrates a link between a specific feature of experimentally inferred plasticity rules and network storage capacity.

Exotic spin-spin-velocity-dependent interactions, predicted in extensions of the standard model involving new bosonic fields, could resolve fundamental puzzles from dark matter to cosmic asymmetry. However, exploring these weak potential interactions at centimeter scales presents formidable challenges, primarily due to the overwhelming dominance of electromagnetic backgrounds that can easily obscure the weak exotic signals. Here, we utilize a levitated magnet force sensor with ultrahigh electron spin density to probe these interactions. We constrain two interactions individually through a designed spin source and a multilayer magnetic shielding system that suppresses electromagnetic backgrounds. In this Letter, we constrain two types of interactions: the $V_6$ potential at force ranges from ${10}^{-3}$ to $6\times {10}^{-2}\mathrm{m}$ and the $V_{14}$ potential at ranges greater than ${10}^{-3}\mathrm{m}$. Our measurements establish 95% confidence-level bounds of $|f_6|\le 2.12\times {10}^{-13}$ and $|f_{14}|\le 2.34\times {10}^{-23}$ at $\lambda =1.6\times {10}^{-2}\mathrm{m}$, improving prior limits by up to 12 and 13 orders of magnitude, respectively. Our result demonstrates the levitated magnet as a highly sensitive probe for detecting new bosonic fields in extensions of the standard model.

We consider the anomalous dimension ${\gamma }_{gg}^{(3)}(N)$ of the twist-two gluon operator of arbitrary Lorentz spin $N$ in the quark flavor singlet sector of a general gauge theory at four loops and construct its contribution proportional to $\zeta (3)$ in analytic form by applying the Lenstra-Lenstra-Lovász algorithm to the available low-$N$ moments. We exploit generalized Gribov-Liptov reciprocity, establish new self-tuning relations for the anomalous dimension matrix of the singlet sector, and inject information from $\mathcal{N}=1$, 4 supersymmetric Yang-Mills theories. We also present the contribution to the rational part of ${\gamma }_{gg}^{(3)}(N)$ with color factor $C_F^2{n}_f^2$. Exact contributions to the four-loop splitting function $P_{gg}^{(3)}(x)$ hence resulting via inverse Mellin transformation help us to reduce theoretical uncertainties in scaling violations of parton distribution functions in QCD.

The anomalous Hall conductivity in magnetic Weyl semimetals scales linearly with the momentum separation between Weyl nodes, establishing a geometric paradigm for three-dimensional Hall responses. Here, we discover an analogous phenomenon in the spin Hall effect: a quantized spin Hall conductivity (SHC) in nodal-ring semimetals that scales linearly with the nodal-ring radius $R$. From an ideal model with a single nodal ring, we derive analytically that the SHC inside the spin-orbit-coupled gap obeys ${\sigma }_{\alpha \beta }^{S,3\mathrm{D}}={\sigma }_0^{S,2\mathrm{D}}(\pi R/2\pi )$, where ${\sigma }_0^{S,2\mathrm{D}}=(e^2/h)(\hslash /2e)$ is the two-dimensional quantum spin Hall conductance. Crucially, the symmetry of the spin-orbit coupling acts as an independent switch: Rashba coupling generates purely conventional SHC components, while Weyl coupling additionally activates unconventional ones, providing separate control over response magnitude and tensor symmetry. We validate this principle in yttrium nitride, where strain tunes $R$ and symmetry breaking toggles between response types. Our Letter establishes a new paradigm for engineering quantized geometric responses in three dimensions, opening pathways to tailored spin-orbit functionalities.

The quantum XXZ spin-$1/2$ chain features non-Gaussian spin current fluctuations in the regime of easy-axis anisotropy. Using ballistic macroscopic fluctuation theory, we derive the exact asymptotic probability distribution of typical spin-current fluctuations in thermal equilibrium at zero average magnetization. The obtained nested Gaussian distribution is fully characterized by its variance, which we analytically relate to the spin diffusion constant and static spin susceptibility, comparing our prediction with numerical simulations. By unveiling how the same mechanism which leads to anomalous charge current fluctuations in single-file systems manifests itself in the XXZ chain, our approach establishes the universal hydrodynamic origin of the observed anomalous fluctuations.