Real-to-complex spectral transitions and the associated spontaneous symmetry breaking of eigenstates are central to non-Hermitian physics, yet a comprehensive and universal theory that precisely describes the underlying physical mechanisms for each individual state remains elusive. Here, we resolve the mystery by employing the complex path integral formalism and developing a generalized Gutzwiller trace formula. These methodologies enable us to establish a universal quantum-classical correspondence that precisely links the real or complex nature of individual energy levels to the symmetry properties of their corresponding semiclassical orbits. Specifically, in systems with a general $\eta$-pseudo-Hermitian symmetry, real energy levels are quantized along periodic orbits that preserve the corresponding classical $S_{\eta }$ symmetry. In contrast, complex conjugate energy levels arise from semiclassical orbits that individually break the $S_{\eta }$ symmetry but together form $S_{\eta }$-symmetric pairs. This framework provides a unified explanation for the spectral behaviors in various continuous non-Hermitian models and for the $\mathcal{P}\mathcal{T}$ transition in two-level systems. Moreover, we demonstrate that the exceptional point is inherently a quantum phenomenon, as it cannot be described by a single classical orbit. Our Letter uncovers the physical mechanism of non-Hermitian symmetry breaking and introduces a new perspective with broad implications for the control and application of non-Hermitian phenomena.

We present the first theoretical study of the polarization of lepton pairs produced in $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$ $\mathrm{Pb}+\mathrm{Pb}$ collisions at the LHC, using next-to-leading order (NLO) dilepton emission rates. These calculations employ a multistage framework to simulate the evolution of relativistic heavy-ion collisions, and to explore the sensitivity of polarization to early times. It is found that the intermediate invariant-mass dileptons are indeed probes of the thermal equilibration process, and go beyond the reach of hadronic observables. We compute the polarization anisotropy coefficient obtained with LO dilepton rates, and show that the LO and NLO results differ radically, both in trend and in magnitude, at low and intermediate lepton pair invariant masses.

Spectroscopy with entanglement has shown great potential to break limitations of traditional spectroscopic measurements, yet the role of entanglement in spectroscopic multiparameter joint measurement, particularly in the infrared optical range, remains elusive. Here, we find an uncertain relation that constrains the precision of infrared spectroscopic multiparameter measurements using entangled photon pairs. Under such a relation, we demonstrate a trade-off between the measurement precisions of the refractive index and the absorption coefficient of the medium in the infrared range, and also illustrate how to balance their respective estimation errors. Our work shall provide guidance toward future experimental designs and applications in entanglement-assisted spectroscopy.

Ensembles of dipolar emitters which couple collectively to the radiation field display sub- and superradiance. These terms refer to a reduction or an enhancement of photon emission rates due to the interference of emission channels. Arrays of trapped neutral atoms constitute a promising platform for harnessing this phenomenon in technological applications, e.g., for excitation storage, single-photon switches, and mirrors. However, quantum and thermally induced vibrations of the atoms within their traps lead to position fluctuations that entangle the motion and the internal atomic degrees of freedom. We develop here a theory for collective atom-light coupling in the presence of this quantized motion within the Lamb-Dicke limit. We show the existence of sub- and superradiant states that are hybrids of electronic and vibrational excitations, investigate their properties for analytically and numerically efficiently solvable cases, and discuss how a finite temperature affects the collective photon emission.

We report the observation of neutrino interactions without final state muons at the LHC, with a significance of $6.4\sigma$. A dataset of proton-proton collisions at $\sqrt{s}=13.6\mathrm{TeV}$ collected by SND@LHC in 2022 and 2023 is used, corresponding to an integrated luminosity of $68.6{\mathrm{fb}}^{-1}$. Neutrino interactions without a reconstructed muon are selected, resulting in an event sample consisting mainly of neutral-current and electron neutrino charged-current interactions in the detector. After selection cuts, 9 neutrino interaction candidate events are observed with an estimated background of 0.32 events.

The top quark mass is a key parameter of the standard model, yet measuring it precisely at the Large Hadron Collider (LHC) is challenging. Inspired by the use of standard candles in cosmology, we propose a novel energy correlator-based observable, which directly accesses the dimensionless quantity $m_t/m_W$. We perform a Monte Carlo study to demonstrate the feasibility of the top mass extraction from Run 2, 3, and High-Luminosity LHC datasets. Our resulting $m_t$ can be defined in a well-controlled short-distance mass scheme and exhibits remarkably small uncertainties from nonperturbative effects, as well as insensitivity to parton distribution functions, outlining a roadmap for a record precision measurement at the LHC.

Rare-earth emitters in solids are well suited for implementing efficient, long-lived quantum memory coupled to integrated photonics for scalable quantum technologies. They are typically introduced as dopants in a solid-state host, but this introduces disorder and limits the available density of emitters. Stoichiometric materials can offer high densities with narrow optical linewidths. The regular spacing of emitters also opens possibilities for quantum information processing and collective effects. Here, we show narrow optical linewidths in a layered stoichiometric crystalline material, $\mathrm{NaEu}{({\mathrm{IO}}_3)}_4$. We observed an inhomogeneous linewidth of 2.2(1) GHz and a homogeneous linewidth of 120(4) kHz. Using spectral hole-burning techniques, we observe a hyperfine spin lifetime of 1.9(4) s. Furthermore, we demonstrate an atomic frequency comb delay of up to 800 ns.

In situ nuclear forward scattering shows a thermally induced cation exchange between a ${{}^{57}\mathrm{Fe}}_3{\mathrm{O}}_4$ thin-film and a ${\mathrm{Fe}}_3{\mathrm{O}}_4$ (001) substrate predominantly in the octahedral sublattice for a temperature range between 470 and 710 K. The overall activation barrier in this temperature range is found to be $19\pm 32\mathrm{kJ}/\mathrm{mol}$, which is significantly lower than expected from extrapolating a bulk diffusion model. This observation can be attributed to the large out-of-equilibrium cation deficit as determined by surface x-ray diffraction. Despite the relatively low hopping barrier, the diffusion constant is about 5 orders of magnitude lower than expected for magnetite having an equilibrium cation stoichiometry. The results are relevant for applications relying on the near-surface structure and stoichiometry of magnetite, and we argue that the correlation between cation diffusion and stoichiometry may play a role for a wider range of oxide materials.

The spin pumping in ferromagnet/nonmagnetic materials ($\mathrm{FM}/\mathrm{NM}$) heterostructures is an effective technique to inject spin current into NM, which provides the possibility of ultrafast, low-power consumption spintronic devices. Previous work demonstrates that the high order terms in $\mathbf{k}·\mathbf{p}$ theory can induce a large warping effect, and consequently snowflakelike Fermi contour in topological insulator (TI). Unfortunately, the effect of warped topological surface state (TSS) on pure spin absorption in $\mathrm{FM}/\mathrm{TI}$ heterostructures is completely unknown. Here, by considering strength of spin accumulation, we identified a mechanism for the anisotropic absorption of spin current in a $\mathrm{FM}/\mathrm{TI}$ heterostructure with a large warping effect. If the density of states (DOS) of TSS dominates at the Fermi surface, the warping effect results in an anisotropic Gilbert damping at nanosecond timescale and almost isotropic ultrafast demagnetization time at femtosecond timescale. The anisotropy of Gilbert damping is found to decrease as bulk state contributions become more significant in thicker ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ films. Our theoretical predictions regarding the warping effect-induced spin current absorption at nanosecond and subpicosecond timescales have been experimentally validated in $\mathrm{Fe}/{\mathrm{Bi}}_2{\mathrm{Te}}_3$ heterostructures by ferromagnetic resonance and time-resolved magneto-optical Kerr effect (TRMOKE) results, respectively. Our work provides a more intuitional way to understand the spin transfer mechanism, and lays the groundwork for advancing anisotropic spintronics.

${\text{YbB}}_6$ is a predicted topological insulator, with experimental evidence for conducting surface states of yet-unproven origin. However, its lack of a natural cleavage plane, and resultant surface-dependent polarity, has obscured its study. We use scanning tunneling microscopy to image the cleaved surface of ${\mathrm{YbB}}_6$, which exhibits several coexisting terminations with distinct atomic structures. Our spectroscopic measurements reveal band bending between the terminations, resulting in both conducting and fully gapped domains. In the conducting domains, we observe spectral peaks that are suggestive of Van Hove singularities arising from Rashba spin-split quantum well states. The insulating domains rule out the possibility that ${\mathrm{YbB}}_6$ is a strong topological insulator, while the spin-polarized conducting domains suggest possible utility for spintronic devices.

The layer Hall effect is an intriguing phenomenon observed in magnetic topological layered materials, where the Hall response arises from the opposite deflection of electrons on top and bottom layers. To realize the layer Hall effect, space-time $\mathcal{PT}$ symmetry is typically broken by applying an external electric field. In this Letter, we propose a new mechanism to realize the layer Hall effect by introducing inequivalent exchange fields on both surfaces of a topological insulator thin film in the absence of an electric field. This approach yields a distinct Hall response compared to the conventional electric-field-induced layer Hall effect, particularly with respect to the Fermi level. Taking the topological insulator ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ as a concrete example, we demonstrate the feasibility of inducing the layer Hall effect only by coupling the top and bottom surfaces of ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ with different magnetic insulators. Notably, we show that both built-in electric-field-induced and inequivalent exchange-field-induced layer Hall effects can be achieved by tuning the stacking order between ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ and the magnetic layers. Given the well-established experimental techniques for fabricating topological insulator thin films, our work offers a viable pathway for realizing layer Hall effect without external electric field.

We consider translationally invariant quantum spin-$\frac{1}{2}$ chains with local interactions and a discrete symmetry that is spontaneously broken at zero temperature. We envision experimenters switching off the couplings between two parts of the system and preparing them in independent equilibrium states. One side of the chain is prepared in a disordered phase, and the other in a symmetry-breaking ground state. When the couplings are switched back on, time evolution ensues. We argue that in integrable systems the front separating the ordered region recedes at the maximal velocity of quasiparticle excitations over the ground state. We infer that, generically, the order parameters should vary on a subdiffusive scale of order $t^{1/3}$, where $t$ is time, and their fluctuations should exhibit the same scaling. This interfacial region exhibits full range correlations, indicating that it cannot be decomposed into nearly uncorrelated subsystems. Using the transverse-field Ising chain as a case study, we demonstrate that all order parameters follow the same universal scaling functions. Through an analysis of the skew information, we uncover that the breakdown of cluster decomposition has a quantum contribution: each subsystem within the interfacial region, with extent comparable to the region, exists in a macroscopic quantum state.

We provide an intuitive understanding of the collective low-energy spin excitation of the one-dimensional spin-$\frac{1}{2}$ antiferromagnetic Heisenberg chain, known as the spinon. To this end, we demonstrate how a single spinon can be excited by adding one extra spin to the ground state. This procedure accurately reproduces all key features of the spinon’s dispersion. These follow from the vanishing norm of the excited state which is triggered by the ground state entanglement. Next, we show that the spinon dispersion can be approximately reproduced if we replace the true ground state with the simplest valence-bond solid. This proves that the spinon of the one-dimensional Heisenberg model can be understood as a single spin flowing through a valence-bond solid.

Networks are powerful tools for modeling interactions in complex systems. While traditional networks use scalar edge weights, many real-world systems involve multidimensional interactions. For example, in social networks, individuals often have multiple interconnected opinions that can affect different opinions of other individuals, which can be better characterized by matrices. We propose a general framework for modeling such multidimensional interacting dynamics: matrix-weighted networks (MWNs). We present the mathematical foundations of MWNs and examine consensus dynamics and random walks within this context. Our results reveal that the coherence of MWNs gives rise to nontrivial steady states that generalize the notions of communities and structural balance in traditional networks.