The leading-order perturbative QCD (pQCD) predictions for nucleon electromagnetic form factors were first made in late 1970s. In this Letter, for the first time, we accomplish the calculation of the next-to-leading-order (NLO) QCD corrections to nucleon Dirac form factors at large momentum transfer to leading-twist accuracy in the collinear factorization approach, specifically within the Krankl and Manashov renormalization scheme. The effect of NLO perturbative corrections turns out to be positive and substantial. Taking the nucleon leading-twist light-cone distribution amplitudes determined from the recent lattice simulations as input, we find that the state-of-the-art pQCD predictions significantly underestimate the available nucleon Dirac form factors in both spacelike and timelike domains. This nuisance indicates that some additional soft nonfactorizable contribution might be called for to account for the measured nucleon electromagnetic form factor data up to $Q^2\approx 30{\mathrm{GeV}}^2$.

Here, we propose a platform based on ultracold fermionic molecules trapped in optical lattices to simulate nonadiabatic effects, as they appear in certain molecular dynamical problems. The idea consists of a judicious choice of two rotational states as the simulated electronic or nuclear degrees of freedom, in which their dipolar interactions induce the required attractive or repulsive interactions between them. We benchmark our proposal by studying the scattering of an electron or a proton against a hydrogen atom, showing the effect of electronic exchange and inelastic ionization as the mass ratio between the simulated nuclei and electrons—a tunable experimental parameter in our simulator—becomes comparable. These benchmarks illustrate how the simulator can qualitatively emulate phenomena like those appearing in molecular dynamical problems even if the simulated interaction occurs in two dimensions with a dipolar scaling. Beyond the molecular implementation proposed here, our proposal can be readily extrapolated to other atomic platforms, e.g., based on fermionic Rydberg atoms.

Microcombs, formed in optical microresonators driven by continuous-wave lasers, are miniaturized optical frequency combs. Leveraging integrated photonics and laser self-injection locking, compact microcombs can be constructed via hybrid integration of a semiconductor laser with a chip-based microresonator. While the current linear self-injection locking theory has successfully addressed the linear coupling between the laser cavity and the external microresonator, it fails to describe the complicated nonlinear processes, especially for dark-pulse microcomb formation. Here, we investigate—theoretically, numerically, and experimentally—the Kerr-thermal dynamics of a semiconductor laser self-injection locked to an integrated silicon nitride microresonator. We unveil intriguing yet universal dark-pulse formation and switching behavior with discrete steps, and establish a theoretical model scrutinizing the synergy of laser-microresonator mutual coupling, Kerr nonlinearity, and photothermal effect. Numerical simulation confirms the experimental result and identifies the origins. Exploiting this unique phenomenon, we showcase an application on low-noise photonic microwave generation with phase noise purified by 23.5 dB. Our study not only adds critical insight of pulse formation in laser-microresonator hybrid systems, but also enables all-passive, photonic-chip-based microwave oscillators with high spectral purity.

The lanthanide elements have long been reported as having a common series of structural phase transitions on compression, but recent diffraction studies have revealed two series of transitions: one in the low-Z lanthanides (Nd and Sm) involving an 8-atom orthorhombic structure ($oF8$), also seen in some actinide elements, and another in the high-Z lanthanides (Gd, Tb, Dy, and Ho) involving an isosymmetric 16-atom structure ($oF16$), unique to the lanthanides. No element has yet been found to exhibit both structures. We have followed the structural evolution of Tb to 308 GPa and find that $oF16$-Tb transforms to $oF8$-Tb at 234 GPa, which is stable to at least 308 GPa. This transition is confirmed by theoretical results which show the $oF8$ phase becoming energetically favorable above 280 GPa. This observation of the $oF16\to oF8$ transition unites the two phase-transition sequences and suggests that there is a common $oF16\to oF8\to oC4\to tI2$ transition sequence in the lanthanide elements under pressure.

Vibronic excitations of molecules at nanoscale interfaces are important for molecular electronics and spintronics and have therefore attracted considerable attention. For single molecules in mechanically controlled break junctions or in a scanning tunneling microscope (STM), vibronic excitations are typically described by a double-barrier tunneling junction model. In this model, a homogeneous electric field is considered and the atomic structure of the metal contacts is neglected. Here, we report experimental STM data of a new nonplanar organometallic complex, [$\mathrm{Mo}{(\mathrm{CO})}_3({\text{Pyridine}}_3{\mathrm{S}}_3)$], on Ag(111). Spatially resolved maps of the vibronic excitations show several features related to the reordering of the occupied molecular orbitals due to the rapidly decaying potential of the tip apex. Such rearrangement leads to a significant shift in the vibronic levels as the tip position is changed. These observations, together with our modelling results, demonstrate that the molecular orbitals can be controlled by the field of the STM tip, whose atomic-scale variation deserves more attention in studies of nonplanar molecules.

Halide perovskites are known for their rich phase diagram and superior performance in diverse optoelectronics applications. The latter property is often attributed to the long electron-hole recombination time, whose underlying physical mechanism has been a long-standing controversy. In this Letter, we investigate the transport and localization properties of electron and hole carriers in a prototypical halide perovskite (${\mathrm{CsPbBr}}_3$), through ab initio tight-binding nonadiabatic dynamics approach for large-scale (tens of nm size) supercell calculations, to simulate electron and ion dynamics on the same footing. We found distinct structural, lattice polarization, and electron-phonon coupling properties at low (below 100 K) and high temperatures, consistent with experimental observations. In particular, at low temperature we find spontaneous formation of polar grain boundaries in the nonpolar bulk systems, which result in two-dimensional polarization patterns that serve to localize and separate electrons and holes. We reveal phonon-assisted variable-range hopping mostly responsible for low-temperature transport, and their characteristic frequency correlates with temperature-dependent phonon power spectrum and energy oscillation frequency in nonadiabatic dynamics. We answer the critical questions of long electron-hole recombination lifetime at low temperature and offer the correlation among polarization domains, electron-phonon couplings, and photocarrier dynamics.

We investigate the effect of easy-axis metamagnetic crossover on superconductivity in ${\mathrm{UTe}}_2$ along the $a$ axis through measurements of ac susceptibility, magnetization, and the magnetocaloric effect. In ultraclean single crystals, we identify a field-induced phase transition within the superconducting state at 5.6 T, driven by metamagnetism. This transition leads to a high-field superconducting state, significantly increasing the upper critical field to 12 T. A sudden increase in entropy at the transition suggests a self-reconstruction of the order parameter, enabling multicomponent superconducting states to adapt to external perturbations.

Recently, exotic superconductivity emerging from a spin-and-valley-polarized metallic phase has been discovered in rhombohedral tetralayer graphene. To explain this observation, we study the role of electron-electron interactions in driving flavor symmetry breaking, using the Hartree-Fock (HF) approximation, and in stabilizing superconductivity mediated by repulsive interactions. Though mean-field HF correctly predicts the isospin flavors and reproduces the experimental phase diagram, it overestimates the band renormalization near the Fermi energy and suppresses superconducting instabilities. To address this, we introduce a physically motivated scheme that includes internal screening in the HF calculation. Using this formalism, we find superconductivity arising from the spin-valley polarized phase, on the electron-doped side, for a range of electric fields and electron dopings. Our findings reproduce the experimental observations and reveal a $p$-wave, finite-momentum, time-reversal-symmetry-broken superconducting state, encouraging further investigation into exotic phases in graphene multilayers.

Simulating large, strongly interacting fermionic systems remains a major challenge for existing numerical methods. In this Letter, we introduce Gutzwiller projected hidden fermion determinant states (G-HFDS) to simulate the strongly interacting limit of the Fermi-Hubbard model, namely the $t\text{−}J$ model, across the entire doping regime. We demonstrate that the G-HFDS achieve energies competitive with matrix product states on lattices as large as $10\times 10$ sites while using several orders of magnitude fewer parameters, suggesting the potential for efficient application to even larger system sizes. This remarkable efficiency enables us to probe low-energy physics across the full doping range, providing new insights into the competition between kinetic and magnetic interactions and the nature of emergent quasiparticles. Starting from the low-doping regime, where magnetic polarons dominate the low energy physics, we track their evolution with increasing doping and different next-nearest neighbor hopping amplitudes through analyses of spin and polaron correlation functions as well as the Fermi surface. Our findings demonstrate the potential of determinant-based neural quantum states with an inherent fermionic sign structure, opening the way for simulating large-scale fermionic systems at any particle filling.

Interfacial Dzyaloshinskii-Moriya interaction (DMI) is a key ingredient in the stabilization of chiral magnetic states in thin films. Its sign and strength often determine crucial properties of magnetic objects, like their topology or how they can be manipulated with currents. A few experimental techniques are currently available to measure DMI quantitatively, based on the study of domain walls, spin waves, or spin-orbit torques. In this Letter, we propose a qualitative variant of spin wave methods. We rely on magnetic noise from confined thermal spin waves in domain walls and skyrmions in perpendicularly magnetized thin films, which we probe with scanning nitrogen-vacancy center relaxometry. We show both numerically and experimentally that the sign of the DMI can be inferred from the amplitude of the detected noise, which is affected by the nonreciprocity in the spin wave dispersion. Furthermore, we also demonstrate that the noise distribution around the contour of magnetic skyrmions reveals their Néel or Bloch nature, giving therefore also insight into the strength of DMI involved in their stabilization.

Biological systems commonly combine intrinsically out-of-equilibrium active components with passive polymeric inclusions to produce unique material properties. To explore these composite systems, idealized models—such as polymers in active fluids—are essential to develop a predictive theoretical framework. We simulate a single, freely jointed passive chain in two-dimensional active turbulence. Active flows advect the polymer, producing a substantially enhanced diffusivity. Our results reveal that the dimensionless diffusivity obeys scaling laws governed by the Péclet, Weissenberg, and Ericksen numbers, which paves the way for designing active/polymeric hybrid materials with predictable properties that differ significantly from those of nondeformable inclusions.

We propose a novel tensor-network method to achieve accurate and efficient simulations of Abelian lattice gauge theories (LGTs) in $(2+1)\mathrm{D}$ for both ground-state and real-time dynamics. The first key is to identify a gauge canonical form of gauge-invariant tensor-network states, which already simplifies existing algorithms for $(1+1)\mathrm{D}$ LGTs. The second key is to employ the gauge canonical form of a projected entangled-pair state (PEPS) combining with variational Monte Carlo, enabling efficient computations for $(2+1)\mathrm{D}$ LGTs. We demonstrate the versatile capability of this approach for accurate ground-state simulation of pure ${\mathbb{Z}}_2$, ${\mathbb{Z}}_3$, and ${\mathbb{Z}}_4$ gauge theory, odd-${\mathbb{Z}}_2$ gauge theories, and ${\mathbb{Z}}_2$ gauge theory coupled to hard-core bosons, on square lattices up to $32\times 32$. Furthermore, we demonstrate that it allows for accurate simulations of real-time dynamics up to long time, exemplified by the dynamics of elementary excitations of the deconfined ${\mathbb{Z}}_2$ gauge field at $10\times 10$. This is also the first example of simulating the real-time dynamics of PEPS with variational Monte Carlo, whose impact may extend beyond gauge theory. Our Letter establishes gauge-invariant PEPS as a powerful approach for both ground-state and dynamical simulations, opening up a new avenue for nonperturbatively studying $(2+1)\mathrm{D}$ LGTs.

The ability to perform fast and accurate rotations between the computational basis states of quantum bits is one of the most fundamental requirements for building a quantum computer. Because physical qubits generally contain more than two levels, faster gates often result in a higher leakage rate outside of the computational space. In this Letter, we enhance the state-of-the-art single qubit gate by introducing active leakage cancellation. This is accomplished via a second drive tone near the leakage transition such that we cancel the leakage caused by the main drive. Furthermore, we describe a measurement sequence that can be used to calibrate the parameters of this leakage cancellation drive. Finally, we apply the technique to superconducting transmon qubits and achieve leakage suppression by up to a factor of 20 when compared to pulses shaped with the standard derivative removal by adiabatic gate technique. This results in a coherence-limited gate infidelity of $7.5\times {10}^{-5}$ with leakage below ${10}^{-5}$ level, for a 10 ns $\pi /2$ gate and 196 MHz qubit anharmonicity.

Trotterization is one of the central approaches for simulating quantum many-body dynamics on quantum computers or tensor networks. In addition to its simple implementation, recent studies have revealed that its error and cost can be reduced if the initial state is closed in the low-energy subspace. However, the improvement by the low-energy property diminishes rapidly as the Trotter order grows in the previous studies, and thus, it is mysterious whether there exists a genuine advantage of low-energy initial states. In this Letter, we resolve this problem by proving the optimal error bound and cost of Trotterization for low-energy initial states. For generic local Hamiltonians composed of positive-semidefinite terms, we show that the Trotter error is at most linear in the initial state energy $\mathrm{\Delta }$ and polylogarithmic in the system size $N$. As a result, the computational cost becomes substantially small for low-energy states with $\mathrm{\Delta }\in o(Ng)$ compared to the one for arbitrary initial states, where $g$ denotes the energy per site and $Ng$ means the whole-system energy. Our error bound and cost of Trotterization achieve the theoretically best scaling in the initial state energy $\mathrm{\Delta }$. In addition, they can be partially extended to weakly correlated initial states having low-energy expectation values, which are not necessarily closed in the low-energy subspace. Our results will pave the way for fast and accurate simulations of low-energy states, which are one of the central targets in condensed matter physics and quantum chemistry.

Resolving frequencies in a time-dependent field is classically limited by the measurement bandwidth. Using tools from quantum metrology and quantum control may overcome this limit, yet the full advantage afforded by entanglement so far remains elusive. Here we map the problem of frequency measurement to that of estimating a global dephasing quantum channel. In this way, we determine the ultimate quantum limits of frequency estimation in stochastic ac sensing. We find exact quantum Fisher information bounds for estimating frequency and frequency differences of stochastic fields. In particular, given two close signals with frequency separation ${\omega }_r$, we find that the quantum Fisher information for the separation estimation is approximately $2/{\omega }_r^2$, i.e., inversely proportional to the separation parameter. The bounds are achievable in certain regimes by superpositions of Dicke states. GHZ states are suboptimal but improve precision over unentangled states, achieving Heisenberg scaling in the low-bandwidth limit. This Letter establishes a robust framework for stochastic ac signal sensing that can be extended to arbitrary time-dependent and stochastic fields.

We construct wave functions for unitary irreducible representations (UIRs) of the Bondi-Metzner-Sachs (BMS) group, i.e., BMS particles, and show that they describe quantum superpositions of (Poincaré) particles propagating on inequivalent gravity vacua. This follows from reconsidering McCarthy’s classification of BMS group UIRs through a unique, Lorentz-invariant, but nonlinear, decomposition of supermomenta into hard and soft pieces.

Two decades ago the ${\chi }_{c1}(3872)$ state was discovered in the hadron spectrum with two heavy quarks. The discovery fueled a surge in experimental research, uncovering dozens of so called $XYZ$ exotics states lying outside the conventional quark model, as well as theoretical investigations into new forms of matter, such as quark-gluon hybrids, tetraquarks, and pentaquarks, with the potential of disclosing new information about the fundamental strong force. Among the $XYZ\mathrm{s}$, the ${\chi }_{c1}(3872)$ and $T_{cc}^{+}(3875)$ states stand out for their striking characteristics and unleashed many discussions about their nature. Here, we address this question using the Born-Oppenheimer effective field theory (BOEFT) and show how QCD settles the issue of their composition. Not only do we describe well the main features of the ${\chi }_{c1}(3872)$ and $T_{cc}^{+}(3875)$ states, but we also obtain predictions in the bottomonium sector. This opens the way to systematic applications of BOEFT to all $XYZ\mathrm{s}$.