The growth of simple operators is essential for the emergence of chaotic dynamics and quantum thermalization. Recent studies have proposed different measures, including the out-of-time-order correlator and Krylov complexity. It is established that the out-of-time-order correlator serves as the signature of quantum many-body chaos, while the Krylov complexity provides its upper bound. However, there exist nonchaotic systems in which Krylov complexity grows exponentially, indicating that the Krylov complexity itself is not a witness of many-body chaos. In this Letter, we introduce the missing ingredient called the Krylov metric $K_{mn}$, which probes the size of the Krylov basis. We propose that the universal criteria for fast scramblers include (i) the exponential growth of Krylov complexity, (ii) the diagonal elements $K_{nn}\sim n^h$ with $h\in (0,1]$, and (iii) the negligibility of off-diagonal elements $K_{mn}$ with $m\ne n$. We further show that $h=\varkappa /2\alpha$ is a ratio between the quantum Lyapunov exponent $\varkappa$ and the Krylov exponent $\alpha$. This proposal is supported by both generic arguments and explicit examples, including solvable Sachdev-Ye-Kitaev models, Luttinger liquids, and many-body localized systems. Our results provide a refined understanding of how chaotic dynamics emerge from the Krylov space perspective.

We introduce a method that ensures efficient computation of one-dimensional quantum systems with long-range interactions across all temperatures. Our algorithm operates within a quasipolynomial run-time for inverse temperatures up to $\beta =\mathrm{poly}(\ln (n))$. At the core of our approach is the density matrix renormalization group algorithm, which typically does not guarantee efficiency. We have created a new truncation scheme for the matrix product operator of the quantum Gibbs states, which allows us to control the error analytically. Additionally, our method can be applied to simulate the time evolution of systems with long-range interactions, achieving significantly better precision than that offered by the Lieb-Robinson bound.

This Letter augments the recently introduced stabilizer tensor network (STN) protocol with magic state injection, reporting a new framework with significantly enhanced ability to simulate circuits with an extensive number of non-Clifford operations. Specifically, for random $T$-doped $N$-qubit Clifford circuits the computational cost of circuits prepared with magic state injection scales as $\mathcal{O}[\mathrm{poly}(N)]$ when the circuit has $t\lesssim N$ $T$ gates compared to an exponential scaling for the STN approach, which is demonstrated in systems of up to 200 qubits. In the case of the hidden bit shift circuit, a paradigmatic benchmarking system for extended stabilizer methods with a tunable amount of magic, we report that our magic state injected STN framework can efficiently simulate 4000 qubits and $320T$ gates. These findings provide a promising outlook for the use of this protocol in the classical modeling of quantum circuits that are conventionally difficult to simulate efficiently.

Determining a beam’s full trajectory requires tracking both its position and momentum (angular) information. However, the product of position and momentum uncertainty in a simultaneous measurement of the two parameters is bound by the Heisenberg uncertainty limit (HUL). In this work, we present a proof-of-principle demonstration of a quantum-enhanced beam tracking technique, leveraging the inherent position and momentum entanglement between photons produced via spontaneous parametric down-conversion (SPDC). We show that quantum entanglement can be exploited to achieve a beam tracking accuracy beyond the HUL in a simultaneous measurement. Moreover, with existing detection technologies, it is already possible to achieve near real-time beam tracking capabilities at the single-photon level. The technique also exhibits high resilience to background influences, with negligible reduction in tracking accuracy even when subjected to a disruptive beam that is significantly brighter than SPDC.

Two universal predictions of general relativity are the propagation of gravitational waves of large momentum along null geodesics and the isospectrality of quasinormal modes in many families of black holes. In extensions of general relativity, these properties are typically lost: quasinormal modes are no longer isospectral and gravitational wave propagation is no longer geodesic and it exhibits birefringence—polarization-dependent speed. We study these effects in an effective-field-theory extension of general relativity with up to eight-derivative terms and show that there is a unique Lagrangian that has a nonbirefringent dispersion relation for gravitational waves and isospectral quasinormal modes in the eikonal limit. We argue that both properties are related through a generalized correspondence between eikonal quasinormal modes and unstable photon-sphere orbits. These properties define a special class of theories that we denote as isospectral effective field theories. We note that the lowest-order isospectral correction to general relativity coincides with the quartic-curvature correction arising from type II string theory, suggesting that isospectrality might be a key feature of quantum gravity.

We present the high-precision result for the zero-jettiness soft function at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. At this perturbative order, the soft function is the last missing ingredient required for the computation of a hadronic color singlet production or a color singlet decay into two jets using the zero-jettiness variable as the slicing parameter. Furthermore, the knowledge of the N3LO soft function enables the resummed description of the thrust distribution in the process $e^{+}{e}^{-}\to \text{hadrons}$ through next-to-next-to-next-to-leading logarithmic order, which is important for the extraction of the strong coupling constant using this shape variable. On the methodological side, the complexity of the zero-jettiness variable forced us to develop a new semi-analytic method for phase-space integration in the presence of constraints parameterized through Heaviside functions which, hopefully, will be useful for further development of the $N$-jettiness slicing scheme.

The model underlying physics of guiding light in single-mode fibers—the one-dimensional nonlinear Schrödinger equation (NLSE)—reveals a remarkable balance of the fiber dispersion and nonlinearity, leading to the existence of optical solitons. With the inverse scattering transform (IST) method and its perturbation theory extension, one can go beyond single-soliton physics and investigate nonlinear dynamics of complex optical pulses driven by soliton interactions. Here, advancing the IST perturbation theory approach, we introduce the eigenvalue response functions, which provide an intuitively clear way to manipulate individual characteristics of solitons even in the case of their entire overlapping, i.e., very strong interactions. The response functions reveal the spatial sensitivity of the multisoliton pulse concerning its instantaneous perturbations, allowing one to manipulate the velocities and amplitudes of each soliton. Based on a recirculating optical fiber loop system and homodyne measurement, our experimental setup enables observation of long-distance spatiotemporal NLSE dynamics and complete phase-amplitude characterization of optical pulses containing several solitons, which provides accurate experimental IST spectra. Adding a localized phase perturbation on a box-shaped wave field, we change individual soliton characteristics and can detach solitons selectively from the whole pulse. The detached solitons exhibit velocities very close to the theoretical predictions, thereby demonstrating the efficiency and robustness of the response functions approach.

We revisited the influence of electron-electron scattering on the resistivity of a two-dimensional system with a linear spectrum. In conventional systems with a parabolic spectrum, where umklapp scattering is either prohibited or ineffective due to the small Fermi surface, particle-particle scattering does not contribute to conductivity because it does not change the total momentum. However, within the framework of the Boltzmann kinetic model, we demonstrate that electron-electron scattering in Dirac systems can significantly contribute to conductivity, producing distinct temperature-dependent corrections: a $T^4$ behavior at low temperatures and a $T^2$ dependence at moderate temperatures. While the predicted $T^4$ scaling is not observed experimentally—likely suppressed by dominant weak localization effects—the $T^2$ scaling is clearly confirmed in our measurements. Specifically, temperature-dependent resistivity data from a gapless single-valley HgTe quantum well exhibit $T^2$ corrections, which align well with theoretical predictions. Thus, we challenge the paradigm that the $T^2$ term in resistivity is absent in single-band 2D metals.

We demonstrate that periodically driven Fermions coupled to simple bosonic baths have steady state occupations of Floquet Bloch bands that generically display nonanalyticities at certain momenta that resemble the Fermi surfaces of equilibrium non-Fermi liquids. Remarkably these nonequilibrium Fermi surfaces remain sharp even when the bath is at finite temperature, leading to critical power-law decaying correlations at finite temperature, a phenomenon with no analog in equilibrium. We also show that generically there is in-gap current rectification for clean metals lacking inversion symmetry, and explain why this occurs universally regardless of the details of collisions.

The dynamics of an electron-hole plasma governed by strong Coulomb interaction is a challenging many-body problem. We report on experimental realization of electron-hole many-body states in the picosecond time scale, with tunable densities in a representative semiconductor ${\mathrm{Cu}}_2\mathrm{O}$. By using time-resolved optical-pump terahertz third-harmonic-generation spectroscopy, we study the nonlinear terahertz dynamical characteristics of the many-body electron-hole states. We find not only efficient and nonperturbative terahertz third-harmonic yield associated with the excitonic formation but also a nonmonotonic dependence of the excitonic nonlinear response on the electron-hole density, reflecting the exciton dissociation at high charge density. Our results provide an efficient excitonic sensing of the far-from-equilibrium electron-hole many-body states.

Logarithmic aging phenomena are prevalent in various systems, including electronic materials and biological structures. This Letter utilizes a generalized continuous-time random walk framework to investigate the mechanisms behind the logarithmic aging phenomena. By incorporating non-Markovian processes with significant memory effects, we modify traditional diffusion models to exhibit logarithmic decay in both survival and returning probabilities. Importantly, we analyze the impact of aging on autocorrelation functions, illustrating how long-term memory behaviors affect the temporal evolution of physical observables. These results connect microscopic models to macroscopic manifestations in real-world systems, advancing the understanding of ultraslow dynamics in disordered systems.

Monodisperse spherical colloidal particles confined within emulsion droplets can crystallize into icosahedral clusters. Experimentally, it was observed that a few large colloidal particles added as defects preferentially migrate to the vertices of the icosahedral clusters. To understand this structure formation phenomenon, we simulate the confined self-assembly of hard spheres in the presence of a small number of larger particles. The results demonstrate that large spheres are significantly influenced by concentric shells of small spheres near the crystallization transition. Entropic forces drive the large spheres to the cluster surface, where they settle into free energy minima at the icosahedron vertices. Notably, the addition of twelve large spheres results in the formation of a perfect icosahedral frame. Free energy calculations via umbrella sampling are used to quantify this process and show that both the migration to the cluster surface and the trapping at the vertices with trapping strength of multiple $k_{\mathrm{B}}T$ results from free energy minimization. Moreover, our study reveals that the crystallization pathway and dynamics of large spheres are consistent across different systems, suggesting robustness of entropic trapping.

We present an explicit construction of a relativistic quantum computing architecture using a variational quantum circuit approach that is shown to allow for universal quantum computing. The variational quantum circuit consists of tunable single-qubit rotations and entangling gates that are implemented successively. The single-qubit rotations are parameterized by the proper time intervals of the qubits’ trajectories and can be tuned by varying their relativistic motion in spacetime. The entangling layer is mediated by a relativistic quantum field instead of through direct coupling between the qubits. Within this setting, we give a prescription for how to use quantum field-mediated entanglement and manipulation of the relativistic motion of qubits to obtain a universal gate set, for which compact nonperturbative expressions that are valid for general spacetimes are also obtained. We also derive a lower bound on the channel fidelity that shows the existence of parameter regimes in which all entangling operations are effectively unitary, despite the noise generated from the presence of a mediating quantum field. Finally, we consider an explicit implementation of the quantum Fourier transform with relativistic qubits.

Superradiant lasers, which consist of incoherently driven atoms coupled to a lossy cavity, are a promising source of coherent light due to their stable frequency and superior narrow linewidth. We show that when a fraction of the atoms is not driven, a shift in the lasing frequency and a broadening of the linewidth occur, limiting the performance of a superradiant laser. We explain this behavior by identifying nonreciprocal interactions between driven and undriven atoms, i.e., competing alignment and antialignment of their dipoles. Our results have implications for the realization of superradiant lasers, establishing the relevance of nonreciprocal phenomena for quantum technologies.

We introduce a theoretical framework that allows for the systematic and efficient description of the ultrafast nonlinear response of molecular polaritons, i.e., hybrid light-matter states, in the collective regime of large numbers of molecules $\mathcal{N}$ coupled to the cavity photon mode. Our approach is based on a semiclassical, mean-field evolution of the molecular Hamiltonian and the cavity field, which is complemented by a perturbative expansion of both light and matter counterparts in the input fields entering the cavity. In addition, expansion in terms of the pulse phases enables us to disentangle different excitation pathways in Liouville space, thereby distinguishing contributions to the nonlinear response. The formalism extends traditional free-space nonlinear spectroscopy by incorporating the feedback of matter onto the light field via the induced polarization. We demonstrate the utility of the framework by applying it to the calculation of pump-probe polariton spectra and show how, by storing the pulses, the cavity facilitates additional excitation pathways, which can be used to isolate purely bright state contributions. Our method, which does not scale with $\mathcal{N}$, is broadly applicable and can be extended to model a wide range of current experiments investigating the dynamical nonlinear response of hybrid light-matter states.

We study a three-orbital Hubbard-Kanamori model relevant for iron-based superconductors using variational wave functions explicitly including spatial correlations and electron pairing. We span the nonmagnetic sector from filling $n=4$, which is representative of undoped iron-based superconductors, to $n=3$, where a Mott insulating state with each orbital at half filling is found. In the strong-coupling regime, when the electron density is increased, we find a spontaneous differentiation between the occupation of $d_{xz}$ and $d_{yz}$ orbitals, leading to an orbital-selective state with a nematic character that becomes stronger at increasing density. One of these orbitals stays half filled for all densities while the other one hosts (together with the $d_{xy}$ orbital) the excess of electron density. Most importantly, in this regime long-range pairing correlations appear in the orbital with the largest occupation. Our results highlight a strong link between orbital-selective correlations, nematicity, and superconductivity, which requires the presence of a significant Hund’s coupling.

Collective excitations of charged particles under the influence of an electromagnetic field give rise to a rich variety of hybrid light-matter quasiparticles with unique properties. In metals, intraband collective response manifested by negative permittivity leads to plasmon polaritons with extreme field confinement, wavelength “squeezing,” and potentially low propagation losses. In contrast, photons in semiconductors commonly couple to interband collective response in the form of exciton polaritons, which give rise to completely different polaritonic properties, described by a superposition of the photon and exciton and an anti-crossing of the eigenstates. In this work, we identify the existence of plasmon-like collective excitations originating from the interband excitonic response of biased bilayer and trilayer graphene, in the form of graphene exciton polaritons (GEPs). We find that GEPs possess electrically tunable polaritonic properties and discover that such excitations follow a universal dispersion law for all surface polaritons in 2D excitonic systems. Accounting for nonlocal corrections to the excitonic response, we find that the GEPs exhibit confinement factors that can exceed those of graphene plasmons, and with moderate losses that would enable their observation in cryo-SNOM experiments. These predictions of plasmon-like interband collective excitations in biased graphene systems open up new research avenues for tunable plasmonic phenomena based on excitonic systems, and the ability to control and manipulate such phenomena at the atomic scale.