Rényi entropies are conceptually valuable and experimentally relevant generalizations of the celebrated von Neumann entanglement entropy. After a quantum quench in a clean quantum many-body system they generically display a universal linear growth in time followed by saturation. While a finite subsystem is essentially at local equilibrium when the entanglement saturates, it is genuinely out of equilibrium in the growth phase. In particular, the slope of the growth carries vital information on the nature of the system’s dynamics, and its characterization is a key objective of current research. Here we show that the slope of Rényi entropies can be determined by means of a spacetime duality transformation. In essence, we argue that the slope coincides with the stationary density of entropy of the model obtained by exchanging the roles of space and time. Therefore, very surprisingly, the slope of the entanglement is expressed as an equilibrium quantity. We use this observation to find an explicit exact formula for the slope of Rényi entropies in all integrable models treatable by thermodynamic Bethe ansatz and evolving from integrable initial states. Interestingly, this formula can be understood in terms of a quasiparticle picture only in the von Neumann limit.

We investigate an experimental toy-model system of a pseudospin-half square-lattice Hubbard Hamiltonian in $[{({\mathrm{SrIrO}}_3)}_1/{({\mathrm{CaTiO}}_3)}_1]$ to include both nontrivial complex hopping and moderate electron correlation. While the former induces electronic Berry phases as anticipated from the weak-coupling limit, the latter stabilizes an antiferromagnetic Mott insulator ground state analogous to the strong-coupling limit. Their combined results in the real system are found to be an anomalous Hall effect with a nonmonotonic temperature dependence due to the competition of the antiferromagnetic order and charge excitations in the Mott state, and an exceptionally large Ising anisotropy that is captured as a giant magnon gap beyond the superexchange approach. The unusual phenomena highlight the rich interplay of electronic topology and electron correlation in the intermediate-coupling regime that is largely unexplored and challenging in theoretical modeling.

Purifying a high-temperature ensemble of quantum particles toward a known state is a key requirement to exploit quantum many-body effects. An alternative to passive cooling, which brings a system to its ground state, is active feedback, which stabilizes the system at a chosen target state. This alternative, if realized, offers additional control capabilities for the design of quantum states. Here we present a feedback algorithm applied to a quantum system, which is capable of stabilizing the collective state of an ensemble from its maximum entropy state to the limit of single quantum fluctuations. Our algorithmic approach maximizes the rate of state purification given the system’s physical constants; thus it remains the optimal feedback approach even in the presence of dissipation and disorder. We test experimentally the robustness of this feedback on the highly inhomogeneous nuclear-spin ensemble of a semiconductor quantum dot, reducing nuclear-spin fluctuations 83-fold, down to 5.7(2) spin macrostates. Simulations demonstrate that without system-specific inhomogeneities, our algorithm can purify the system down to single-spin fluctuations. Further, we exploit our algorithmic approach to tailor nontrivial nuclear-spin distributions that go beyond simple polarization, including weighted bimodality and latticed multistability. This control is a precursor toward quantum-correlated macrostates, which an extended version of our algorithm could generate in homogeneous systems.

By leveraging shared entanglement between a pair of qubits, one can teleport a quantum state from one particle to another. Recent advances have uncovered an intrinsically many-body generalization of quantum teleportation, with an elegant and surprising connection to gravity. In particular, the teleportation of quantum information relies on many-body dynamics, which originate from strongly interacting systems that are holographically dual to gravity; from the gravitational perspective, such quantum teleportation can be understood as the transmission of information through a traversable wormhole. Here, we propose and analyze a new mechanism for many-body quantum teleportation—dubbed peaked-size teleportation. Intriguingly, peaked-size teleportation utilizes precisely the same type of quantum circuit as traversable wormhole teleportation yet has a completely distinct microscopic origin: It relies upon the spreading of local operators under generic thermalizing dynamics and not gravitational physics. We demonstrate the ubiquity of peaked-size teleportation, both analytically and numerically, across a diverse landscape of physical systems, including random unitary circuits, the Sachdev-Ye-Kitaev model (at high temperatures), one-dimensional spin chains, and a bulk theory of gravity with stringy corrections. Our results pave the way toward using many-body quantum teleportation as a powerful experimental tool for (i) characterizing the size distributions of operators in strongly correlated systems and (ii) distinguishing between generic and intrinsically gravitational scrambling dynamics. To this end, we provide a detailed experimental blueprint for realizing many-body quantum teleportation in both trapped ions and Rydberg atom arrays; effects of decoherence and experimental imperfections are analyzed.

Monopole operators are studied in a large family of quantum critical points between Dirac spin liquids and topological quantum spin liquids (QSLs): chiral and $Z_2$ QSLs. These quantum phase transitions are described by conformal field theories (CFTs): quantum electrodynamics in $2+1$ dimensions with $2N$ flavors of two-component massless Dirac fermions and a four-fermion interaction term. For the transition to a chiral spin liquid, it is the Gross-Neveu interaction (${\mathrm{QED}}_3\text{−}\mathrm{GN}$), while for the transitions to $Z_2$ QSLs, it is a superconducting pairing term with general spin and valley structure (generalized ${\mathrm{QED}}_3\text{−}{Z}_2\mathrm{GN}$). Using the state-operator correspondence, we obtain monopole scaling dimensions to subleading order in $1/N$. For monopoles with a minimal topological charge $q=1/2$, the scaling dimension is $2N\times 0.26510$ at leading order, with the quantum correction being 0.118911(7) for the chiral spin liquid, and 0.102846(9) for the simplest $Z_2$ case (the expression is also given for a general pairing term). Although these two anomalous dimensions are nearly equal, the underlying quantum fluctuations possess distinct origins. The analogous result in ${\mathrm{QED}}_3$ is also obtained, and we find a subleading contribution of $-0.038138(5)$, which is slightly different from the value $-0.0383$ first obtained in the literature. The scaling dimension of a ${\mathrm{QED}}_3\text{−}\mathrm{GN}$ monopole with minimal charge is very close to the scaling dimensions of other operators predicted to be equal by a conjectured duality between ${\mathrm{QED}}_3\text{−}\mathrm{GN}$ with $2N=2$ flavors and the ${\mathrm{C}\mathrm{P}}^1$ model. Additionally, nonminimally charged monopoles with equal charges on both sides of the duality have similar scaling dimensions. By studying the large-$q$ asymptotics of the scaling dimensions in ${\mathrm{QED}}_3$, ${\mathrm{QED}}_3\text{−}\mathrm{GN}$, and ${\mathrm{QED}}_3\text{−}{Z}_2\mathrm{GN}$, we verify that the constant $O(q^0)$ coefficient precisely matches the universal nonperturbative prediction for CFTs with a global U(1) symmetry. Finally, we identify numerous open questions regarding the fate of monopoles and their hierarchies at transitions to spin liquids and ordered phases.

Collisionless plasmas exhibit nonthermal and anisotropic particle distributions after being energized; as a consequence, they enter a state of low Boltzmann-Gibbs (BG) entropy relative to the thermal state. The Vlasov equations predict that in a collisionless plasma with closed boundaries, BG entropy is formally conserved, along with an infinite set of other Casimir invariants; this provides a seemingly strong constraint that may explain how plasmas maintain low entropy. Nevertheless, it is commonly believed that entropy production is enabled by phase mixing or nonlinear entropy cascades. The question of whether such anomalous entropy production occurs, and of how to characterize it quantitatively, is a fundamental problem in plasma physics. We construct a new theoretical framework for characterizing entropy production (in a generalized sense) based on a set of ideally conserved dimensional quantities derived from the Casimir invariants; these are referred to as the “Casimir momenta,” and they generalize the BG entropy. The growth of the Casimir momenta relative to the average particle momentum indicates entropy production. We apply this framework to quantify entropy production in particle-in-cell simulations of laminar flows and turbulent flows driven in relativistic plasma, where efficient nonthermal particle acceleration is enabled. We demonstrate that a large amount of anomalous entropy is produced by turbulence despite nonthermal features. The Casimir momenta grow to cover a range of energies in the nonthermal tail of the distribution, and we correlate their growth with spatial structures. These results have implications for reduced modeling of nonthermal particle acceleration and for diagnosing irreversible dissipation in collisionless plasmas such as the solar wind and Earth’s magnetosphere. Dimensional representations of generalized entropy analogous to the Casimir momenta may be useful for other problems in statistical physics.

Generating high-quality data (e.g., images or video) is one of the most exciting and challenging frontiers in unsupervised machine learning. Utilizing quantum computers in such tasks to potentially enhance conventional machine-learning algorithms has emerged as a promising application but poses big challenges due to the limited number of qubits and the level of gate noise in available devices. In this work, we provide the first practical and experimental implementation of a quantum-classical generative algorithm capable of generating high-resolution images of handwritten digits with state-of-the-art gate-based quantum computers. In our quantum-assisted machine-learning framework, we implement a quantum-circuit-based generative model to learn and sample the prior distribution of a generative adversarial network. We introduce a multibasis technique which leverages the unique possibility of measuring quantum states in different bases, hence enhancing the expressivity of the prior distribution. We train this hybrid algorithm on an ion-trap device based on ${}^{171}{\mathrm{Yb}}^{+}$ ion qubits to generate high-quality images and quantitatively outperform comparable classical generative adversarial networks trained on the popular MNIST dataset for handwritten digits.

The mechanism of unconventional topological superconductivity (TSC) remains a long-standing issue. We investigate the quantum phase diagram of the extended $t\text{−}J\text{−}{J}_{\chi }$ model including spin chiral interactions on triangular lattice based on state-of-the-art density matrix renormalization group simulations. We identify distinct classes of superconducting phases characterized by nonzero topological Chern numbers $C=1$ and 2 and a nematic $d$-wave superconducting phase with a zero Chern number. The TSC states are shown to emerge from doping either a magnetic insulator or chiral spin liquid, which opens new opportunities for experimental discovery. In addition, we further classify the $C=2$ class of TSC phases into an isotropic and a nematic TSC phase and present evidence of continuous quantum phase transitions from the nematic TSC phase to both isotropic TSC and nematic $d$-wave phases. These results provide new insight into the mechanism of TSC with an emphasis on the role played by hole dynamics, which changes spin background and drives a topological phase transition at a hole doping level around 3% upon doping a magnetic insulator to enable the emergence of TSC.

In cuprate high-$T_c$ superconductors, resonant excitation of certain lattice vibrations has been shown to induce transient terahertz reflectivity features suggestive of nonequilibrium superconductivity above the critical temperature $T_c$. A microscopic mechanism for these observations is still lacking. Here, time-resolved measurements of scattering-angle- and polarization-dependent second-harmonic generation in driven ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ reveal a three-order-of-magnitude amplification of a 2.5-THz electronic mode, which is unique because of its symmetry, momentum, and temperature dependence. A theory for amplification of finite-momentum Josephson plasma polaritons, which are assumed to be well formed below $T_c$ but incoherent throughout the pseudogap phase, explains all these observations. A theoretical solution for the Fresnel-Floquet reflection that starts from the coherently oscillating Josephson plasma polaritons provides a possible mechanism for the nonequilibrium superconductorlike terahertz reflectivity reported earlier. Beyond the immediate case of cuprates, this work underscores the role of nonlinear mode mixing to amplify fluctuating modes above the transition temperature in a wide range of materials.

We show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has nonzero lattice momentum, i.e., if it is an eigenstate of the translation symmetry with eigenvalue $e^{iP}\ne 1$. Equivalently, any state that can be connected with a nonzero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. Some nontrivial consequences follow immediately from our theorem: (i) Several different types of Lieb-Schultz-Mattis-Oshikawa-Hastings theorems, including a previously unknown version involving only a discrete ${\mathbb{Z}}_n$ symmetry, can be derived in a simple manner from our result; (ii) a gapped topological order (in space dimension $d>1$) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum—this generalizes the familiar physics of Tao-Thouless; (iii) our result provides further evidence of the “smoothness” assumption widely used in the classification of crystalline symmetry-protected topological phases.

Mixtures of filaments and molecular motors form active materials with diverse dynamical behaviors that vary based on their constituents’ molecular properties. To develop a multiscale of these materials, we map the nonequilibrium phase diagram of microtubules and tip-accumulating kinesin-4 molecular motors. We find that kinesin-4 can drive either global contractions or turbulentlike extensile dynamics, depending on the concentrations of both microtubules and a bundling agent. We also observe a range of spatially heterogeneous nonequilibrium phases, including finite-sized radial asters, 1D wormlike chains, extended 2D bilayers, and system-spanning 3D active foams. Finally, we describe intricate kinetic pathways that yield microphase separated structures and arise from the inherent frustration between the orientational order of filamentous microtubules and the positional order of tip-accumulating molecular motors. Our work reveals a range of novel active states. It also shows that the form of active stresses is not solely dictated by the properties of individual motors and filaments, but is also contingent on the constituent concentrations and spatial arrangement of motors on the filaments.

Quantifying and comparing patterns of dynamical ecological systems requires averaging over measurable quantities. For example, to infer variation in movement and behavior, metrics such as step length and velocity are averaged over large ensembles. Yet, in nonergodic systems, such averaging is inconsistent; thus, identifying ergodicity breaking is essential in ecology. Using rich, high-resolution, movement data sets (greater than $7\times {10}^7$ localizations) from 70 individuals and continuous-time random walk modeling, we find subdiffusive behavior and ergodicity breaking in the localized movement of three species of avian predators. Small-scale, within-patch movement was found to be qualitatively different, not inferrable and separated from large-scale interpatch movement. Local search is characterized by long, power-law-distributed waiting times with a diverging mean, giving rise to ergodicity breaking in the form of considerable variability uniquely observed at this scale. This implies that wild animal movement is scale specific, with no typical waiting time at the local scale.

Semiconductor quantum dots in which electrons or holes are isolated via electrostatic potentials generated by surface gates are promising building blocks for semiconductor-based quantum technology. Here, we investigate double-quantum-dot (DQD) charge qubits in GaAs capacitively coupled to high-impedance superconducting quantum interference device array and Josephson-junction array resonators. We tune the strength of the electric-dipole interaction between the qubit and the resonator in situ using surface gates. We characterize the qubit-resonator coupling strength, the qubit decoherence, and the detuning noise affecting the charge qubit for different electrostatic DQD configurations. We find all quantities to be systematically tunable over more than one order of magnitude, resulting in reproducible decoherence rates ${\mathrm{\Gamma }}_2/2\pi <5\mathrm{MHz}$ in the limit of high interdot capacitance. In the opposite limit, by reducing the interdot capacitance, we increase the DQD electric-dipole strength and, therefore, its coupling to the resonator. Employing a Josephson-junction array resonator with an impedance of approximately $4\mathrm{k}\mathrm{\Omega }$ and a resonance frequency of ${\omega }_r/2\pi \sim 5.6\mathrm{GHz}$, we observe a coupling strength of $g/2\pi \sim 630\mathrm{MHz}$, demonstrating the possibility to operate electrons hosted in a semiconductor DQD in the ultrastrong-coupling regime (USC). The presented results are essential for further increasing the coherence of quantum-dot-based qubits and investigating USC physics in semiconducting QDs.

Efficient energy transfer often occurs between oscillation modes in a resonator when they are tuned to internal resonance. We design the eigenfrequencies of two vibrational modes of an electromechanical resonator to be close to a ratio of $3:1$ and demonstrate that the energy supplied to the upper mode can be controllably transferred to the lower mode. With the lower mode vibrating with a period tripled that of the upper mode, the discrete time-translation symmetry imposed by the periodic drive is broken. The lower mode settles into one of three stable period-tripled states with different phases. This channel for energy transfer from the upper mode can be turned on or off without changing system parameters. When the upper mode itself becomes multistable under strong resonant or parametric drive, additional sets of coexisting period-tripled states emerge in the lower mode. In the latter case, we measure a total of six coexisting vibration states with identical amplitude but phases differing by $\pi /3$. Excitation of coexisting states with three different phases could open new opportunities in designing mechanical memory based on ternary logic. Coupled resonators with period-tripled states can also be used to model complex interacting systems with spin equal to one.

Macroscopic descriptions of ferroelectrics have an obvious appeal in terms of efficiency and physical intuition. Their predictive power, however, has often been thwarted by the lack of a systematic procedure to extract the relevant materials parameters from the microscopics. Here we address this limitation by establishing an unambiguous two-way mapping between spatially inhomogeneous fields and discrete lattice modes. This yields a natural treatment of gradient couplings in the macroscopic regime via a long-wavelength expansion of the crystal Hamiltonian. Our analysis reveals an inherent arbitrariness in both the flexoelectric and polarization gradient coefficients, which we ascribe to a translational freedom in the definition of the polar distortion pattern. Remarkably, such arbitrariness cancels out in all physically measurable properties (relaxed atomic structure and energetics) derived from the model, pointing to a generalized translational covariance in the continuum description of inhomogeneous ferroelectric structures. We demonstrate our claims with extensive numerical tests on 180° domain walls in common ferroelectric perovskites, finding excellent agreement between the continuum model and direct first-principles calculations.

${\text{CeRh}}_2{\mathrm{As}}_2$ is an unconventional superconductor with multiple superconducting phases and $T_c=0.26\mathrm{K}$. When $H\parallel c$, it shows a field-induced transition at ${\mu }_0{H}^{*}=4\mathrm{T}$ from a low-field superconducting state SC1 to a high-field state SC2 with a large critical field of ${\mu }_0{H}_{c2}=14\mathrm{T}$. In contrast, for $H\perp c$, only the SC1 with ${\mu }_0{H}_{c2}=2\mathrm{T}$ is observed. A simple model based on the crystal symmetry was able to reproduce the phase diagrams and their anisotropy, identifying SC1 and SC2 with even and odd parity superconducting states, respectively. However, additional orders were observed in the normal state which might have an influence on the change of the superconducting state at $H^{*}$. Here, we present a comprehensive study of the angle dependence of the upper critical fields using magnetic ac susceptibility, specific heat, and torque on single crystals of ${\mathrm{CeRh}}_2{\mathrm{As}}_2$. The experiments show that the state SC2 is strongly suppressed when rotating the magnetic field away from the $c$ axis and it disappears for an angle of 35°. This behavior agrees perfectly with our extended model of a pseudospin triplet state with $\overrightarrow{d}$ vector in the plane and hence allows us to conclude that SC2 is indeed the suggested odd-parity state.

The interplay between electronic transport and antiferromagnetic order has attracted a surge of interest as recent studies show that a moderate change in the spin orientation of a collinear antiferromagnet may have a significant effect on the electronic band structure. Among numerous electrical probes to read out such a magnetic order, unidirectional magnetoresistance (UMR), where the resistance changes under the reversal of the current direction, can provide rich insights into the transport properties of spin-orbit-coupled systems. However, UMR has never been observed in antiferromagnets before, given the absence of intrinsic spin-dependent scattering. Here, we report a UMR in the antiferromagnetic phase of a $\mathrm{FeRh}/\mathrm{Pt}$ bilayer, which undergoes a sign change and then increases strongly with an increasing external magnetic field, in contrast to UMRs in ferromagnetic and nonmagnetic systems. We show that Rashba spin-orbit coupling alone cannot explain the sizable UMR in the antiferromagnetic bilayer and that field-induced spin canting distorts the Fermi contours to greatly enhance the UMR by 2 orders of magnitude. Our results can motivate the growing field of antiferromagnetic spintronics and suggest a route to the development of tunable antiferromagnet-based spintronics devices.

Explaining the mechanism of superconductivity in the high-$T_c$ cuprates requires an understanding of what causes electrons to form Cooper pairs. Pairing can be mediated by phonons, the screened Coulomb force, spin or charge fluctuations, excitons, or by a combination of these. An excitonic pairing mechanism has been postulated, but experimental evidence for coupling between conduction electrons and excitons in the cuprates is sporadic. Here we use resonant inelastic x-ray scattering to monitor the temperature dependence of the $\underset{\_}{d}d$ exciton spectrum of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8-x}$ crystals with different charge carrier concentrations. We observe a significant change of the $\underset{\_}{d}d$ exciton spectra when the materials pass from the normal state into the superconductor state. Our observations show that the $\underset{\_}{d}d$ excitons start to shift up (down) in the overdoped (underdoped) sample when the material enters the superconducting phase. We attribute the superconductivity-induced effect and its sign reversal from underdoped to overdoped to the exchange coupling of the site of the $\underset{\_}{d}d$ exciton to the surrounding copper spins.

It has been proposed that an extended version of the Hubbard model which potentially hosts rich correlated physics may be well simulated by the transition metal dichalcogenide (TMD) moiré heterostructures. Motivated by recent reports of continuous metal-insulator transition (MIT) at half filling, as well as correlated insulators at various fractional fillings in TMD moiré heterostructures, we propose a theory for the potentially continuous MIT with fractionalized electric charges. The charge fractionalization at the MIT will lead to various experimental observable effects, such as a large resistivity as well as large universal resistivity jump at the continuous MIT. These predictions are different from previously proposed theory for interaction-driven continuous MIT. Physics in phases near the MIT will also be discussed.

The fundamental, or first, band gap is of unmatched importance in the study of photonic crystals. Here, we address precisely where this gap can be opened in the band structure of three-dimensional photonic crystals. Although strongly constrained by symmetry, this problem cannot be addressed directly with conventional band-symmetry analysis due to the existence of a photonic polarization vortex at zero frequency. We develop an approach for overcoming the associated symmetry singularity by incorporating fictitious, auxiliary longitudinal modes. Our strategy also enables us to extend recent developments in symmetry-based topological analysis to the fundamental gap of three-dimensional photonic crystals. Exploiting this, we systematically study the topology of the minimal fundamental gaps. This reveals the existence of topological gap obstructions that push the fundamental gap higher than what a conventional analysis would suggest. Our work demonstrates that topology can play a crucial role in the opening of the fundamental photonic gap and informs future theoretical and experimental searches for conventional and topological band gaps in three-dimensional photonic crystals.