A remarkable recent experiment has observed Mott insulator and proximate superconductor phases in twisted bilayer graphene when electrons partly fill a nearly flat miniband that arises a “magic” twist angle. However, the nature of the Mott insulator, the origin of superconductivity, and an effective low-energy model remain to be determined. We propose a Mott insulator with intervalley coherence that spontaneously breaks $U(1)$ valley symmetry and describe a mechanism that selects this order over the competing magnetically ordered states favored by the Hund’s coupling. We also identify symmetry-related features of the nearly flat band that are key to understanding the strong correlation physics and constrain any tight-binding description. First, although the charge density is concentrated on the triangular-lattice sites of the moiré pattern, the Wannier states of the tight-binding model must be centered on different sites which form a honeycomb lattice. Next, spatially localizing electrons derived from the nearly flat band necessarily breaks valley and other symmetries within any mean-field treatment, which is suggestive of a valley-ordered Mott state, and also dictates that additional symmetry breaking is present to remove symmetry-enforced band contacts. Tight-binding models describing the nearly flat miniband are derived, which highlight the importance of further neighbor hopping and interactions. We discuss consequences of this picture for superconducting states obtained on doping the valley-ordered Mott insulator. We show how important features of the experimental phenomenology may be explained and suggest a number of further experiments for the future. We also describe a model for correlated states in trilayer graphene heterostructures and contrast it with the bilayer case.

We build symmetry-adapted maximally localized Wannier states and construct the low-energy tight-binding model for the four narrow bands of twisted bilayer graphene. We do so when the twist angle is commensurate near the “magic” value and the narrow bands are separated from the rest of the bands by energy gaps. On each layer and sublattice, every Wannier state has three peaks near the triangular moiré lattice sites. However, each Wannier state is localized and centered around a site of the honeycomb lattice that is dual to the triangular moiré lattice. The space group and the time-reversal symmetries are realized locally. The corresponding tight-binding model provides a starting point for studying the correlated many-body phases.

We develop an effective extended Hubbard model to describe the low-energy electronic properties of the twisted bilayer graphene. By using the Bloch states in the effective continuum model and with the aid of the maximally localized algorithm, we construct the Wannier orbitals and obtain an effective tight-binding model on the emergent honeycomb lattice. We find that the Wannier state takes a peculiar three-peak form in which the amplitude maxima are located at the triangle corners surrounding the center. We estimate the direct Coulomb interaction and the exchange interaction between the Wannier states. At the filling of two electrons per supercell, in particular, we find an unexpected coincidence in the direct Coulomb energy between a charge-ordered state and a homogeneous state, which could possibly lead to an unconventional many-body state.

The ability to prepare a physical system in a desired quantum state is central to many areas of physics such as nuclear magnetic resonance, cold atoms, and quantum computing. Yet, preparing states quickly and with high fidelity remains a formidable challenge. In this work, we implement cutting-edge reinforcement learning (RL) techniques and show that their performance is comparable to optimal control methods in the task of finding short, high-fidelity driving protocol from an initial to a target state in nonintegrable many-body quantum systems of interacting qubits. RL methods learn about the underlying physical system solely through a single scalar reward (the fidelity of the resulting state) calculated from numerical simulations of the physical system. We further show that quantum-state manipulation viewed as an optimization problem exhibits a spin-glass-like phase transition in the space of protocols as a function of the protocol duration. Our RL-aided approach helps identify variational protocols with nearly optimal fidelity, even in the glassy phase, where optimal state manipulation is exponentially hard. This study highlights the potential usefulness of RL for applications in out-of-equilibrium quantum physics.

The ${\mathrm{H}}^{+}+\mathrm{H}$ and ${\mathrm{D}}^{+}+\mathrm{D}$ collisions represent the simplest examples of collisions involving identical fermions and bosons, respectively. We report a study of these collisions in the range of energies corresponding to 0–40 K at a resolution of 100 mK based on a half-collision approach. Using the technique of pulsed-field-ionization zero-kinetic-energy photoelectron spectroscopy (PFI-ZEKE-PES), which relies on the pulsed field ionization of nonpenetrating Rydberg states of very high principal quantum number ($n\ge 250$), we have measured the positions and widths of all low-lying shape resonances of this collision and compare them with the results of ab initio calculations that consider nonadiabatic, relativistic, and radiative corrections to the Born-Oppenheimer energies. Excellent agreement between calculated and measured widths and positions is found except for the $X^{+}(v^{+}=25,N^{+}=8)$ shape resonance, the width of which is calculated to be narrower than observed. Comparison with similar observations made for the ${\mathrm{H}}^{+}+\mathrm{H}$ collision [Beyer and Merkt Phys. Rev. Lett. 116, 093001 (2016)] indicates that the shape resonances measured by PFI-ZEKE-PES are broadened by the effects of the localization of the charge of the dissociating ion core arising from a nonadiabatic coupling between ion core and Rydberg electron. A simple model is presented that enables one to predict which shape resonances are likely to be affected and to correct for the resulting broadening. Two shape resonances of ${{\mathrm{D}}_2}^{+}$, the $X^{+}(v^{+}=26,N^{+}=5)$ and the $A^{+}(v^{+}=0,N^{+}=5)$ resonances, have electric-dipole-allowed transitions to bound states of ${{\mathrm{D}}_2}^{+}$ and are shown to facilitate the radiative association at low temperature. The results are used to determine the elastic cross sections of the ${\mathrm{H}}^{+}+\mathrm{H}$ and ${\mathrm{D}}^{+}+\mathrm{D}$ collisions for partial waves up to $N^{+}=11$ and the radiative-association cross sections and rate constants in the range between 10 mK and 100 000 K.

Machine learning with artificial neural networks is revolutionizing science. The most advanced challenges require discovering answers autonomously. In the domain of reinforcement learning, control strategies are improved according to a reward function. The power of neural-network-based reinforcement learning has been highlighted by spectacular recent successes such as playing Go, but its benefits for physics are yet to be demonstrated. Here, we show how a network-based “agent” can discover complete quantum-error-correction strategies, protecting a collection of qubits against noise. These strategies require feedback adapted to measurement outcomes. Finding them from scratch without human guidance and tailored to different hardware resources is a formidable challenge due to the combinatorially large search space. To solve this challenge, we develop two ideas: two-stage learning with teacher and student networks and a reward quantifying the capability to recover the quantum information stored in a multiqubit system. Beyond its immediate impact on quantum computation, our work more generally demonstrates the promise of neural-network-based reinforcement learning in physics.

Ultrahigh-field (UHF) magnetic resonance imaging (MRI) systems are getting a lot of attention as they ensure high intrinsic signal-to-noise ratio resulting in higher spatial and temporal resolutions as well as better contrast. This promises improved clinical results with regard to morphological as well as functional and metabolic capabilities. Traditionally, MRI relies on volume coils (birdcage) able to deliver a homogeneous radio frequency field exciting the nuclei magnetic spin. However, this strategy is hindered at UHF because of the rf field inhomogeneities yielded by the increased Larmor frequency. A standard approach consists of inserting passive dielectric elements within the volume coil in order to locally enhance the rf field and mitigate these inhomogeneities. However, the lack of control over their electromagnetic properties prevents the development of optimal solutions. Here, a single meta-atom is used to achieve efficient and tunable rf field control in UHF MRI. We demonstrate theoretically and experimentally a full overlap between the electric dipolar and magnetic dipolar resonances of the meta-atom. This interaction is precisely tuned to reach the so-called Kerker scattering conditions when illuminated in the near field by a birdcage coil. At these conditions, a strong enhancement or suppression of the rf field is achieved in the vicinity of the meta-atom within the MRI volume coil.

We speed up thermal simulations of quantum many-body systems in both one- (1D) and two-dimensional (2D) models in an exponential way by iteratively projecting the thermal density matrix $\widehat{\rho }=e^{-\beta \widehat{H}}$ onto itself. We refer to this scheme of doubling $\beta$ in each step of the imaginary time evolution as the exponential tensor renormalization group (XTRG). This approach is in stark contrast to conventional Trotter-Suzuki-type methods which evolve $\widehat{\rho }$ on a linear quasicontinuous grid in inverse temperature $\beta \equiv 1/T$. As an aside, the large steps in XTRG allow one to swiftly jump across finite-temperature phase transitions, i.e., without the need to resolve each singularly expensive phase-transition point right away, e.g., when interested in low-energy behavior. A fine temperature resolution can be obtained, nevertheless, by using interleaved temperature grids. In general, XTRG can reach low temperatures exponentially fast and, thus, not only saves computational time but also merits better accuracy due to significantly fewer truncation steps. For similar reasons, we also find that the series expansion thermal tensor network approach benefits in both efficiency and precision, from the logarithmic temperature scale setup. We work in an (effective) 1D setting exploiting matrix product operators (MPOs), which allows us to fully and uniquely implement non-Abelian and Abelian symmetries to greatly enhance numerical performance. We use our XTRG machinery to explore the thermal properties of Heisenberg models on 1D chains and 2D square and triangular lattices down to low temperatures approaching ground-state properties. The entanglement properties, as well as the renormalization-group flow of entanglement spectra in MPOs, are discussed, where logarithmic entropies (approximately $\ln \beta$) are shown in both spin chains and square-lattice models with gapless towers of states. We also reveal that XTRG can be employed to accurately simulate the Heisenberg $XXZ$ model on the square lattice which undergoes a thermal phase transition. We determine its critical temperature based on thermal physical observables, as well as entanglement measures. Overall, we demonstrate that XTRG provides an elegant, versatile, and highly competitive approach to explore thermal properties, including finite-temperature thermal phase transitions as well as the different ordering tendencies at various temperature scales for frustrated systems.

Excursions far from their equilibrium structures can bring crystalline solids through collective transformations including transitions into new phases that may be transient or long-lived. The direct spectroscopic observation of far-from-equilibrium rearrangements provides fundamental mechanistic insight into chemical and structural transformations and a potential route to practical applications, including ultrafast optical control over material structure and properties. However, in many cases, photoinduced transitions are irreversible or only slowly reversible, or the light fluence required exceeds material damage thresholds. This requirement precludes conventional ultrafast spectroscopy, in which optical excitation and probe pulses irradiate the sample many times, each measurement providing information about the sample response at just one probe delay time following excitation, with each measurement at a high repetition rate and with the sample fully recovering its initial state in between measurements. Using a single-shot, real-time measurement method, we are able to observe the photoinduced phase transition from the semimetallic, low-symmetry phase of crystalline bismuth into a high-symmetry phase whose existence at high electronic excitation densities is predicted based on earlier measurements at moderate excitation densities below the damage threshold. Our observations indicate that coherent lattice vibrational motion launched upon photoexcitation with an incident fluence above $10\mathrm{mJ}/{\mathrm{cm}}^2$ in bulk bismuth brings the lattice structure directly into the high-symmetry configuration for several picoseconds, after which carrier relaxation and diffusion restore the equilibrium lattice configuration.

It is known that purely repulsive self-propelled colloids can undergo bulk liquid-vapor phase separation. In experiments and large-scale simulations, however, more complex steady states are also seen, comprising a dynamic population of dense clusters in a sea of vapor, or dilute bubbles in a liquid. Here, we show that these microphase-separated states should emerge generically in active matter, without any need to invoke system-specific details. We give a coarse-grained description of them and predict transitions between regimes of bulk phase separation and microphase separation. We achieve these results by extending the ${\varphi }^4$ field theory of passive phase separation to allow for all local currents that break detailed balance at leading order in the gradient expansion. These local active currents, whose form we show to emerge from coarse graining of microscopic models, include a mixture of irrotational and rotational contributions and can be viewed as arising from an effective nonlocal chemical potential. Such contributions influence, and in some parameter ranges reverse, the classical Ostwald process that would normally drive bulk phase separation to completion.

While Hermiticity lies at the heart of quantum mechanics, recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. Examples include parity-time-symmetric optical systems with gain and loss, dissipative Bose-Einstein condensates, exciton-polariton systems, and biological networks. A particular interest centers on the topological properties of non-Hermitian systems, which exhibit unique phases with no Hermitian counterparts. However, no systematic understanding in analogy with the periodic table of topological insulators and superconductors has been achieved. In this paper, we develop a coherent framework of topological phases of non-Hermitian systems. After elucidating the physical meaning and the mathematical definition of non-Hermitian topological phases, we start with one-dimensional lattices, which exhibit topological phases with no Hermitian counterparts and are found to be characterized by an integer topological winding number even with no symmetry constraint, reminiscent of the quantum-Hall insulator in Hermitian systems. A system with a nonzero winding number, which is experimentally measurable from the wave-packet dynamics, is shown to be robust against disorder, a phenomenon observed in the Hatano-Nelson model with asymmetric hopping amplitudes. We also unveil a novel bulk-edge correspondence that features an infinite number of (quasi)edge modes. We then apply the $K$ theory to systematically classify all the non-Hermitian topological phases in the Altland-Zirnbauer (AZ) classes in all dimensions. The obtained periodic table unifies time-reversal and particle-hole symmetries, leading to highly nontrivial predictions such as the absence of non-Hermitian topological phases in two dimensions. We provide concrete examples for all the nontrivial non-Hermitian AZ classes in zero and one dimensions. In particular, we identify a ${\mathbb{Z}}_2$ topological index for arbitrary quantum channels (completely positive trace-preserving maps). Our work lays the cornerstone for a unified understanding of the role of topology in non-Hermitian systems.

We use scanning optical magnetometry to study the broadband frequency spectra of spontaneous magnetization fluctuations, or “magnetization noise,” in an archetypal ferromagnetic film that can be smoothly tuned through a spin-reorientation transition (SRT). The SRT is achieved by laterally varying the magnetic anisotropy across an ultrathin $\mathrm{Pt}/\mathrm{Co}/\mathrm{Pt}$ trilayer, from the perpendicular to in-plane direction, via graded ${\mathrm{Ar}}^{+}$ irradiation. In regions exhibiting perpendicular anisotropy, the power spectrum of the magnetization noise $S(\nu )$ exhibits a remarkably robust ${\nu }^{-3/2}$ power law over frequencies $\nu$ from 1 kHz to 1 MHz. As the SRT region is traversed, however, $S(\nu )$ spectra develop a steadily increasing critical frequency ${\nu }_0$, below which the noise power is spectrally flat, indicating an evolving low-frequency cutoff for magnetization fluctuations. The magnetization noise depends strongly on applied in- and out-of-plane magnetic fields, revealing local anisotropies and also a field-induced emergence of fluctuations in otherwise stable ferromagnetic films. Finally, we demonstrate that higher-order correlators can be computed from the noise. These results highlight broadband spectroscopy of thermodynamic fluctuations as a powerful tool to characterize the interplay between thermal and magnetic energy scales, and as a means of characterizing phase transitions in ferromagnets.

Huygens’ metasurfaces demonstrate almost arbitrary control over the shape of a scattered beam; however, its spatial profile is typically fixed at the fabrication time. The dynamic reconfiguration of this beam profile with tunable elements remains challenging, due to the need to maintain the Huygens’ condition across the tuning range. In this work, we experimentally demonstrate that a time-varying metadevice which performs frequency conversion can steer transmitted or reflected beams in an almost arbitrary manner, with fully dynamic control. Our time-varying Huygens’ metadevice is made of both electric and magnetic meta-atoms with independently controlled modulation, and the phase of this modulation is imprinted on the scattered parametric waves, controlling their shapes and directions. We develop a theory which shows how the scattering directionality, phase, and conversion efficiency of sidebands can be manipulated almost arbitrarily. We demonstrate novel effects including all-angle beam steering and frequency-multiplexed functionalities at microwave frequencies around 4 GHz, using varactor diodes as tunable elements. We believe that the concept can be extended to other frequency bands, enabling metasurfaces with an arbitrary phase pattern that can be dynamically tuned over the complete $2\pi$ range.

Pursuing complementary field-theoretic and numerical methods, we here paint the global phase diagram of a three-dimensional dirty Weyl system. The generalized Harris criterion, augmented by a perturbative renormalization-group analysis shows that weak disorder is an irrelevant perturbation at the Weyl semimetal (WSM)-insulator quantum-critical point. But, a metallic phase sets in through a quantum phase transition (QPT) at strong disorder across a multicritical point. The field-theoretic predictions for the correlation length exponent $\nu =2$ and dynamic scaling exponent $z=5/4$ at this multicritical point are in good agreement with the ones extracted numerically, yielding $\nu =1.98\pm 0.10$ and $z=1.26\pm 0.05$, from the scaling of the average density of states (DOS). Deep inside the WSM phase, generic disorder is also an irrelevant perturbation, while a metallic phase appears at strong disorder through a QPT. We here demonstrate that in the presence of generic but strong disorder, the WSM-metal QPT is ultimately always characterized by the exponents $\nu =1$ and $z=3/2$ (to one-loop order), originating from intranode or chiral-symmetric (e.g., regular and axial potential) disorder. We here anchor such emergent chiral superuniversality through complementary renormalization-group calculations, controlled via $\epsilon$ expansions, and numerical analysis of average DOS across WSM-metal QPT. In addition, we also discuss a subsequent QPT (at even stronger disorder) of a Weyl metal into an Anderson insulator by numerically computing the typical DOS at zero energy. The scaling behavior of various physical observables, such as residue of quasiparticle pole, dynamic conductivity, specific heat, Grüneisen ratio, inside various phases as well as across various QPTs in the global phase diagram of a dirty Weyl liquid, are discussed.

The Tomonaga-Luttinger liquid (TLL) concept is believed to generically describe the strongly correlated physics of one-dimensional systems at low temperatures. A hallmark signature in 1D conductors is the quantum phase transition between metallic and insulating states induced by a single impurity. However, this transition impedes experimental explorations of real-world TLLs. Furthermore, its theoretical treatment, explaining the universal energy rescaling of the conductance at low temperatures, has so far been achieved exactly only for specific interaction strengths. Quantum simulation can provide a powerful workaround. Here, a hybrid metal-semiconductor dissipative quantum circuit is shown to implement the analogue of a TLL of adjustable electronic interactions comprising a single, fully tunable scattering impurity. Measurements reveal the renormalization group “beta function” for the conductance that completely determines the TLL universal crossover to an insulating state upon cooling. Moreover, the characteristic scaling energy locating at a given temperature the position within this conductance renormalization flow is established over nine decades versus circuit parameters, and the out-of-equilibrium regime is explored. With the quantum-simulator quality demonstrated from the precise parameter-free validation of existing and novel TLL predictions, quantum simulation is achieved in a strong sense, by elucidating interaction regimes which resist theoretical solutions.

Topologically protected waves in classical media provide unique opportunities for one-way wave transport and immunity to defects. Contrary to acoustics and electromagnetics, their observation in elastic solids has so far been elusive because of the presence of multiple modes and their tendency to hybridize at interfaces. Here, we report on the experimental investigation of topologically protected helical edge modes in elastic plates patterned with an array of triangular holes, along with circular holes that produce an accidental degeneracy of two Dirac cones. Such a degeneracy is subsequently lifted by careful breaking of the symmetry along the thickness direction, which emulates the spin orbital coupling in the quantum spin Hall effect. The joining of two plates that are mirror-symmetric copies of each other about the plate midthickness introduces a nontrivial interface that supports helical edge waves. The experimental observation of these topologically protected wave modes in elastic continuous plates opens avenues for the practical realization of structural components with topologically nontrivial waveguiding properties and their application to elastic waveguiding and confinement.

Transitions metal dichalcogenides (TMDs) are direct gap semiconductors in the monolayer (ML) limit with fascinating optical and spin-valley properties. The strong optical absorption of up to 20% for a single ML is governed by excitons, electron-hole pairs bound by Coulomb attraction. Excited exciton states in ${\mathrm{MoSe}}_2$ and ${\mathrm{MoTe}}_2$ monolayers have so far been elusive because of their low oscillator strength and strong inhomogeneous broadening. Here, we show that encapsulation in hexagonal boron nitride results in an emission line width of the $\mathrm{A}:1s$ exciton below 1.5 meV and 3 meV in our ${\mathrm{MoSe}}_2$ and ${\mathrm{MoTe}}_2$ monolayer samples, respectively. This allows us to investigate the excited exciton states by photoluminescence upconversion spectroscopy for both monolayer materials. The excitation laser is tuned into resonance with the $\mathrm{A}:1s$ transition, and we observe emission of excited exciton states up to 200 meV above the laser energy. We demonstrate bias control of the efficiency of this nonlinear optical process. We discuss the origin of the upconversion effect. Our model calculations suggest an exciton-exciton (Auger) scattering mechanism specific to TMD MLs involving an excited conduction band, thus generating high-energy excitons with small wave vectors. The optical transitions are further investigated by white light reflectivity, photoluminescence excitation, and resonant Raman scattering, confirming their origin as excited excitonic states in monolayer thin semiconductors.

Spatiotemporal correlations in brain activity are functionally important and have been implicated in perception, learning and plasticity, exploratory behavior, and various aspects of cognition. Neurons in the cerebral cortex are strongly interacting. Their activity is temporally irregular and can exhibit substantial correlations. However, how the collective dynamics of highly recurrent and strongly interacting neurons can evolve into a state in which the activity of individual cells is highly irregular yet macroscopically correlated is an open question. Here, we develop a general theory that relates the strength of pairwise correlations to the anatomical features of networks of strongly coupled neurons. To this end, we investigate networks of binary units. When interactions are strong, the activity is irregular in a large region of parameter space. We find that despite the strong interactions, the correlations are generally very weak. Nevertheless, we identify architectural features, which if present, give rise to strong correlations without destroying the irregularity of the activity. For networks with such features, we determine how correlations scale with the network size and the number of connections. Our work shows the mechanism by which strong correlations can be consistent with highly irregular activity, two hallmarks of neuronal dynamics in the central nervous system.

Multiplex networks have been intensively studied during the last few years as they offer a more realistic representation of many interdependent and multilevel complex networked systems. However, even if most real networks have some degree of directionality, the vast majority of the existent literature deals with multiplex networks where all layers are undirected. Here, we study the dynamics of diffusion processes acting on coupled multilayer networks where at least one layer consists of a directed graph; we call these directed multiplex networks. We reveal a new and unexpected signature of diffusion dynamics on directed multiplex networks, namely, that different from their undirected counterparts, they can exhibit a nonmonotonic rate of convergence to steady state as a function of the degree of coupling, resulting in a faster diffusion at an intermediate degree of coupling than when the two layers are fully coupled. We use synthetic multiplex examples and real-world topologies to illustrate the characteristics of the underlying dynamics that give rise to a regime in which an optimal coupling exists. We further provide analytical and numerical evidence that this new phenomenon is solely a property of directed multiplex, where at least one of the layers exhibits sufficient directionality quantified by a normalized metric of asymmetry in directional path lengths. Given the ubiquity of both directed and multilayer networks in nature, our results have important implications for studying the dynamics of multilevel complex systems.