swap algorithms can shift the glass transition to lower temperatures, a recent unexplained observation constraining the nature of this phenomenon. Here we show that swap dynamics is governed by an effective potential describing both particle interactions as well as their ability to change size. Requiring its stability is more demanding than for the potential energy alone. This result implies that stable configurations appear at lower energies with swap dynamics, and thus at lower temperatures when the liquid is cooled. The magnitude of this effect is predicted to be proportional to the width of the radii distribution, and to decrease with compression for finite-range purely repulsive interaction potentials. We test these predictions numerically and discuss the implications of our findings for the glass transition. These results are extended to the case of hard spheres where swap is argued to destroy metastable states of the free energy coarse grained on vibrational timescales. Our analysis unravels the soft elastic modes responsible for the speed-up induced by swap, and allows us to predict the structure and the vibrational properties of glass configurations reachable with swap. In particular, for continuously polydisperse systems we predict the jamming transition to be dramatically altered, as we confirm numerically. A surprising practical outcome of our analysis is a new algorithm that generates ultrastable glasses by a simple descent in an appropriate effective potential.

Exchange coupling is a key ingredient for spin-based quantum technologies since it can be used to entangle spin qubits and create logical spin qubits. However, the influence of the electronic valley degree of freedom in silicon on exchange interactions is presently the subject of important open questions. Here we investigate the influence of valleys on exchange in a coupled donor–quantum-dot system, a basic building block of recently proposed schemes for robust quantum information processing. Using a scanning tunneling microscope tip to position the quantum dot with sub-nm precision, we find a near monotonic exchange characteristic where lattice-aperiodic modulations associated with valley degrees of freedom comprise less than 2% of exchange. From this we conclude that intravalley tunneling processes that preserve the donor’s $\pm x$ and $\pm y$ valley index are filtered out of the interaction with the $\pm z$ valley quantum dot, and that the $\pm x$ and $\pm y$ intervalley processes where the electron valley index changes are weak. Complemented by tight-binding calculations of exchange versus donor depth, the demonstrated electrostatic tunability of donor–quantum-dot exchange can be used to compensate the remaining intravalley $\pm z$ oscillations to realize uniform interactions in an array of highly coherent donor spins.

Symmetry-protected topological (SPT) states have boundary ’t Hooft anomalies that obstruct the effective boundary theory realized in its own dimension with UV completion and with an on-site $G$-symmetry. In this work, yet we show that a certain anomalous non-on-site $G$-symmetry along the boundary becomes on-site when viewed as an extended $H$-symmetry, via a suitable group extension $1\to K\to H\to G\to 1$. Namely, a nonperturbative global (gauge or gravitational) anomaly in $G$ becomes anomaly free in $H$. This guides us to construct an exactly soluble lattice path integral and Hamiltonian of symmetric gapped boundaries applicable to any SPT state of any finite symmetry group, including on-site unitary and antiunitary time-reversal symmetries. The resulting symmetric gapped boundary can be described either by an $H$-symmetry extended boundary in any spacetime dimension or, more naturally, by a topological emergent $K$-gauge theory with a global symmetry $G$ on a $3+1\mathrm{D}$ bulk or above. The excitations on such a symmetric topologically ordered boundary can carry fractional quantum numbers of the symmetry $G$, described by representations of $H$. (Applying our approach to a $1+1\mathrm{D}$ boundary of $2+1\mathrm{D}$ bulk, we find that a deconfined gauge boundary indeed has spontaneous symmetry breaking with long-range order. The deconfined symmetry-breaking phase crosses over smoothly to a confined phase without a phase transition.) In contrast to known gapped boundaries or interfaces obtained via symmetry breaking (either global symmetry breaking or the Anderson-Higgs mechanism for gauge theory), our approach is based on symmetry extension. More generally, applying our approach to SPT states, topologically ordered gauge theories, and symmetry enriched topologically ordered (SET) states leads to generic boundaries or interfaces constructed with a mixture of symmetry breaking, symmetry extension, and dynamical gauging.

Entanglement in multipartite systems is a key resource for quantum information and communication protocols, making its verification in complex systems a necessity. Because an exact calculation of arbitrary entanglement probes is impossible, we derive and implement a numerical method to construct multipartite witnesses to uncover entanglement in arbitrary systems. Our technique is based on a substantial generalization of the power iteration—an essential tool for computing eigenvalues—and it is a solver for the separability eigenvalue equations, enabling the general formulation of optimal entanglement witnesses. Beyond our rigorous derivation and direct implementation of this method, we apply our approach to several examples of complexly quantum-correlated states and benchmark its general performance. Consequently, we provide a generally applicable numerical tool for the identification of multipartite entanglement.

Topological defects are crucial to the thermodynamics and structure of condensed matter systems. For instance, when incorporated into crystalline membranes like graphene, disclinations with positive and negative topological charge elastically buckle the material into conical and saddlelike shapes, respectively. A recently uncovered mapping between the interelement spacing in 2D columnar structures and the metric properties of curved surfaces motivates basic questions about the interplay between defects in the cross section of a columnar bundle and its 3D shape. Such questions are critical to the structure of a broad class of filamentous materials, from biological assemblies like protein fibers to nanostructured or microstructured synthetic materials like carbon nanotube bundles. Here, we explore the buckling behavior for elementary disclinations in hexagonal bundles using a combination of continuum elasticity theory and numerical simulations of discrete filaments. We show that shape instabilities are controlled by a single material-dependent parameter that characterizes the ratio of interfilament to intrafilament elastic energies. Along with a host of previously unknown shape equilibria—the filamentous analogs to the conical and saddlelike shapes of defective membranes—we find a profoundly asymmetric response to positive and negative topologically charged defects in the infinite length limit that is without parallel to the membrane analog. The highly nonlinear dependence on the sign of the disclination charge is shown to have a purely geometric origin, stemming from the distinct compatibility (or incompatibility) of effectively positive- (or negative-)curvature geometries with lengthwise-constant filament spacing.

There has been great interest in experimental studies of charged particles in artificial gauge fields. Here, we perform the first cold-atom explorations of the combination of artificial gauge fields and disorder. Using synthetic lattice techniques based on parametrically coupled atomic momentum states, we engineer zigzag chains with a tunable homogeneous flux. The breaking of time-reversal symmetry by the applied flux leads to analogs of spin-orbit coupling and spin-momentum locking, which we observe directly through the chiral dynamics of atoms initialized to single lattice sites. We additionally introduce precisely controlled disorder in the site-energy landscape, allowing us to explore the interplay of disorder and large effective magnetic fields. The combination of correlated disorder and controlled intrarow and interrow tunneling in this system naturally supports energy-dependent localization, relating to a single-particle mobility edge. We measure the localization properties of the extremal eigenstates of this system, the ground state and the most-excited state, and demonstrate clear evidence for a flux-dependent mobility edge. These measurements constitute the first direct evidence for energy-dependent localization in a lower-dimensional system, as well as the first explorations of the combined influence of artificial gauge fields and engineered disorder. Moreover, we provide direct evidence for interaction shifts of the localization transitions for both low- and high-energy eigenstates in correlated disorder, relating to the presence of a many-body mobility edge. The unique combination of strong interactions, controlled disorder, and tunable artificial gauge fields present in this synthetic lattice system should enable myriad explorations into intriguing correlated transport phenomena.

The topological nodal-line semimetal state, serving as a fertile ground for various topological quantum phases, where a topological insulator, Dirac semimetal, or Weyl semimetal can be realized when the certain protecting symmetry is broken, has only been experimentally studied in very few materials. In contrast to discrete nodes, nodal lines with rich topological configurations can lead to more unusual transport phenomena. Utilizing angle-resolved photoemission spectroscopy and first-principles calculations, here, we provide compelling evidence of nodal-line fermions in centrosymmetric semimetal ${\mathrm{TiB}}_2$ with a negligible spin-orbit coupling effect. With the band crossings just below the Fermi energy, two groups of Dirac nodal rings are clearly observed without any interference from other bands, one surrounding the Brillouin zone (BZ) corner in the horizontal mirror plane ${\sigma }_h$ and the other surrounding the BZ center in the vertical mirror plane ${\sigma }_v$. The linear dispersions forming Dirac nodal rings are as wide as 2 eV. We further observe that the two groups of nodal rings link together along the $\mathrm{\Gamma }‐K$ direction, composing a nodal-link configuration. The simple electronic structure with Dirac nodal links mainly constituting the Fermi surfaces suggests ${\mathrm{TiB}}_2$ as a remarkable platform for studying and applying the novel physical properties related to nodal-line fermions.

Quantum key distribution allows remote parties to generate information-theoretic secure keys. The bottleneck throttling its real-life applications lies in the limited communication distance and key generation speed, due to the fact that the information carrier can be easily lost in the channel. For all the current implementations, the key rate is bounded by the channel transmission probability $\eta$. Rather surprisingly, by matching the phases of two coherent states and encoding the key information into the common phase, this linear key-rate constraint can be overcome—the secure key rate scales with the square root of the transmission probability $O(\sqrt{\eta })$, as proposed in twin-field quantum key distribution [M. Lucamarini et al. Overcoming the Rate–Distance Limit of Quantum Key Distribution without Quantum Repeaters, Nature (London) 557, 400 (2018)]. To achieve this, we develop an optical-mode-based security proof that is different from the conventional qubit-based security proofs. Furthermore, the proposed scheme is measurement device independent; i.e., it is immune to all possible detection attacks. The simulation result shows that the key rate can even exceed the transmission probability $\eta$ between two communication parties. In addition, we apply phase postcompensation to devise a practical version of the scheme without phase locking, which makes the proposed scheme feasible with the current technology. This means that quantum key distribution can enjoy both sides of the world—practicality and security.

Landau’s description of the excitations in a macroscopic system in terms of quasiparticles stands out as one of the highlights in quantum physics. It provides an accurate description of otherwise prohibitively complex many-body systems and has led to the development of several key technologies. In this paper, we investigate theoretically the Landau effective interaction between quasiparticles, so-called Bose polarons, formed by impurity particles immersed in a Bose-Einstein condensate (BEC). In the limit of weak interactions between the impurities and the BEC, we derive rigorous results for the effective interaction. They show that it can be strong even for a weak impurity-boson interaction, if the transferred momentum-energy between the quasiparticles is resonant with a sound mode in the BEC. We then develop a diagrammatic scheme to calculate the effective interaction for arbitrary coupling strengths, which recovers the correct weak-coupling results. Using this scheme, we show that the Landau effective interaction, in general, is significantly stronger than that between quasiparticles in a Fermi gas, mainly because a BEC is more compressible than a Fermi gas. The interaction is particularly large near the unitarity limit of the impurity-boson scattering or when the quasiparticle momentum is close to the threshold for momentum relaxation in the BEC. Finally, we show how the Landau effective interaction leads to a sizable shift of the quasiparticle energy with an increasing impurity concentration, which should be detectable with present-day experimental techniques.

We study the effect of gate-induced electric fields on the properties of semiconductor-superconductor hybrid nanowires which represent a promising platform for realizing topological superconductivity and Majorana zero modes. Using a self-consistent Schrödinger-Poisson approach that describes the semiconductor and the superconductor on equal footing, we are able to access the strong tunneling regime and identify the impact of an applied gate voltage on the coupling between semiconductor and superconductor. We discuss how physical parameters such as the induced superconducting gap and Landé $g$ factor in the semiconductor are modified by redistributing the density of states across the interface upon application of an external gate voltage. Finally, we map out the topological phase diagram as a function of magnetic field and gate voltage for InAs/Al nanowires.

Hybrid superconductor-semiconductor devices are currently one of the most promising platforms for realizing Majorana zero modes. Their topological properties are controlled by the band alignment of the two materials, as well as the electrostatic environment, which are currently not well understood. Here, we seek to fill in this gap and address the role of band bending and superconductor-semiconductor hybridization in such devices by analyzing a gated single Al-InAs interface using a self-consistent Schrödinger-Poisson approach. Our numerical analysis shows that the band bending leads to an interface quantum well, which localizes the charge in the system near the superconductor-semiconductor interface. We investigate the hybrid band structure and analyze its response to varying the gate voltage and thickness of the Al layer. This is done by studying the hybridization degrees of the individual subbands, which determine the induced pairing and effective $g$ factors. The numerical results are backed by approximate analytical expressions which further clarify key aspects of the band structure. We find that one can obtain states with strong superconductor-semiconductor hybridization at the Fermi energy, but this requires a fine balance of parameters, with the most important constraint being on the width of the Al layer. In fact, in the regime of interest, we find an almost periodic dependence of the hybridization degree on the Al width, with a period roughly equal to the thickness of an Al monolayer. This implies that disorder and shape irregularities, present in realistic devices, may play an important role for averaging out this sensitivity and, thus, may be necessary for stabilizing the topological phase.

We propose a theoretical framework for the study of spreading processes in structured metapopulations, with heterogeneous agents, subjected to different recurrent mobility patterns. We propose to represent the heterogeneity in the composition of the metapopulations as layers in a multiplex network, where nodes would correspond to geographical areas and layers account for the mobility patterns of agents of the same class. We analyze classical epidemic models within this framework and obtain an excellent agreement with extensive Monte Carlo simulations. This agreement allows us to derive analytical expressions of the epidemic threshold and to face the challenge of characterizing a real multiplex metapopulation, the city of Medellín in Colombia, where different recurrent mobility patterns are observed depending on the socioeconomic class of the agents. Our framework allows us to unveil the geographical location of those patches that trigger the epidemic state at the critical point. A careful exploration reveals that social mixing between classes and mobility crucially determines these critical patches and, more importantly, it can produce abrupt changes of the critical properties of the epidemic onset.

Elements composing complex systems usually interact in several different ways, and as such, the interaction architecture is well modeled by a network with multiple layers—a multiplex network—where the system’s complex dynamics is often the result of several intertwined processes taking place at different levels. However, only in a few cases can such multilayered architecture be empirically observed, as one usually only has experimental access to such structure from an aggregated projection. A fundamental challenge is thus to determine whether the hidden underlying architecture of complex systems is better modeled as a single interaction layer or if it results from the aggregation and interplay of multiple layers. Assuming a prior of intralayer Markovian diffusion, here we show that by using local information provided by a random walker navigating the aggregated network, it is possible to determine, in a robust manner, whether these dynamics can be more accurately represented by a single layer or if they are better explained by a (hidden) multiplex structure. In the latter case, we also provide Bayesian methods to estimate the most probable number of hidden layers and the model parameters, thereby fully reconstructing its architecture. The whole methodology enables us to decipher the underlying multiplex architecture of complex systems by exploiting the non-Markovian signatures on the statistics of a single random walk on the aggregated network. In fact, the mathematical formalism presented here extends above and beyond detection of physical layers in networked complex systems, as it provides a principled solution for the optimal decomposition and projection of complex, non-Markovian dynamics into a Markov switching combination of diffusive modes. We validate the proposed methodology with numerical simulations of both (i) random walks navigating hidden multiplex networks (thereby reconstructing the true hidden architecture) and (ii) Markovian and non-Markovian continuous stochastic processes (thereby reconstructing an effective multiplex decomposition where each layer accounts for a different diffusive mode). We also state and prove two existence theorems guaranteeing that an exact reconstruction of the dynamics in terms of these hidden jump-Markov models is always possible for arbitrary finite-order Markovian and fully non-Markovian processes. Finally, we showcase the applicability of the method to experimental recordings from (i) the mobility dynamics of human players in an online multiplayer game and (ii) the dynamics of RNA polymerases at the single-molecule level.

We analyze the production of entropy along nonequilibrium processes in quantum systems coupled to generic environments. First, we show that the entropy production due to final measurements and the loss of correlations obeys a fluctuation theorem in detailed and integral forms. Second, we discuss the decomposition of the entropy production into two positive contributions, adiabatic and nonadiabatic, based on the existence of invariant states of the local dynamics. Fluctuation theorems for both contributions hold only for evolutions verifying a specific condition of quantum origin. We illustrate our results with three relevant examples of quantum thermodynamic processes far from equilibrium.

Information processing typically occurs via the composition of modular units, such as the universal logic gates found in discrete computation circuits. The benefit of modular information processing, in contrast to globally integrated information processing, is that complex computations are more easily and flexibly implemented via a series of simpler, localized information processing operations that only control and change local degrees of freedom. We show that, despite these benefits, there are unavoidable thermodynamic costs to modularity—costs that arise directly from the operation of localized processing and that go beyond Landauer’s bound on the work required to erase information. Localized operations are unable to leverage global correlations, which are a thermodynamic fuel. We quantify the minimum irretrievable dissipation of modular computations in terms of the difference between the change in global nonequilibrium free energy, which captures these global correlations, and the local (marginal) change in nonequilibrium free energy, which bounds modular work production. This modularity dissipation is proportional to the amount of additional work required to perform a computational task modularly, measuring a structural energy cost. It determines the thermodynamic efficiency of different modular implementations of the same computation, and so it has immediate consequences for the architecture of physically embedded transducers, known as information ratchets. Constructively, we show how to circumvent modularity dissipation by designing internal ratchet states that capture the information reservoir’s global correlations and patterns. Thus, there are routes to thermodynamic efficiency that circumvent globally integrated protocols and instead reduce modularity dissipation to optimize the architecture of computations composed of a series of localized operations.

Impurities usually play an important role in modifying the bulk properties of electronic or electromagnetic materials. In this work, we demonstrate a way to break this discipline and realize the extraordinary physical property of impurity-immunity, which leads to perfect transmission irrespective of embedded impurities of almost any material and shape. This extraordinary property comes from the exceptional points of a pair of parity-time ($PT$)-symmetric metasurfaces sandwiching a slab of epsilon-near-zero medium. By systematically investigating the $PT$-symmetric metasurfaces sandwiching a slab of dielectrics or metamaterials, we obtain the two complementary solutions of exceptional points corresponding to perfect transmission. Interestingly, when the permittivity of the slab approaches zero, the two solutions of exceptional points coalesce into one exceptional point. At such a critical point, we find that the original “doping” effect of impurities in epsilon-near-zero media, proposed by Nader Engheta’s group very recently [I. Liberal et al., Science 355, 1058 (2017)], is significantly suppressed. Our work shows that exceptional points can be used to eliminate scattering of impurities in a bulk medium.

X-ray free-electron lasers (XFELs) made available a new regime of x-ray intensities, revolutionizing the ultrafast structure determination and laying the foundations of the novel field of nonlinear x-ray optics. Although earlier studies revealed nanoplasma formation when an XFEL pulse interacts with any nanometer-scale matter, the formation process itself has never been decrypted and its timescale was unknown. Here we show that time-resolved ion yield measurements combined with a near-infrared laser probe reveal a surprisingly ultrafast population ($\sim 12\mathrm{fs}$), followed by a slower depopulation ($\sim 250\mathrm{fs}$) of highly excited states of atomic fragments generated in the process of XFEL-induced nanoplasma formation. Inelastic scattering of Auger electrons and interatomic Coulombic decay are suggested as the mechanisms populating and depopulating, respectively, these excited states. The observed response occurs within the typical x-ray pulse durations and affects x-ray scattering, thus providing key information on the foundations of x-ray imaging with XFELs.

The iron-based superconductors are characterized by multiple-orbital physics where all the five Fe $3d$ orbitals get involved. The multiple-orbital nature gives rise to various novel phenomena like orbital-selective Mott transition, nematicity, and orbital fluctuation that provide a new route for realizing superconductivity. The complexity of multiple-orbital physics also requires us to disentangle the relationship between orbital, spin, and nematicity, and to identify dominant orbital ingredients that dictate superconductivity. The bulk FeSe superconductor provides an ideal platform to address these issues because of its simple crystal structure and unique coexistence of superconductivity and nematicity. However, the orbital nature of the low-energy electronic excitations and its relation to the superconducting gap remain controversial. Here, we report direct observation of the highly anisotropic Fermi surface and extremely anisotropic superconducting gap in the nematic state of the FeSe superconductor by high-resolution laser-based angle-resolved photoemission measurements. We find that the low-energy excitations of the entire hole pocket at the Brillouin zone center are dominated by the single $d_{xz}$ orbital. The superconducting gap exhibits an anticorrelation relation with the $d_{xz}$ spectral weight near the Fermi level; i.e., the gap size minimum (maximum) corresponds to the maximum (minimum) of the $d_{xz}$ spectral weight along the Fermi surface. These observations provide new insights in understanding the orbital origin of the extremely anisotropic superconducting gap in the FeSe superconductor and the relation between nematicity and superconductivity in the iron-based superconductors.

The recent observation of a half-integer quantized thermal Hall effect in $\alpha \text{−}{\mathrm{RuCl}}_3$ is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A similar quantized thermal Hall effect is expected in chiral topological superconductors. The unavoidable presence of gapless acoustic phonons, however, implies that, in contrast to the quantized electrical conductivity, the thermal Hall conductivity ${\kappa }_{xy}$ is never exactly quantized in real materials. Here, we investigate how phonons affect the quantization of the thermal conductivity, focusing on the edge theory. As an example, we consider a Kitaev spin liquid gapped by an external magnetic field coupled to acoustic phonons. The coupling to phonons destroys the ballistic thermal transport of the edge mode completely, as energy can leak into the bulk, thus drastically modifying the edge picture of the thermal Hall effect. Nevertheless, the thermal Hall conductivity remains approximately quantized, and we argue that the coupling to phonons to the edge mode is a necessary condition for the observation of the quantized thermal Hall effect. The strength of this edge coupling does, however, not affect the conductivity. We argue that for sufficiently clean systems the leading correction to the quantized thermal Hall effect, $\mathrm{\Delta }{\kappa }_{xy}/T\sim \mathrm{sign}(\mathrm{B})T^2$, arises from an intrinsic anomalous Hall effect of the acoustic phonons due to Berry phases imprinted by the chiral (spin) liquid in the bulk. This correction depends on the sign but not the amplitude of the external magnetic field.