We construct entanglement renormalization schemes that provably approximate the ground states of noninteracting-fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice. These schemes give hierarchical quantum circuits that build up the states from unentangled degrees of freedom. The circuits are based on pairs of discrete wavelet transforms, which are approximately related by a “half-shift”: translation by half a unit cell. The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit architecture to properly capture the entanglement in the ground state. We show how the error in the approximation can be controlled without ever performing a variational optimization.

Optical cavity QED provides a platform with which to explore quantum many-body physics in driven-dissipative systems. Single-mode cavities provide strong, infinite-range photon-mediated interactions among intracavity atoms. However, these global all-to-all couplings are limiting from the perspective of exploring quantum many-body physics beyond the mean-field approximation. The present work demonstrates that local couplings can be created using multimode cavity QED. This is established through measurements of the threshold of a superradiant, self-organization phase transition versus atomic position. Specifically, we experimentally show that the interference of near-degenerate cavity modes leads to both a strong and tunable-range interaction between Bose-Einstein condensates (BECs) trapped within the cavity. We exploit the symmetry of a confocal cavity to measure the interaction between real BECs and their virtual images without unwanted contributions arising from the merger of real BECs. Atom-atom coupling may be tuned from short range to long range. This capability paves the way toward future explorations of exotic, strongly correlated systems such as quantum liquid crystals and driven-dissipative spin glasses.

We present the first experimental observation of accelerating beams in curved space. More specifically, we demonstrate, experimentally and theoretically, shape-preserving accelerating beams propagating on spherical surfaces: closed-form solutions of the wave equation manifesting nongeodesic self-similar evolution. Unlike accelerating beams in flat space, these wave packets change their acceleration trajectory due to the interplay between interference effects and the space curvature, and they focus and defocus periodically due to the spatial curvature of the medium in which they propagate.

In this work, we present a model of the surface states of nonsymmorphic semimetals. These are derived from surface mass terms that lift the high degeneracy imposed on the band structure by the nonsymmorphic bulk symmetries. Reflecting the reduced symmetry at the surface, the bulk bands are strongly modified. This leads to the creation of two-dimensional floating or unpinned bands, which are distinct from Shockley states, quantum well states, or topologically protected surface states. We focus on the layered semimetal ZrSiS to clarify the origin of its surface states. We demonstrate an excellent agreement between density functional theory calculations and angle-resolved photoemission spectroscopy measurements and present an effective four-band model in which similar surface bands appear. Finally, we emphasize the role of the surface chemical potential by comparing the surface density of states in samples with and without potassium coating. Our findings can be extended to related compounds and generalized to other crystals with nonsymmorphic symmetries.

We study the spin-excitation spectrum (dynamic structure factor) of the spin-$1/2$ square-lattice Heisenberg antiferromagnet and an extended model (the $J\text{−}Q$ model) including four-spin interactions $Q$ in addition to the Heisenberg exchange $J$. Using an improved method for stochastic analytic continuation of imaginary-time correlation functions computed with quantum Monte Carlo simulations, we can treat the sharp ($\delta$-function) contribution to the structure factor expected from spin-wave (magnon) excitations, in addition to resolving a continuum above the magnon energy. Spectra for the Heisenberg model are in excellent agreement with recent neutron-scattering experiments on $\mathrm{Cu}(\mathrm{DCOO}{)}_2·4{\mathrm{D}}_2\mathrm{O}$, where a broad spectral-weight continuum at wave vector $q=(\pi ,0)$ was interpreted as deconfined spinons, i.e., fractional excitations carrying half of the spin of a magnon. Our results at $(\pi ,0)$ show a similar reduction of the magnon weight and a large continuum, while the continuum is much smaller at $q=(\pi /2,\pi /2)$ (as also seen experimentally). We further investigate the reasons for the small magnon weight at $(\pi ,0)$ and the nature of the corresponding excitation by studying the evolution of the spectral functions in the $J\text{−}Q$ model. Upon turning on the $Q$ interaction, we observe a rapid reduction of the magnon weight to zero, well before the system undergoes a deconfined quantum phase transition into a nonmagnetic spontaneously dimerized state. Based on these results, we reinterpret the picture of deconfined spinons at $(\pi ,0)$ in the experiments as nearly deconfined spinons—a precursor to deconfined quantum criticality. To further elucidate the picture of a fragile $(\pi ,0)$-magnon pole in the Heisenberg model and its depletion in the $J\text{−}Q$ model, we introduce an effective model of the excitations in which a magnon can split into two spinons that do not separate but fluctuate in and out of the magnon space (in analogy to the resonance between a photon and a particle-hole pair in the exciton-polariton problem). The model can reproduce the reduction of magnon weight and lowered excitation energy at $(\pi ,0)$ in the Heisenberg model, as well as the energy maximum and smaller continuum at $(\pi /2,\pi /2)$. It can also account for the rapid loss of the $(\pi ,0)$ magnon with increasing $Q$ and the remarkable persistence of a large magnon pole at $q=(\pi /2,\pi /2)$ even at the deconfined critical point. The fragility of the magnons close to $(\pi ,0)$ in the Heisenberg model suggests that various interactions that likely are important in many materials—e.g., longer-range pair exchange, ring exchange, and spin-phonon interactions—may also destroy these magnons and lead to even stronger spinon signatures than in $\mathrm{Cu}(\mathrm{DCOO}{)}_2·4{\mathrm{D}}_2\mathrm{O}$.

Neural tissues have been consistently observed to be spontaneously active and to generate highly variable (scale-free distributed) outbursts of activity in vivo and in vitro. Understanding whether these heterogeneous patterns of activity stem from the underlying neural dynamics operating at the edge of a phase transition is a fascinating possibility, as criticality has been argued to entail many possible important functional advantages in biological computing systems. Here, we employ a well-accepted model for neural dynamics to elucidate an alternative scenario in which diverse neuronal avalanches, obeying scaling, can coexist simultaneously, even if the network operates in a regime far from the edge of any phase transition. We show that perturbations to the system state unfold dynamically according to a “neutral drift” (i.e., guided only by stochasticity) with respect to the background of endogenous spontaneous activity, and that such a neutral dynamics—akin to neutral theories of population genetics and of biogeography—implies marginal propagation of perturbations and scale-free distributed causal avalanches. We argue that causal information, not easily accessible to experiments, is essential to elucidate the nature and statistics of neural avalanches, and that neutral dynamics is likely to play an important role in the cortex functioning. We discuss the implications of these findings to design new empirical approaches to shed further light on how the brain processes and stores information.

Why is it difficult to refold a previously folded sheet of paper? We show that even crease patterns with only one designed folding motion inevitably contain an exponential number of “distractor” folding branches accessible from a bifurcation at the flat state. Consequently, refolding a sheet requires finding the ground state in a glassy energy landscape with an exponential number of other attractors of higher energy, much like in models of protein folding (Levinthal’s paradox) and other NP-hard satisfiability (SAT) problems. As in these problems, we find that refolding a sheet requires actuation at multiple carefully chosen creases. We show that seeding successful folding in this way can be understood in terms of subpatterns that fold when cut out (“folding islands”). Besides providing guidelines for the placement of active hinges in origami applications, our results point to fundamental limits on the programmability of energy landscapes in sheets.

We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure in all physically relevant dimensions. The algorithm applies to crystals without time-reversal, particle-hole, chiral, or any other anticommuting or anti-unitary symmetries. The results presented match the mathematical structure underlying the topological classification of these crystals in terms of $K$-theory and therefore elucidate this abstract mathematical framework from a simple combinatorial perspective. Using a straightforward counting procedure, we classify all allowed topological phases of spinless particles in crystals in class $A$. Employing this classification, we study transitions between topological phases within class $A$ that are driven by band inversions at high-symmetry points in the first Brillouin zone. This enables us to list all possible types of phase transitions within a given crystal structure and to identify whether or not they give rise to intermediate Weyl semimetallic phases.

We study broken symmetry states at integer Landau-level fillings in multivalley quantum Hall systems whose low-energy dispersions are anisotropic. When the Fermi surface of individual pockets lacks twofold rotational symmetry, like in bismuth (111) [Feldman et al. , Observation of a Nematic Quantum Hall Liquid on the Surface of Bismuth, Science 354, 316 (2016)] and in ${\mathrm{Sn}}_{1-x}{\mathrm{Pb}}_x\mathrm{Se}$ (001) [Dziawa et al., Topological Crystalline Insulator States in ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Se}$, Nat. Mater. 11, 1023 (2012)] surfaces, interactions tend to drive the formation of quantum Hall ferroelectric states. We demonstrate that the dipole moment in these states has an intimate relation to the Fermi surface geometry of the parent metal. In quantum Hall nematic states, like those arising in AlAs quantum wells, we demonstrate the existence of unusually robust Skyrmion quasiparticles.

Chromium dioxide ${\mathrm{CrO}}_2$ belongs to a class of materials called ferromagnetic half-metals, whose peculiar aspect is that they act as a metal in one spin orientation and as a semiconductor or insulator in the opposite one. Despite numerous experimental and theoretical studies motivated by technologically important applications of this material in spintronics, its fundamental properties such as momentum-resolved electron dispersions and the Fermi surface have so far remained experimentally inaccessible because of metastability of its surface, which instantly reduces to amorphous ${\mathrm{Cr}}_2{\mathrm{O}}_3$. In this work, we demonstrate that direct access to the native electronic structure of ${\mathrm{CrO}}_2$ can be achieved with soft-x-ray angle-resolved photoemission spectroscopy whose large probing depth penetrates through the ${\mathrm{Cr}}_2{\mathrm{O}}_3$ layer. For the first time, the electronic dispersions and Fermi surface of ${\mathrm{CrO}}_2$ are measured, which are fundamental prerequisites to solve the long debate on the nature of electronic correlations in this material. Since density functional theory augmented by a relatively weak local Coulomb repulsion gives an exhaustive description of our spectroscopic data, we rule out strong-coupling theories of ${\mathrm{CrO}}_2$. Crucial for the correct interpretation of our experimental data in terms of the valence-band dispersions is the understanding of a nontrivial spectral response of ${\mathrm{CrO}}_2$ caused by interference effects in the photoemission process originating from the nonsymmorphic space group of the rutile crystal structure of ${\mathrm{CrO}}_2$.

One of the central questions in the cuprate research is the nature of the normal state that develops into high-temperature superconductivity (HTSC). In the normal state of hole-doped cuprates, the existence of a charge density wave (CDW) is expected to shed light on the mechanism of HTSC. With evidence emerging for CDW order in the electron-doped cuprates, the CDW is thought to be a universal phenomenon in high-$T_{\mathrm{c}}$ cuprates. However, the CDW phenomena in electron-doped cuprates are quite different than those in hole-doped cuprates. Here, we study the nature of the putative CDW in an electron-doped cuprate through direct comparisons between as-grown and postannealed ${\mathrm{Nd}}_{1.86}{\mathrm{Ce}}_{0.14}{\mathrm{CuO}}_4$ (NCCO) single crystals using Cu $L_3$-edge resonant soft x-ray scattering (RSXS) and angle-resolved photoemission spectroscopy (ARPES). The RSXS result reveals that the nonsuperconducting NCCO shows the same reflections at the wave vector ($\sim 1/4$, 0, $l$) as the reported superconducting NCCO. This superconductivity-insensitive signal is quite different from the CDW reflection in hole-doped cuprates. Moreover, the ARPES result suggests that the fermiology cannot account for such wave vectors. These results call into question the universality of the CDW phenomenon in the cuprates.

Stokes’s law for the friction of a sphere in water has been argued to work down to molecular scales, provided the effective hydrodynamic radius includes the hydration layer. In interpretations of experiments and in theoretical models, it is tacitly assumed that the solvent friction experienced by a solute does not depend on whether an external confinement potential acts on the solute. Using a novel method to extract the friction memory function from molecular dynamics simulations, we show that the solvent friction of a strongly harmonically confined methane molecule in water increases by 60% compared to its free-solution value, which is caused by an amplification of the slowest component of the memory function. The friction enhancement occurs for potential strengths typical of physical and chemical bonds and is accompanied by a significant slowing-down of the hydration water dynamics. Thus, the solvent friction acting on molecular solutes is not determined by solvent properties and solute-solvent interactions alone but results from the coupling between solute and solvent dynamics and thereby can be tuned by an external potential acting on the solute. This also explains why simulations of positionally constrained solutes do not reproduce free-solution diffusivities. Dynamic scaling arguments suggest similar effects also for macromolecular solutes provided the solution viscosity is sufficiently enhanced.

Understanding grain growth is key for controlling the microstructure and the mechanical properties of most polycrystalline materials, including metals, alloys, and ceramics. However, the precise mechanisms and kinetics of grain growth remain poorly understood both at the theoretical level and experimentally as direct observation is cumbersome in atomic systems. Here, we study the grain growth process in a polycrystalline monolayer of colloidal hard spheres. We find that the bond-orientational correlation function satisfies the dynamic scaling hypothesis and has the general scaling form predicted for systems containing random domain walls. However, the associated correlation length grows slower than $\sim t^{1/2}$, which corresponds to normal curvature-driven grain growth. To understand the origin of this anomalous grain growth, we directly monitor the evolution of the grain boundary network by measuring the so-called grain boundary character distribution. We show that there is a strong annihilation of large-angle grain boundaries while small-angle grain boundaries become relatively more present. Using scaling arguments, we derive the time dependence of the correlation length and show its good agreement with the data. We conclude that the origin of anomalous grain growth is the curvature-driven coarsening of the large-angle grain boundaries at a rate that depends on their relative length in the total grain boundary network.

Coherent many-body quantum dynamics lies at the heart of quantum simulation and quantum computation. Both require coherent evolution in the exponentially large Hilbert space of an interacting many-body system. To date, trapped ions have defined the state of the art in terms of achievable coherence times in interacting spin chains. Here, we establish an alternative platform by reporting on the observation of coherent, fully interaction-driven quantum revivals of the magnetization in Rydberg-dressed Ising spin chains of atoms trapped in an optical lattice. We identify partial many-body revivals at up to about ten times the characteristic time scale set by the interactions. At the same time, single-site-resolved correlation measurements link the magnetization dynamics with interspin correlations appearing at different distances during the evolution. These results mark an enabling step towards the implementation of Rydberg-atom-based quantum annealers, quantum simulations of higher-dimensional complex magnetic Hamiltonians, and itinerant long-range interacting quantum matter.

We prove that quantum information encoded in some topological excitations, including certain Majorana zero modes, is protected in closed systems for a time scale exponentially long in system parameters. This protection holds even at infinite temperature. At lower temperatures, the decay time becomes even longer, with a temperature dependence controlled by an effective gap that is parametrically larger than the actual energy gap of the system. This nonequilibrium dynamical phenomenon is a form of prethermalization and occurs because of obstructions to the equilibration of edge or defect degrees of freedom with the bulk. We analyze the ramifications for ordered and topological phases in one, two, and three dimensions, with examples including Majorana and parafermionic zero modes in interacting spin chains. Our results are based on a nonperturbative analysis valid in any dimension, and they are illustrated by numerical simulations in one dimension. We discuss the implications for experiments on quantum-dot chains tuned into a regime supporting end Majorana zero modes and on trapped ion chains.

A quantitative assessment of the progress of small prototype quantum processors towards fault-tolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a necessary and fair criterion for quantum error correction (QEC), which must be achieved in the development of these quantum processors before their sizes are sufficiently big to consider the well-known QEC threshold. We apply this criterion to benchmark the ongoing effort in implementing QEC with topological color codes using trapped-ion quantum processors and, more importantly, to guide the future hardware developments that will be required in order to demonstrate beneficial QEC with small topological quantum codes. In doing so, we present a thorough description of a realistic trapped-ion toolbox for QEC and a physically motivated error model that goes beyond standard simplifications in the QEC literature. We focus on laser-based quantum gates realized in two-species trapped-ion crystals in high-optical aperture segmented traps. Our large-scale numerical analysis shows that, with the foreseen technological improvements described here, this platform is a very promising candidate for fault-tolerant quantum computation.

The volume of ordinary materials decreases in response to a pressure increase exerted by a surrounding gas or liquid, i.e., the material volume compressibility is positive. Recently, poroelastic metamaterial architectures have been suggested theoretically that allow for an unusual negative effective static volume compressibility—which appears to be forbidden for reasons of energy conservation at first sight. The challenge in the three-dimensional (3D) fabrication of these blueprints lies in the necessary many hollow 3D crosses sealed by thin membranes, which we realize in this work by using 3D laser microlithography combined with a serendipitous mechanism. By using optical-microscopy cross-correlation analysis, we determine an extraordinarily large negative metamaterial effective volume compressibility of ${\kappa }_{\mathrm{eff}}=-0.8\%{\mathrm{bar}}^{-1}=-80{\mathrm{GPa}}^{-1}$ under pressure control.