Braiding phases among topological excitations are key data for physically characterizing topological orders. In this paper, we provide a field-theoretical approach toward a complete list of mutually compatible braiding phases of topological orders in $(3+1)\mathrm{D}$ spacetime. More concretely, considering a discrete gauge group as input data, topological excitations in this paper are bosonic particles carrying gauge charges and loops carrying gauge fluxes. Among these excitations, there are three classes of root braiding processes: particle-loop braidings (i.e., the familiar Aharonov-Bohm phase of winding an electric charge around a thin magnetic solenoid), multiloop braidings [Wang and Levin, Phys. Rev. Lett. 113, 080403 (2014)], and particle-loop-loop braidings (i.e., Borromean rings braiding in Chan et al. [Phys. Rev. Lett. 121, 061601 (2018)]). A naive way to exhaust all topological orders is to arbitrarily combine these root braiding processes. Surprisingly, we find that there exist illegitimate combinations in which certain braiding phases cannot coexist, i.e., are mutually incompatible. Thus, the resulting topological orders are illegitimate and must be excluded. It is not obvious to identify these illegitimate combinations. But with the help of the powerful $(3+1)\mathrm{D}$ topological quantum field theories (TQFTs), we find that illegitimate combinations violate gauge invariance. In this way, we are able to obtain all sets of mutually compatible braiding phases and all legitimate topological orders. To illustrate, we work out all details when gauge groups are ${\mathbb{Z}}_{N_1},{\mathbb{Z}}_{N_1}\times {\mathbb{Z}}_{N_2},{\mathbb{Z}}_{N_1}\times {\mathbb{Z}}_{N_2}\times {\mathbb{Z}}_{N_3}$ and ${\mathbb{Z}}_{N_1}\times {\mathbb{Z}}_{N_2}\times {\mathbb{Z}}_{N_3}\times {\mathbb{Z}}_{N_4}$. Finally, we concisely discuss compatible braidings and TQFTs in $(4+1)\mathrm{D}$ spacetime.

Rich hidden unconventional orders with pseudogap formation, such as the intersite bond order (BO), attract increasing attention in condensed matter physics. Here, we investigate the hidden order formation in organic unconventional superconductor $\kappa \text{−}{\left(\text{BEDT-TTF}\right)}_2\mathrm{X}$. We predict the formation of $d$-wave BO at wavelength $\mathit{q}={\mathit{Q}}_{\mathrm{B}}=(\delta ,\delta )$ ($\delta =0.38\pi$) for the first time, based on both the functional renormalization group (fRG) and the density-wave equation theories. The origin of the BO is the quantum interference among antiferromagnetic spin fluctuations. This prediction leads to distinct pseudogap-like reduction in the NMR $1/T_1$ relaxation rate and in the density-of-states, consistently with essential experimental reports. The present theory would be applicable for other strongly correlated metals with pseudogap formation.

Ferromagnetic insulators (FI) can induce a strong exchange field in an adjacent superconductor (S) via the magnetic proximity effect. This manifests as spin splitting of the BCS density of states of the superconductor, an important ingredient for numerous superconducting spintronics applications and the realization of Majorana fermions. A crucial parameter that determines the magnitude of the induced spin splitting in FI/S bilayers is the thickness of the S layer $d$: In very thin samples, the superconductivity is suppressed by the strong magnetism. By contrast, in very thick samples, the spin splitting is absent at distances away from the interface. In this work, we calculate the density of states and critical exchange field of FI/S bilayers of arbitrary thickness. From here, we determine the range of parameters of interest for applications, where the exchange field and superconductivity coexist. We show that for $d>3.0{\xi }_s$, the paramagnetic phase transition is always of the second order, in contrast to the first-order transition in thinner samples at low temperatures. Here ${\xi }_s$ is the superconducting coherence length. Finally, we compare our theory with the tunneling spectroscopy measurements in several $\mathrm{EuS}/\mathrm{Al}/{\mathrm{AlO}}_x/\mathrm{Al}$ samples. If the Al film in contact with the EuS is thinner than a certain critical value, we do not observe superconductivity, whereas, in thicker samples, we find evidence of a first-order phase transition induced by an external field. The complete transition is preceded by a regime in which normal and superconducting regions coexist. We attribute this mixed phase to inhomogeneities of the Al film thickness and the presence of superparamagnetic grains at the EuS/Al interface with different switching fields. The steplike evolution of the tunnel-barrier magnetoresistance supports this assumption. Our results demonstrate on the one hand, the important role of the S layer thickness, which is particularly relevant for the fabrication of high-quality samples suitable for applications. On the other hand, the agreement between theory and experiment demonstrates the accuracy of our theory, which, originally developed for homogeneous situations, is generalized to highly inhomogeneous systems.

Satellite quantum communications are emerging within the panorama of quantum technologies as a more effective strategy to distribute completely secure keys at very long distances, therefore playing an important role in the architecture of a large-scale quantum network. In this work, we apply and extend recent results in free-space quantum communications to determine the ultimate limits at which secret (and entanglement) bits can be distributed via satellites. Our study is comprehensive of the various practical scenarios, encompassing both downlink and uplink configurations, with satellites at different altitudes and zenith angles. It includes effects of diffraction, extinction, background noise, and fading, due to pointing errors and atmospheric turbulence (appropriately developed for slant distances). Besides identifying upper bounds, we also discuss lower bounds, i.e., achievable rates for key generation and entanglement distribution. In particular, we study the composable finite-size secret key rates that are achievable by protocols of continuous variable quantum key distribution, for both downlink and uplink, showing the feasibility of this approach for all configurations. Finally, we present a study with a sun-synchronous satellite, showing that its key distribution rate is able to outperform a ground chain of ideal quantum repeaters.

We investigate morphologies of proliferating cellular tissues using a numerical simulation model for mechanical cell division and migration in two dimensions. The model is applied to a bimodal mixture consisting of stiff cells with a low growth potential and soft cells with a high growth potential; cancer cells are typically considered to be softer than healthy cells. In an even mixture, the soft cells develop into a tissue matrix and the stiff cells into a dendritelike network structure. When soft cells are placed inside a tissue consisting of stiff cells (to model cancer growth), the soft cells develop into a fast-growing tumorlike structure that gradually evacuates the stiff cell matrix. The model also demonstrates (1) how soft cells orient themselves in the direction of the largest effective stiffness as predicted by the theory of Bischofs and Schwarz [Proc. Natl. Acad. Sci. USA 100, 9274 (2003)] and (2) that the orientation and force generation continue a few cell rows behind the soft-stiff interface. With increasing intercell friction, tumor growth slows down, and cell death occurs. The contact force distribution between cells is demonstrated to be highly sensitive to cell type mixtures and cell-cell interactions, which indicates that local mechanical forces can be useful as a regulator of tissue formation. The results shed light on established experimental data.

We look into the minimization of the connection time between nonequilibrium steady states. As a prototypical example of an intrinsically nonequilibrium system, a driven granular gas is considered. For time-independent driving, its natural time scale for relaxation is characterized from an empirical (the relaxation function) and a theoretical (the recently derived classical speed limits) point of view. Using control theory, we find that bang-bang protocols (comprising two steps, heating with the largest possible value of the driving and cooling with zero driving) minimize the connecting time. The bang-bang time is shorter than both the empirical relaxation time and the classical speed limit: in this sense, the natural time scale for relaxation is beaten. Information theory quantities stemming from the Fisher information are also analyzed over these optimal protocols. The implementation of the bang-bang processes in numerical simulations of the dynamics of the granular gas show an excellent agreement with the theoretical predictions. Moreover, general implications of our results are discussed for a wide class of driven nonequilibrium systems. Specifically, we show that analogous bang-bang protocols, with a number of bangs equal to the number of relevant physical variables, give the minimum connecting time under quite general conditions.

Steady-state observables, such as occupation numbers and currents, are crucial experimental signatures in open quantum systems. The time-convolutionless (TCL) master equation, which is both exact and time-local, is an ideal candidate for the perturbative computation of such observables. We develop a diagrammatic approach to evaluate the steady-state TCL generator based on operators rather than superoperators. We obtain the steady-state occupation numbers, extend our formulation to the calculation of currents, and provide a simple physical interpretation of the diagrams. We further benchmark our method on a single noninteracting level coupled to Fermi reservoirs, where we recover the exact expansion to next-to-leading order. The low number of diagrams appearing in our formulation makes the extension to higher orders accessible. Combined, these properties make the steady-state time-convolutionless master equation an effective tool for the calculation of steady-state properties in open quantum systems.

Realizing photonic analogs of the robust, unidirectional edge states of electronic topological insulators would improve our control of light on the nanoscale and revolutionize the performance of photonic devices. Here, we show that new symmetry-protected topological phases can be detected by reformulating energy eigenproblems as Berry curvature eigenproblems. The “Berry bands” span the same eigenspace as the original valence energy bands, but separate into pseudo-spinful and pseudo-spinless subspaces in ${\mathrm{C}}_2\mathcal{T}$-symmetric crystals. We demonstrate the method on the well-known case of Wu and Hu [Phys. Rev. Lett. 114, 223901 (2015)] and a recently discovered fragilely topological crystal, and show that both crystals belong to the same photonic analog of the quantum spin-Hall effect. This work helps unite theory and numerics, and is useful in defining and identifying new symmetry-protected phases in photonics and electronics.

We demonstrate how magnon Kerr nonlinearity creates bistability of quantum states when the magnon mode is strongly driven by a microwave field in a nonlinear cavity magnonic system. Numerical simulation results with experimentally feasible parameters show that the method where the system is driven far from equilibrium is a reliable way to achieve squeezed states for magnons and photons and to carry out magnon-photon entanglement, revealing mysterious phenomena of bistability. In addition, the Kittel mode can jump from one state to another one near two switching points, thus achieving the hysteresis loop phenomenon. Our results indicate that bistable quantum states could provide a way to study macroscopic quantum bistable phenomena in nonlinear systems and also can be found in broad applications in magnetic spintronics.

Finding the fastest path to a desired destination is a vitally important task for microorganisms moving in a fluid flow. We study this problem by building an analytical formalism for overdamped microswimmers on curved manifolds and arbitrary flows. We show that the solution corresponds to the geodesics of a Randers metric, which is an asymmetric Finsler metric that reflects the irreversible character of the problem. Using the examples of spherical and toroidal surfaces, we demonstrate that the swimmer performance that follows this “Randers policy” always beats a more direct policy. Moreover, our results show that the relative gain grows significantly when specific structures related to either the geometry or the flow are exploited by the swimmer. A study of the shape of isochrones reveals features such as self-intersections, cusps, and abrupt nonlinear effects. Our work provides a link between microswimmer physics and geodesics in generalizations of general relativity.

Laser-ablated high-energy-density plasmas offer a promising route to study astrophysically relevant processes underlying collisionless shock formation, magnetic field amplification, and particle acceleration in the laboratory. Using large-scale, multidimensional particle-in-cell simulations, we explore the interpenetration of laser-ablated counter-streaming plasmas for realistic experimental flow profiles. We find that the shock formation and its structure are substantially different from those of more idealized and commonly considered uniform flows: shock formation can be up to 10 times faster due to the transition from small-angle scattering to magnetic reflection, and the shock front develops strong corrugations at the ion gyroradius scale. These findings have important consequences for current experimental programs and open exciting prospects for studying the microphysics of turbulent collisionless shocks with currently available high-energy laser systems.

In three dimensions, gapped phases can support “fractonic” quasiparticle excitations, which are either completely immobile or can only move within a low-dimensional submanifold, a peculiar topological phenomenon going beyond the conventional framework of topological quantum field theory. In this work we explore fractonic topological phases using three-dimensional coupled wire constructions, which have proven to be a successful tool to realize and characterize topological phases in two dimensions. We find that both gapped and gapless phases with fractonic excitations can emerge from the models. In the gapped case, we argue that fractonic excitations are mobile along the wire direction, but their mobility in the transverse plane is generally reduced. We show that the excitations in general have infinite-order fusion structure, distinct from previously known gapped fracton models. Like the two-dimensional coupled-wire constructions, many models exhibit gapless (or even chiral) surface states, which can be described by infinite-component Luttinger liquids. However, the universality class of the surface theory strongly depends on the surface orientation, thus revealing a different type of bulk-boundary correspondence unique to fracton phases.

We observe and comprehend the dynamical Coulomb blockade suppression of the electrical conductance across an electronic quantum channel subjected to a temperature difference. A broadly tunable, spin-polarized Ga(Al)As quantum channel is connected on-chip, through a micron-scale metallic node, to a linear $RC$ circuit. The latter is made up of the node's geometrical capacitance $C$ in parallel with an adjustable resistance $R\in \{1/2,1/3,1/4\}\times h/e^2$ formed by 2–4 quantum Hall channels. The system is characterized by three temperatures: Temperatures of the electrons in the large electrodes ($T$) and in the node ($T_{\mathrm{node}}$), and a temperature of the electromagnetic modes of the $RC$ circuit ($T_{\mathrm{env}}$). The temperature in the node is selectively increased by local Joule dissipation, and characterized from current fluctuations. For a quantum channel in the tunnel regime, a close match is found between conductance measurements and tunnel dynamical Coulomb blockade theory. In the opposite near ballistic regime, we develop a theory that accounts for different electronic and electromagnetic bath temperatures, again in very good agreement with experimental data. Beyond these regimes, for an arbitrary quantum channel set in the far out-of-equilibrium situation where the temperature in the node significantly exceeds the one in the large electrodes, the equilibrium (uniform temperature) prediction for the conductance is recovered, albeit at a rescaled temperature $\alpha T_{\mathrm{node}}$.

Typical higher-order topological systems require the fine-tuning of hopping textures and external fields, which considerably hinders their practical realization. Based on a simple picture that corners are “edges” of edges, we determine that in the already-thoroughly-studied monolayer graphene, higher-order topological corner states appear without introducing any additional effects. Unlike quadrupole insulators, owing to degenerate Dirac points in graphene, the emergence of topological corner states depends on the corner angle and edge geometries. We provide a useful expression for the indication of corner states in graphene by the product of Zak phases. We also discuss the methods for experimental detection of the nontrivial higher-order topology in graphene such as the fractional corner anomaly and the disparity of local density of states between trivial and nontrivial corners.

We study ${\mathbb{Z}}_2$ topologically ordered states enriched by translational symmetry by employing a recently developed two-dimensional (2D) bosonization approach that implements an exact ${\mathbb{Z}}_2$ charge-flux attachment in the lattice. Such states can display “weak symmetry breaking” of translations, in which both the Hamiltonian and ground state remain fully translational invariant but the symmetry is “broken” by its anyon quasiparticles, in the sense that its action maps them into a different superselection sector. We demonstrate that this phenomenon occurs when the fermionic spinons form a weak topological superconductor in the form of a 2D stack of one-dimensional Kitaev wires, leading to the amusing property that there is no local operator that can transport the $\pi$-flux quasiparticle across a single Kitaev wire of fermonic spinons without paying an energy gap in spite of the vacuum remaining fully translational invariant. We explain why this phenomenon occurs hand in hand with other previously identified peculiar features such as ground-state degeneracy dependence on the size of the torus and the appearance of dangling boundary Majorana modes in certain ${\mathbb{Z}}_2$ topologically ordered states. Moreover, by extending the ${\mathbb{Z}}_2$ charge-flux attachment to open lattices and cylinders, we construct a plethora of exactly solvable models providing an exact description of their dispersive Majorana gapless boundary modes. We also review the $\mathbb{Z}\times {\left({\mathbb{Z}}_2\right)}^3$ classification of 2D BdG Hamiltonians (class D) enriched by translational symmetry and provide arguments on its robust stability against interactions and self-averaging disorder that preserve translational symmetry.

Interesting analogies between shallow water dynamics and astrophysical phenomena have offered valuable insight from both the theoretical and experimental point of view. To help organize these efforts, here we analyze systematically the hydrodynamic properties of backwater profiles of the shallow water equations with 2D radial symmetry. In contrast to the more familiar 1D case typical of hydraulics, even in isentropic conditions, a solution with minimum-radius horizon for the flow emerges, similar to the black hole and white hole horizons, where the critical conditions of unitary Froude number provide a unidirectional barrier for surface waves. Beyond these time-reversible solutions, a greater variety of cases arises, when allowing for dissipation by turbulent friction and shock waves (i.e., hydraulic jumps) for both convergent and divergent flows. The resulting taxonomy of the base-flow cases may serve as a starting point for a more systematic analysis of higher-order effects linked, e.g., to wave propagation and instabilities, capillarity, variable bed slope, and rotation.

We consider the spectral statistics of the Floquet operator for disordered, periodically driven spin chains in their quantum chaotic and many-body localized (MBL) phases. The spectral statistics are characterized by the traces of powers $t$ of the Floquet operator, and our approach hinges on the fact that for integer $t$ in systems with local interactions, these traces can be re-expressed in terms of products of dual transfer matrices, each representing a spatial slice of the system. We focus on properties of the dual transfer matrix products as represented by a spectrum of Lyapunov exponents, which we call spectral Lyapunov exponents. In particular, we examine the features of this spectrum that distinguish chaotic and MBL phases. The transfer matrices can be block diagonalized using time-translation symmetry, and so the spectral Lyapunov exponents are classified according to a momentum in the time direction. For large $t$ we argue that the leading Lyapunov exponents in each momentum sector tend to zero in the chaotic phase, while they remain finite in the MBL phase. These conclusions are based on results from three complementary types of calculation. We find exact results for the chaotic phase by considering a Floquet random quantum circuit with on-site Hilbert space dimension $q$ in the large-$q$ limit. In the MBL phase, we show that the spectral Lyapunov exponents remain finite by systematically analyzing models of noninteracting systems, weakly coupled systems, and local integrals of motion. Numerically, we compute the Lyapunov exponents for a Floquet random quantum circuit and for the kicked Ising model in the two phases. As an additional result, we calculate exactly the higher-point spectral form factors (hpSFFs) in the large-$q$ limit and show that the generalized Thouless time scales logarithmically in system size for all hpSFFs in the large-$q$ chaotic phase.

A large number of complex systems, naturally emerging in various domains, are well described by directed networks, resulting in numerous interesting features that are absent from their undirected counterparts. Among these properties is a strong non-normality, inherited by a strong asymmetry that characterizes such systems and guides their underlying hierarchy. In this work, we consider an extensive collection of empirical networks and analyze their structural properties using information-theoretic tools. A ubiquitous feature is observed amongst such systems as the level of non-normality increases. When the non-normality reaches a given threshold, highly directed substructures aiming towards terminal (sink or source) nodes, denoted here as leaders, spontaneously emerge. Furthermore, the relative number of leader nodes describe the level of anarchy that characterizes the networked systems. Based on the structural analysis, we develop a null model to capture features such as the aforementioned transition in the networks' ensemble. We also demonstrate that the role of leader nodes at the pinnacle of the hierarchy is crucial in driving dynamical processes in these systems. This work paves the way for a deeper understanding of the architecture of empirical complex systems and the processes taking place on them.