Complex chemical reaction networks, which underlie many industrial and biological processes, often exhibit non-monotonic changes in chemical species concentrations. Such non-monotonic dynamics are in principle possible even in a linear model if the matrix defining the model is non-normal, as characterized by a necessarily non-orthogonal set of eigenvectors. However, the extent to which non-normality is responsible for non-monotonic behavior remains an open question. Here, using a master equation to model the reaction dynamics, we derive a general condition for observing non-monotonic dynamics of individual species, establishing that non-normality promotes non-monotonicity but is not a requirement for it. In contrast, we show that non-normality is a requirement for non-monotonic dynamics to be observed in the Rényi entropy. Using hydrogen combustion as an example application, we demonstrate that non-monotonic dynamics under experimental conditions are supported by a linear chain of connected components, at variance with the dominance of a single giant component observed in typical random reaction networks. The exact linearity of the master equation enables development of a rigorous theory and simulations for dynamical networks of unprecedented sizes (approaching ${10}^5$ dynamical variables, even for a network of only 20 reactions and involving less than 100 atoms). Our conclusions are expected to hold for other combustion processes, and the general theory we develop is applicable to all chemical reaction networks, including biological ones.

We develop an exact framework for describing the non-Markovian dynamics of an open quantum system interacting with an environment modeled by a generalized spectral density function. The approach relies on mapping the initial system onto an auxiliary configuration, comprising the original open system coupled to a small number of discrete modes, which in turn are each coupled to an independent Markovian reservoir. Based on the connection between the discrete modes and the poles of the spectral density function, we show how expanding the system using the discrete modes allows for the full inclusion non-Markovian effects within an enlarged open system whose dynamics is governed by an exact Lindblad master equation. Initially we apply this result to obtain a generalization of the pseudomode method [B. M. Garraway, Phys. Rev. A. 55, 2290 (1997)] in cases where the spectral density function has a Lorentzian structure. For many other types of spectral density function, we extend our proof to show that an open system dynamics may be modeled physically using discrete modes which admit a non-Hermitian coupling to the system and for such cases determine the equivalent master equation to no longer be of Lindblad form. For applications involving two discrete modes, we demonstrate how to convert between pathological and Lindblad forms of the master equation using the techniques of the pseudomode method.

Machine learning (ML) methods have recently been used as forward solvers to predict the mechanical properties of composite materials. Here, we use a supervised autoencoder (SAE) to perform the inverse design of graphene kirigami, where predicting the ultimate stress or strain under tensile loading is known to be difficult due to nonlinear effects arising from the out-of-plane buckling. Unlike the standard autoencoder, our SAE is able not only to reconstruct cut configurations but also to predict the mechanical properties of graphene kirigami and classify the kirigami with either parallel or orthogonal cuts. By interpolating in the latent space of kirigami structures, the SAE is able to generate designs that mix parallel and orthogonal cuts, despite being trained independently on parallel or orthogonal cuts. Our method allows us to both identify alternate designs and predict, with reasonable accuracy, their mechanical properties, which is crucial for expanding the search space for materials design.

In several Fe-based superconductors, slight $C_4$ symmetry breaking occurs at $T^{*}$, which is tens of degrees Kelvin higher than the structural transition temperature $T_S$. In this “hidden” nematic state at $T_S<T<T^{*}$, the orthorhombicity is tiny $[\varphi =(a-b)/(a+b)\ll 0.1\%]$, but clear evidence of a bulk phase transition has been accumulated. To explain this long-standing mystery, we propose the emergence of antiferro-bond (AFB) order with the AF wave vector $\mathit{q}=(0,\pi )$ at $T=T^{*}$, by which the characteristic phenomena below $T^{*}$ are satisfactorily explained. This AFB order originates from the interorbital nesting between the $d_{xy}$-orbital hole pocket and the electron pocket, and this interorbital bond order naturally explains the pseudogap, band folding, and tiny nematicity that is linear in $T^{*}-T$. The hidden AFB order explains key experiments in both ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ and NaFeAs, but it is not expected to occur in FeSe because of the absence of the $d_{xy}$-orbital hole pocket.

Graphene sandwiched between semiconducting monolayers of ferromagnet ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ and transition-metal dichalcogenide ${\mathrm{WS}}_2$ acquires both spin-orbit (SO) coupling, of valley-Zeeman and Rashba types, and exchange coupling. Using first principles combined with quantum transport calculations, we predict that such doubly proximitized graphene within van der Waals heterostructure will exhibit SO torque driven by unpolarized charge current. This system lacks spin Hall current which is putatively considered as necessary for the efficient damping-like (DL) SO torque that plays a key role in magnetization switching. Instead, it demonstrates how a DL SO torque component can be generated solely by skew scattering off spin-independent potential barrier or impurities in purely two-dimensional electronic transport due to the presence of proximity SO coupling and its spin texture tilted out of plane. This leads to current-driven nonequilibrium spin density emerging in all spatial directions, whose cross product with proximity magnetization yields DL SO torque, unlike the ballistic regime with no scatterers in which only field-like (FL) SO torque appears. In contrast to SO torque on conventional metallic ferromagnets in contact with three-dimensional SO-coupled materials, the ratio of FL and DL components of SO torque can be tuned by more than an order of magnitude via combined top and back gates.

We report measurements on the ${\mathrm{H}}^{+}+{\mathrm{H}}^{+}$ fragmentation channel following direct single-photon double ionization of neutral ${\mathrm{NH}}_3$ at 61.5 eV, where the two photoelectrons and two protons are measured in coincidence using three-dimensional (3D) momentum imaging. We identify four dication electronic states that contribute to ${\mathrm{H}}^{+}+{\mathrm{H}}^{+}$ dissociation, based on our multireference configuration-interaction calculations of the dication potential energy surfaces. The extracted branching ratios between these four dication electronic states are presented. Of the four dication electronic states, three dissociate in a concerted process, while the fourth undergoes a sequential fragmentation mechanism. We find evidence that the neutral NH fragment or intermediate ${\mathrm{NH}}^{+}$ ion is markedly rovibrationally excited. We also identify differences in the relative emission angle between the two photoelectrons as a function of their energy sharing for the four different dication states, which bare some similarities to previous observations made on atomic targets.

Statistical mechanics is based on the interplay between energy and entropy. Here we formalize this interplay via axiomatic bargaining theory (a branch of cooperative game theory), where entropy and negative energy are represented by utilities of two different players. Game-theoretic axioms provide a solution to the thermalization problem, which is complementary to existing physical approaches. We predict thermalization of a nonequilibrium statistical system employing the axiom of affine covariance, related to the freedom of changing initial points and dimensions for entropy and energy, together with the contraction invariance of the entropy-energy diagram. Thermalization to negative temperatures is allowed for active initial states. Demanding a symmetry between players determines the final state to be the Nash solution (well known in game theory), whose derivation is improved as a by-product of our analysis. The approach helps to retrodict nonequilibrium predecessors of a given equilibrium state.

Optically levitated nonspherical particles in vacuum are excellent candidates for torque sensing, rotational quantum mechanics, high-frequency gravitational wave detection, and multiple other applications. Many potential applications, such as detecting the Casimir torque near a birefringent surface, require simultaneous cooling of both the center-of-mass motion and the torsional vibration (or rotation) of a nonspherical nanoparticle. Here we report five-dimensional cooling of a levitated nanoparticle. We cool the three center-of-mass motion modes and two torsional vibration modes of a levitated nanodumbbell in a linearly polarized laser simultaneously. The only uncooled rigid-body degree of freedom is the rotation of the nanodumbbell around its long axis. This free rotation mode does not couple to the optical tweezers directly. Surprisingly, we observe that it strongly affects the torsional vibrations of the nanodumbbell. This work deepens our understanding of the nonlinear dynamics and rotation coupling of a levitated nanoparticle and paves the way towards full quantum control of its motion.

The accurate characterization of nonequilibrium strongly correlated quantum systems has been a longstanding challenge in many-body physics. Notable among them are quantum impurity models, which appear in various nanoelectronic and quantum computing applications. Despite their seeming simplicity, they feature correlated phenomena, including small emergent energy scales and non-Fermi-liquid physics, requiring renormalization group treatment. This has typically been at odds with the description of their nonequilibrium steady state under finite bias, which exposes their nature as open quantum systems. We present a numerically exact method for obtaining the nonequilibrium state of a general quantum impurity coupled to metallic leads at arbitrary voltage or temperature bias, which we call “RL-NESS” (renormalized Lindblad-driven nonequilibrium steady state). It is based on coherently coupling the impurity to discretized leads which are treated exactly. These leads are furthermore weakly coupled to reservoirs described by Lindblad dynamics which impose voltage or temperature bias. Going beyond previous attempts, we exploit a hybrid discretization scheme for the leads together with Wilson's numerical renormalization group, in order to probe exponentially small energy scales. The steady state is then found by evolving a matrix-product density operator via real-time Lindblad dynamics, employing a dissipative generalization of the time-dependent density matrix renormalization group. In the long-time limit, this procedure successfully converges to the steady state at finite bond dimension due to the introduced dissipation, which bounds the growth of entanglement. We thoroughly test the method against the exact solution of the noninteracting resonant level model. We then demonstrate its power using an interacting two-level model, for which it correctly reproduces the known limits, and gives the full $I\text{−}V$ curve between them.

Van der Waals semiconductor heterostructures could be a platform to harness hot photoexcited carriers in the next generation of optoelectronic and photovoltaic devices. The internal quantum efficiency of hot-carrier devices is determined by the relation between photocarrier extraction and thermalization rates. Using ab initio methods we show that the photocarrier thermalization time in single-layer transition metal dichalcogenides strongly depends on the peculiarities of the phonon spectrum and the electronic spin-orbit coupling. In detail, the lifted spin degeneracy in the valence band suppresses the hole scattering on acoustic phonons, slowing down the thermalization of holes by one order of magnitude as compared with electrons. Moreover, the hole thermalization time behaves differently in $\mathrm{Mo}{\mathrm{S}}_2$ and $\mathrm{W}{\mathrm{Se}}_2$ because spin-orbit interactions differ in these seemingly similar materials. We predict that the internal quantum efficiency of a tunneling van der Waals semiconductor heterostructure depends qualitatively on whether $\mathrm{Mo}{\mathrm{S}}_2$ or $\mathrm{W}{\mathrm{Se}}_2$ is used.

We develop optimal protocols for efficient photon transfer in a cavity-QED network. This is executed through stimulated Raman adiabatic passage scheme where time-varying inductive or capacitive couplings (with carefully chosen sweep rate) play a key role. We work in a regime where the semiclassical limit is valid, and we investigate the dynamical chaos caused by the light-matter coupling. We show that this plays a crucial role in estimating the lower bound on the sweep rate for ensuring efficient photon transfer. We present Hermitian as well as an open quantum system extension of the model. Without loss of generality, we study the three cavity and four cavity cases and our results can be adapted to larger networks. Our analysis is also significant in designing transport protocols aimed for nonlinear open quantum systems, in general.

We observe the dissipative dynamics of a dense, strongly interacting gas of bosonic atom pairs in an optical lattice, controlling the strength of the two-body interactions over a wide parameter regime. We study how three-body losses contribute to the lattice dynamics, addressing a number of open questions related to the effects of strong dissipation in a many-body system, including the relationship to the continuous quantum Zeno effect. We observe rapid break-up of bound pairs for weak interactions, and for stronger interactions we see doublon decay rates that are asymmetric when changing from attractive and repulsive interactions and which strongly depend on the interactions and on-site loss rates. By comparing our experimental data with a theoretical analysis of few-body dynamics, we show that these features originate from a nontrivial combination of dissipative dynamics described by a lattice model beyond a standard Bose-Hubbard Hamiltonian, and the modification of three-atom dynamics on a single site, which is generated alongside strong three-body loss. Our results open new possibilities for investigating bosonic atoms with strong three-body loss features and allow for the better understanding of the parameter regimes that are required to realize strong effective three-body interactions.

Recent work has shown that coupling two identical Sachdev-Ye-Kitaev (SYK) models can realize a phase of matter that is holographically dual to an eternal traversable wormhole. This phase supports revival oscillations between two quantum chaotic systems that can be interpreted as information traversing the wormhole. Here we generalize these ideas to a pair of coupled SYK models with complex fermions that respect a global U(1) charge symmetry. Such models show richer behavior than conventional SYK models with Majorana fermions and may be easier to realize experimentally. We consider two different couplings, namely, tunneling and charge-conserving two-body interactions, and obtain the corresponding phase diagram using a combination of numerical and analytical techniques. At low temperature, we find a charge-neutral gapped phase that supports revival oscillations, with a ground state close to the thermofield double, which we argue is dual to a traversable wormhole. We also find two different gapless non-Fermi liquid phases with tunable charge density which we interpret as dual to a “large” and “small” charged black hole. The gapped and gapless phases are separated by a first-order phase transition of the Hawking-Page type. Finally, we discuss an SU(2)-symmetric limit of our model that is closely related to proposed realizations of SYK physics with spinful fermions in graphene, and explain its relevance for future experiments on this system.

We examine the routing scheme of single photons in a one-dimensional periodic chain of two-level quantum emitters (QEs) strongly coupled to two waveguides in a ladder configuration. It is known that for a single-emitter chiral waveguide ladder setting photons can be redirected from one waveguide to another with a 100% probability (deterministically) provided the resonance condition is met and spontaneous emission is completely ignored. However, when the spontaneous emission is included the routing scheme becomes considerably imperfect. In this paper, we present a solution to this issue by considering a chain of QEs where, in addition to the waveguide mediated interaction among emitters, a direct and infinitely long-ranged dipole-dipole interaction (DDI) is taken into account. We show that the collective effects arising from the strong DDI protect the routing scheme from spontaneous emission loss. In particular, we demonstrate that the router operation can be improved from 58 to $\approx 95\%$ in a typical dissipative chiral light-matter interface consisting of nanowire modes strongly interacting with a linear chain of 30 quantum dots. With the recent experimental progress in chiral quantum optics, trapped QEs evanescently coupled to tapered nanofibers can serve as a platform for the experimental realization of this paper.

Lieb-Robinson bounds quantify the maximal speed of information spreading in nonrelativistic quantum systems. We discuss the relation of Lieb-Robinson bounds to out-of-time order correlators, which correspond to different norms of commutators $C(r,t)=[A_i\left(t\right),B_{i+r}]$ of local operators. Using an exact Krylov space-time evolution technique, we calculate these two different norms of such commutators for the spin-1/2 Heisenberg chain with interactions decaying as a power law $1/r^{\alpha }$ with distance $r$. Our numerical analysis shows that both norms (operator norm and normalized Frobenius norm) exhibit the same asymptotic behavior, namely, a linear growth in time at short times and a power-law decay in space at long distance, leading asymptotically to power-law light cones for $\alpha <1$ and to linear light cones for $\alpha >1$. The asymptotic form of the tails of $C(r,t)\propto t/r^{\alpha }$ is described by short-time perturbation theory, which is valid at short times and long distances.

Non-Hermitian (NH) Hamiltonians can be used to describe dissipative systems, notably including systems with gain and loss, and are currently intensively studied in the context of topology. A salient difference between Hermitian and NH models is the breakdown of the conventional bulk-boundary correspondence, invalidating the use of topological invariants computed from the Bloch bands to characterize boundary modes in generic NH systems. One way to overcome this difficulty is to use the framework of biorthogonal quantum mechanics to define a biorthogonal polarization, which functions as a real-space invariant signaling the presence of boundary states. Here, we generalize the concept of the biorthogonal polarization beyond the previous results to systems with any number of boundary modes and show that it is invariant under basis transformations as well as local unitary transformations. Additionally, we focus on the anisotropic Su-Schrieffer-Heeger chain and study gap closings analytically. We also propose a generalization of a previously developed method with which to find all the bulk states of the system with open boundaries to NH models. Using the exact solutions for the bulk and boundary states, we elucidate genuinely NH aspects of the interplay between the bulk and boundary at the phase transitions.

Energy bands of non-Hermitian crystalline systems are described in terms of the generalized Brillouin zone (GBZ) having unique features which are absent in Hermitian systems. In this paper, we show that in one-dimensional non-Hermitian systems with both sublattice symmetry and time-reversal symmetry such as the non-Hermitian Su-Schrieffer-Heeger model, a topological semimetal phase with exceptional points is stabilized by the unique features of the GBZ. Namely, under a change of a system parameter, the GBZ is deformed so that the system remains gapless. It is also shown that each energy band is divided into three regions, depending on the symmetry of the eigenstates, and the regions are separated by the cusps and the exceptional points in the GBZ.

We study 't Hooft anomalies of symmetry-enriched rational conformal field theories (RCFT) in ($1+1$)d. Such anomalies determine whether a theory can be realized in a truly ($1+1$)d system with on-site symmetry, or on the edge of a ($2+1$)d symmetry-protected topological phase. RCFTs with the identical symmetry actions on their chiral algebras may have different 't Hooft anomalies due to additional symmetry charges on local primary operators. To compute the relative anomaly, we establish a precise correspondence between ($1+1$)d nonchiral RCFTs and ($2+1$)d doubled symmetry-enriched topological (SET) phases with a choice of a symmetric gapped boundary. Based on these results we derive a general formula for the relative 't Hooft anomaly in terms of algebraic data that characterizes the SET phase and its boundary.

We classify symmetry fractionalization and anomalies in a (3+1)d U(1) gauge theory enriched by a global symmetry group $G$. We find that, in general, a symmetry-enrichment pattern is specified by four pieces of data: $\rho$, a map from $G$ to the duality symmetry group of this $\mathrm{U}\left(1\right)$ gauge theory which physically encodes how the symmetry permutes the fractional excitations, $\nu \in {\mathcal{H}}_{\rho }^2[G,{\mathrm{U}}_{\mathsf{T}}\left(1\right)]$, the symmetry actions on the electric charge, $p\in {\mathcal{H}}^1[G,{\mathbb{Z}}_{\mathsf{T}}]$, indication of certain domain wall decoration with bosonic integer quantum Hall (BIQH) states, and a torsor $n$ over ${\mathcal{H}}_{\rho }^3[G,\mathbb{Z}]$, the symmetry actions on the magnetic monopole. However, certain choices of $(\rho ,\nu ,p,n)$ are not physically realizable, i.e., they are anomalous. We find that there are two levels of anomalies. The first level of anomalies obstruct the fractional excitations being deconfined, thus are referred to as the deconfinement anomaly. States with these anomalies can be realized on the boundary of a (4+1)d long-range entangled state. If a state does not suffer from a deconfinement anomaly, there can still be the second level of anomaly, the more familiar 't Hooft anomaly, which forbids certain types of symmetry fractionalization patterns to be implemented in an on-site fashion. States with these anomalies can be realized on the boundary of a (4+1)d short-range entangled state. We apply these results to some interesting physical examples.

The simulation complexity of predicting the time evolution of delocalized many-body quantum systems has attracted much recent interest, and simulations of such systems in real quantum hardware are promising routes to demonstrating a quantum advantage over classical machines. In these proposals, random noise is an obstacle that must be overcome for a faithful simulation, and a single error event can be enough to drive the system to a classically trivial state. We argue that this need not always be the case, and consider a modification to a leading quantum sampling problem—time evolution in an interacting Bose-Hubbard chain of transmon qubits [Neill et al., Science 360, 195 (2018)]—where each site in the chain has a driven coupling to a lossy cavity and particle number is no longer conserved. With cavity noise (but not qubit error) now included in the problem definition, the resulting quantum dynamics are still complex and highly nontrivial. We argue that this problem is harder to simulate than the isolated chain, and that it can achieve volume-law entanglement even in the strong noise limit, likely persisting up to system sizes beyond the scope of classical simulation. Further, we show that the metrics which suggest classical intractability for the isolated chain point to similar conclusions in the noisy case. These results suggest that quantum sampling problems including nontrivial noise could be good candidates for demonstrating a quantum advantage in near-term hardware.