We discover a first-order phase transition in the canonical ensemble of random unlabeled networks with a prescribed average number of links. The transition is caused by the nonconcavity of microcanonical entropy. Above the critical point coinciding with the graph symmetry phase transition, the canonical and microcanonical ensembles are equivalent and have a well-behaved thermodynamic limit. Below the critical point, the ensemble equivalence is broken, and the canonical ensemble is a mixture of phases: empty networks and networks with average degrees diverging logarithmically with the network size. As a consequence, networks with bounded average degrees do not survive in the thermodynamic limit, decaying into the empty phase. The celebrated percolation transition in labeled networks is thus absent in unlabeled networks. In view of these differences between labeled and unlabeled ensembles, the question of which one should be used as a null model of different real-world networks cannot be ignored.

Any quantum computation consists of a sequence of unitary evolutions described by a finite set of Hamiltonians. When this set is taken to consist of only products of Pauli operators, we show that the minimal such set generating $\mathfrak{su}(2^N)$ contains $2N+1$ elements. We provide a number of examples of such generating sets and furthermore provide an algorithm for producing a sequence of rotations corresponding to any given Pauli rotation, which is shown to have optimal complexity. We also observe that certain sets generate $\mathfrak{su}(2^N)$ at a faster rate than others, and we show how this rate can be optimized by tuning the fraction of anticommuting pairs of generators. Finally, we briefly comment on implications for measurement-based and trapped ion quantum computation as well as the construction of fault-tolerant gate sets.

In quantum error correction, the Petz map serves as a perfect recovery map when the Knill-Laflamme conditions are satisfied. Notably, while perfect recovery is generally infeasible for most quantum channels of finite dimension, the Petz map remains a versatile tool with near-optimal performance in recovering quantum states. This work introduces and proves, for the first time, the necessary and sufficient conditions for the optimality of the Petz map in terms of entanglement fidelity. In some special cases, the violation of this condition can be easily characterized by a simple commutator that can be efficiently computed. We provide multiple examples that substantiate our new findings.

We present calculations of various electroweak response functions for the ${}^{16}\mathrm{O}$ nucleus obtained using coupled-cluster theory in conjunction with the Lorentz integral transform method. We employ nuclear forces derived at next-to-leading order and next-to-next-to-leading order in chiral effective field theory and perform a Bayesian analysis to assess uncertainties. Our results are in good agreement with available electron-scattering data at $|\mathbf{q}|\approx 326\mathrm{MeV}/\mathrm{c}$. Additionally, we provide several predictions for the weak response functions in the quasielastic peak region at $|\mathbf{q}|=300$ and $400\mathrm{MeV}/\mathrm{c}$, which are critical for long-baseline neutrino experiments.

Bound states in the continuum (BICs) are exceptional resonances with extremely high sensitivity and thus inherently fragile. Introducing topological concepts can fortify BICs against perturbations; however, existing topological BICs (TBICs) often rely on intricate strategies. Here, we explore the universality of TBICs governed by symmetry. Different symmetries naturally segregate wave states into uncoupled Hilbert subspaces, enabling independent topological band structure engineering in each subspace. This results in rich topological features, including TBICs, topological Fano resonance, and even exotic TBICs (eTBICs). Intriguingly, eTBICs inherit core attributes from both topological states and BICs, thereby exhibiting counterintuitive behavior—both strong immunity and high sensitivity. We conceptually and experimentally demonstrate this using an acoustic monolayer topological waveguide, uncovering exotic behavior in the transmission spectrum where the bulk is “muted” and the eTBIC is identified with extreme anisotropic sensitivity. Our findings may enrich the research implications of both topological physics and BICs.

Within the quantum networks scenario we introduce a single scheme allowing one to certify three different types of composite projective measurements acting on a three-qubit Hilbert space: one constructed from genuinely entangled GHZ-like states, one constructed from fully product vectors that exhibit the phenomenon of nonlocality without entanglement, and a hybrid measurement obtained from an unextendible product basis. Noticeably, we certify a basis exhibiting nonlocality without entanglement in the smallest dimension capable of supporting this phenomenon. On the other hand, the possibility of certification of a measurement obtained from an unextendible product basis has an interesting implication that one can also self-test a bound entangled state in the considered quantum network. Such a possibility does not seem to exist in the standard Bell scenario. Furthermore, we also analyze the robustness of our scheme toward experimental errors.

Massive scalar fields are promising candidates for addressing many unresolved problems in fundamental physics. We report the first model-agnostic Bayesian search of massive scalar fields that are nonminimally coupled to gravity in LIGO/Virgo/KAGRA gravitational-wave data. We find no evidence for such fields and place the most stringent upper limits on their coupling for scalar masses $\lesssim 2\times {10}^{-12}\mathrm{eV}$. We exemplify the strength of these bounds by applying them to massive scalar-Gauss-Bonnet gravity, finding the tightest constraints on the coupling constant to date, $\sqrt{{\alpha }_{\mathrm{GB}}}\lesssim 1\mathrm{km}$ for scalar masses $\lesssim {10}^{-13}\mathrm{eV}$ to 90% credible level.

Symmetry is crucial for gaining insights into the fundamental properties of physical systems, bringing possibilities in studying exotic phenomena such as quantum phase transitions and ground-state entanglement. Here, we experimentally simulate a highly controllable extended quantum Rabi model, capable of tuning into the ultrastrong or deep coupling regime, in a spin-motion-coupled trapped ion. We observe that the phonon driven by such a model with ${\mathbb{Z}}_2$ symmetry preserved (broken) would experience double (single) excitation in the ultrastrong coupling regime. Quantum phenomena such as strong ground-state entanglement and quantum superposition in systems occur with parity symmetry, and these phenomena disappear following the symmetry breaking. We also find sensitive responses for the two-level system entropy and phonon Wigner function in the deep coupling regime, depending on the parameter across the symmetry transition point. This Letter offers the prospect of exploring symmetry-controlled quantum phenomena and their applications in high-precision quantum technologies.

We have measured the critical current density, superconducting coherence length, and superconducting transition temperature of single-domain, epitaxially grown $\mathrm{Nb}(110)/\mathrm{Au}(111)/\mathrm{Nb}(110)$ trilayers, all of which show a nonmonotonic dependence on the thickness of the Au layer. These results are compared with the predictions of a relativistic, ab initio theory, which incorporates superconducting correlations. We find good agreement with experiment, coming from a rich interplay between superconducting proximity and quantum size effects, mediated by Andreev bound states. These results suggest that quantum size effects could provide a systematic method of controlling the transport properties of superconducting multilayers.

Through laser-heated diamond anvil cell experiments, we synthesize a series of rubidium superhydrides and explore their properties with synchrotron x-ray powder diffraction and Raman spectroscopy measurements, combined with density functional theory calculations. Upon heating rubidium monohydride embedded in ${\mathrm{H}}_2$ at a pressure of 18 GPa, we form ${\mathrm{RbH}}_9\text{−}\mathrm{I}$, which is stable upon decompression down to 8.7 GPa, the lowest stability pressure of any known superhydride. At 22 GPa, another polymorph, ${\mathrm{RbH}}_9\text{−}\mathrm{II}$ is synthesised at high temperature. Unique to the Rb-H system among binary metal hydrides is that further compression does not promote the formation of polyhydrides with higher hydrogen content. Instead, heating above 87 GPa yields ${\mathrm{RbH}}_5$, which exhibits two polymorphs (${\mathrm{RbH}}_5\text{−}\mathrm{I}$ and ${\mathrm{RbH}}_5\text{−}\mathrm{II}$). All of the crystal structures comprise a complex network of quasimolecular ${\mathrm{H}}_2$ units and ${\mathrm{H}}^{-}$ anions, with ${\mathrm{RbH}}_5$ providing the first experimental evidence of linear ${\mathrm{H}}_3^{-}$ anions.

The phase diagram of the $S=1/2$ easy-axis triangular-lattice $J_1\text{−}{J}_2$ model is investigated using the density-matrix renormalization group and analytical insights. We find a significant spin-liquid region extending from the Heisenberg limit and residing between the Y phase—known as the magnetic analogue of the “supersolid”—and collinear stripe phase. The order parameters of the supersolid are analyzed and an understanding of its lack of a ferromagnetic moment is suggested.

Altermagnets are magnetic materials with antiferromagnetic spin ordering but exhibit ferromagnetic properties. Understanding the microscopic origin of the latter is a central problem. Ferromagnetlike properties such as the anomalous Hall effect are linked with weak ferromagnetism, whose microscopic origin in altermagnets remains unclear however. We show theoretically that the alternating $g$-tensor anisotropy in altermagnets can induce weak orbital ferromagnetism even when the Dzyaloshinskii-Moriya interaction is forbidden. We demonstrate this mechanism to explain weak ferromagnetism for both collinear and noncollinear spin altermagnets. Our findings provide new insights into the origin of weak ferromagnetism and suggest orbital-based ways for manipulating magnetic configurations in altermagnets.

We investigated the infrared-active phonons in ferromagnetic Weyl semimetal ${\mathrm{Co}}_3{\text{Sn}}_2{\mathrm{S}}_2$ using optical spectroscopy. Below the Curie temperature ($T_C\approx 175\mathrm{K}$), we observed asymmetric Fano line shapes of phonons peaks in the optical conductivities, reflecting the presence of electron-phonon coupling. Additionally, the detected phonon signals by the polar Kerr rotation and the ellipticity spectroscopy indicate the circular dichroism (CD) of phonons. We attribute the CD of phonons to their distinct couplings with charge excitations on the tilted Weyl nodal rings in two circularly polarized channels. Our findings provide experimental evidence that, without external fields, phonons can also become circularly polarized by coupling with the electronic topology. Since the magnetic exchange splitting gradually shifts the topological bands in ${\mathrm{Co}}_3{\text{Sn}}_2{\mathrm{S}}_2$, the CD of phonons exhibits significant temperature dependence, hinting at a promising approach for manipulation.

Chiral phonons are vibrational modes in a crystal that possess a well-defined handedness or chirality, typically found in materials that lack inversion symmetry. Here, we report the discovery of chiral phonon modes in the kagome ferromagnetic Weyl semimetal ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$, a material that preserves inversion symmetry but breaks time-reversal symmetry. Using helicity-resolved magneto-Raman spectroscopy, we observe the spontaneous splitting of the doubly degenerate in-plane $E_g$ modes into two distinct chiral phonon modes of opposite helicity when the sample is zero-field cooled below the Curie temperature in the absence of an external magnetic field. As we sweep the out-of-plane magnetic field, this $E_g$ phonon splitting exhibits a well-defined hysteresis loop directly correlated with the material’s magnetization. The observed spontaneous splitting reaches up to $1.27{\mathrm{cm}}^{-1}$ at low temperatures, progressively diminishes with increasing temperature, and completely vanishes near the Curie temperature. Our findings highlight the role of the magnetic order in inducing chiral phonons, paving the way for novel methods to manipulate chiral phonons through magnetization and vice versa. Additionally, our Letter introduces new possibilities for controlling chiral Weyl fermions using chiral phonons.

The concept of spin symmetries has gained renewed interest as a valuable tool for classifying unconventional magnetic phases, including altermagnets and recently identified $p$-wave magnets. In this work, we show that in compounds with weak spin-orbit coupling, the dominant spin and charge photoresponse is determined by spin group rather than the conventional magnetic group symmetry. As a concrete realization we consider the nonlinear shift photocurrent in ${\mathrm{Mn}}_5{\mathrm{Si}}_3$, a material that features the two possible classes of unconventional $p$-wave magnetism in the form of two competing spin structures, a coplanar and noncoplanar one. While both are predicted to generate shift currents based on magnetic symmetry considerations, only the noncoplanar configuration survives the spin symmetry requirements. This is numerically confirmed by our ab initio calculations, providing a protocol to experimentally identify the spin configuration of this promising material in photogalvanic or transport measurements.

The persistence exponent, which characterizes the long-time decay of the survival probability of stochastic processes in the presence of an absorbing target, plays a key role in quantifying the dynamics of fluctuating systems. Determining this exponent for non-Markovian processes is known to be a difficult task, and exact results remain scarce despite sustained efforts. In this Letter, we consider the fundamental class of self-interacting random walks (SIRWs), which display long-range memory effects that result from the interaction of the random walker at time $t$ with the territory already visited at earlier times $t^{\prime }<t$. We compute exactly the persistence exponent for all physically relevant SIRWs. As a byproduct, we also determine the splitting probability of these processes. Besides their intrinsic theoretical interest, these results provide a quantitative characterization of the exploration process of SIRWs, which are involved in fields as diverse as foraging theory, cell biology, and nonreversible Monte Carlo methods.

The celebrated Ott-Antonsen Ansatz for coupled oscillators provides a useful framework for working with deterministic systems in the thermodynamic limit, but it fails to capture many features of stochastic systems. Several solutions have been recently proposed to accurately describe the behavior of the order parameters in coupled oscillator systems. However, a fluctuating description of such order parameters has been still elusive. In this Letter, I construct for the first time a general mesoscopic description of finite-size populations of oscillators subject to white noise. The theory allows one to derive Langevin equations for the Kuramoto-Daido order parameters, opening the door to study features of synchronization phase transitions and finite-size effects, which were inaccessible before. The analysis of the fluctuations in the stochastic Kuramoto model uncovered highly accurate, closed analytical expressions for the average Kuramoto order parameter which outperforms previous approaches.

Quantifying the minimum entanglement needed to prepare quantum states and implement quantum processes is a key challenge in quantum information theory. In this Letter, we develop computable and faithful lower bounds on the entanglement cost under quantum operations that completely preserve the positivity of partial transpose (PPT operations), by introducing the generalized divergence of $k$-negativity, a generalization of logarithmic negativity. Our bounds are efficiently computable via semidefinite programming and provide nontrivial values for all states that are non-PPT (NPT), establishing their faithfulness for the resource theory of NPT entanglement. Notably, we find and affirm the irreversibility of asymptotic entanglement manipulation under PPT operations for full-rank entangled states. Furthermore, we extend our methodology to derive lower bounds on the entanglement cost of both point-to-point and bipartite quantum channels. Our bound demonstrates improvements over previously known computable bounds for a wide range of quantum states and channels. These findings push the boundaries of understanding the structure of entanglement and the fundamental limits of entanglement manipulation.