Topologically ordered phases of matter, although stable against local perturbations, are usually restricted to relatively small regions in phase diagrams. Thus, their preparation requires a precise fine-tunning of the system’s parameters, a very challenging task in most experimental setups. In this work, we investigate a model of spinless fermions interacting with dynamical ${\mathbb{Z}}_2$ gauge fields on a cross-linked ladder and show evidence of topological order throughout the full parameter space. In particular, we show how a magnetic flux is spontaneously generated through the ladder due to an Aharonov-Bohm instability, giving rise to topological order even in the absence of a plaquette term. Moreover, the latter coexists here with a symmetry-protected topological phase in the matter sector, which displays fractionalized gauge-matter edge states and intertwines with it by a flux-threading phenomenon. Finally, we unveil the robustness of these features through a gauge frustration mechanism, akin to geometric frustration in spin liquids, allowing topological order to survive to arbitrarily large quantum fluctuations. In particular, we show how, at finite chemical potential, topological solitons are created in the gauge field configuration, which bound to fermions and form ${\mathbb{Z}}_2$ deconfined quasiparticles. The simplicity of the model makes it an ideal candidate for 2D gauge theory phenomena, as well as exotic topological effects, to be investigated using cold-atom quantum simulators.

Recent studies on superconductivity in ${\mathrm{NbSe}}_2$ have demonstrated a large anisotropy in the superconducting critical field when the material is reduced to a single monolayer. Motivated by this recent discovery, we use density-functional theory (DFT) calculations to quantitatively address the superconducting properties of bulk and monolayer ${\mathrm{NbSe}}_2$. We demonstrate that ${\mathrm{NbSe}}_2$ is close to a ferromagnetic instability, and analyze our results in the context of experimental measurements of the spin susceptibility in ${\mathrm{NbSe}}_2$. We show how this magnetic instability, which is pronounced in a single monolayer, can enable sizable singlet-triplet mixing of the superconducting order parameter, contrary to contemporary considerations of the pairing symmetry in monolayer ${\mathrm{NbSe}}_2$, and discuss approaches as to how this degree of mixing can be addressed quantitatively within our DFT framework. Our calculations also enable a quantitative description of the large anisotropy of the superconducting critical field, using DFT calculations of monolayer ${\mathrm{NbSe}}_2$ in the normal state.

The predominant Ni-multiorbital nature of infinite-layer neodynium nickelate at stoichiometry and with doping is revealed. We investigate the correlated electronic structure of ${\mathrm{NdNiO}}_2$ at lower temperatures and show that first-principles many-body theory may account for Kondo(-lattice) features. Yet, those features are not only based on localized $\mathrm{Ni}\text{−}{d}_{x^2-y^2}$ and a Nd-dominated self-doping band, but they heavily build on the participation of $\mathrm{Ni}\text{−}{d}_{z^2}$ in a Hund-assisted manner. In a tailored three-orbital study, the half-filled regime of the former in-plane Ni orbital remains surprisingly robust even for substantial hole doping $\delta$. Reconstructions of the interacting Fermi surface designate the superconducting region within the experimental phase diagram. Furthermore, they provide clues to recent Hall measurements, as well as to the astounding weakly insulating behavior at larger experimental $\delta$. Finally, a strong asymmetry between electron and hole doping, with a revival of Ni single-orbital features in the former case, is predicted. Unlike cuprates, superconductivity in ${\mathrm{Nd}}_{1-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_2$ is of distinct multiorbital kind, building up on nearly localized $\mathrm{Ni}\text{−}{d}_{x^2-y^2}$ and itinerant $\mathrm{Ni}\text{−}{d}_{z^2}$.

A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod-kagome lattice material ${\mathrm{Ho}}_3{\mathrm{Mg}}_2{\mathrm{Sb}}_3{\mathrm{O}}_{14}$ unites an icelike magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the ${\mathrm{Ho}}^{3+}$ ground-state doublet, which is further coupled to a nuclear spin bath. Using neutron scattering and thermodynamic experiments, we observe a symmetry-breaking transition at $T^{*}\approx 0.32\mathrm{K}$ to a remarkable state with three peculiarities: a concurrent recovery of magnetic entropy associated with the strongly coupled electronic and nuclear degrees of freedom; a fragmentation of the spin into periodic and icelike components; and persistent inelastic magnetic excitations down to $T\approx 0.12\mathrm{K}$. These observations deviate from expectations of classical spin fragmentation on a kagome lattice, but can be understood within a model of dipolar kagome ice under a homogeneous transverse magnetic field, which we survey with exact diagonalization on small clusters and mean-field calculations. In ${\mathrm{Ho}}_3{\mathrm{Mg}}_2{\mathrm{Sb}}_3{\mathrm{O}}_{14}$, hyperfine interactions dramatically alter the single-ion and collective properties, and suppress possible quantum correlations, rendering the fragmentation with predominantly single-ion quantum fluctuations. Our results highlight the crucial role played by hyperfine interactions in frustrated quantum magnets and motivate further investigations of the role of quantum fluctuations on partially ordered magnetic states.

In certain analytically tractable quantum chaotic systems, the calculation of out-of-time-order correlation functions, entanglement entropies after a quench, and other related dynamical observables reduces to an effective theory of an “entanglement membrane” in spacetime. These tractable systems involve an average over random local unitaries defining the dynamical evolution. We show here how to make sense of this membrane in more realistic models, which do not involve an average over random unitaries. Our approach relies on introducing effective pairing degrees of freedom in spacetime, describing a pairing of forward and backward Feynman trajectories, inspired by the structure emerging in random unitary circuits. This viewpoint provides a framework for applying ideas of coarse graining to dynamical quantities in chaotic systems. We apply the approach to some translationally invariant Floquet spin chains studied in the literature. We show that a consistent line tension may be defined for the entanglement membrane and that there are qualitative differences in this tension between generic models and “dual-unitary” circuits. These results allow scaling pictures for out-of-time-order correlators and for entanglement to be taken over from random circuits to nonrandom Floquet models. We also provide an efficient numerical algorithm for determining the entanglement line tension in $1+1\mathrm{D}$.

In one-dimensional (1D) metallic systems, the diverging electron susceptibility and electron-phonon coupling collaboratively drive the electrons into a charge density wave (CDW) state. However, a strictly 1D system is unstable against perturbations, whose effect on CDW order requires clarification ideally with altered coupling to surroundings. Here, we fabricate such a system with nanowires of ${\mathrm{Mo}}_6{\mathrm{Se}}_6$ bundles, which are either attached to edges of monolayer ${\mathrm{MoSe}}_2$ or isolated freely, by postannealing the preformed ${\mathrm{MoSe}}_2$. Using scanning tunneling microscopy, we visualize charge modulations and CDW gaps with prominent coherent peaks in the edge-attached nanowires. Astonishingly, the CDW order becomes suppressed in the isolated nanowires, showing CDW correlation gaps without coherent peaks. The contrasting behavior, as revealed with theoretical modeling, is interpreted as the effect of phason polarons on the 1D CDW state. Our work elucidates a possibly unprecedented many-body effect that may be generic to strictly 1D system but undermined in a quasi-1D system.

Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and they require solving the grand-challenge problem of the many-electron Schrödinger equation. An infinite chain of equispaced hydrogen atoms is perhaps the simplest realistic model for a bulk material, embodying several central themes of modern condensed-matter physics and chemistry while retaining a connection to the paradigmatic Hubbard model. Here, we report a combined application of cutting-edge computational methods to determine the properties of the hydrogen chain in its quantum-mechanical ground state. Varying the separation between the nuclei leads to a rich phase diagram, including a Mott phase with quasi-long-range antiferromagnetic order, electron density dimerization with power-law correlations, an insulator-to-metal transition, and an intricate set of intertwined magnetic orders.

Direct detection of single photons at wavelengths beyond $2\mu \mathrm{m}$ under ambient conditions remains an outstanding technological challenge. One promising approach is frequency upconversion into the visible (VIS) or near-infrared (NIR) domain, where single-photon detectors are readily available. Here, we propose a nanoscale solution based on a molecular optomechanical platform to up-convert photons from the far- and mid-infrared (covering part of the terahertz gap) into the VIS-NIR domain. We perform a detailed analysis of its outgoing noise spectral density and conversion efficiency with a full quantum model. Our platform consists in doubly resonant nanoantennas focusing both the incoming long-wavelength radiation and the short-wavelength pump laser field into the same active region. There, infrared active vibrational modes are resonantly excited and couple through their Raman polarizability to the pump field. This optomechanical interaction is enhanced by the antenna and leads to the coherent transfer of the incoming low-frequency signal onto the anti-Stokes sideband of the pump laser. Our calculations demonstrate that our scheme is realizable with current technology and that optimized platforms can reach single-photon sensitivity in a spectral region where this capability remains unavailable to date.

The classification and lattice model construction of symmetry-protected topological (SPT) phases in interacting fermion systems are very interesting but challenging. In this paper, we give a systematic fixed-point wave function construction of fermionic SPT (FSPT) states for generic fermionic symmetry group $G_f={\mathbb{Z}}_2^f{\times }_{{\omega }_2}{G}_b$ which is a central extension of bosonic symmetry group $G_b$ (may contain time-reversal symmetry) by the fermion parity symmetry group ${\mathbb{Z}}_2^f=\{1,P_f\}$. Our construction is based on the concept of an equivalence class of finite-depth fermionic symmetric local unitary transformations and decorating symmetry domain wall picture, subjected to certain obstructions. We also discuss the systematical construction and classification of boundary anomalous SPT states which leads to a trivialization of the corresponding bulk FSPT states. Thus, we conjecture that the obstruction-free and trivialization-free constructions naturally lead to a classification of FSPT phases. Each fixed-point wave function admits an exactly solvable commuting-projector Hamiltonian. We believe that our classification scheme can be generalized to point and space group symmetry as well as continuum Lie group symmetry.

We present the first experimental determination of the intra-atomic exchange energy between the inner $4f$ and the outer $6s5d$ shells in rare-earth elements. Inelastic electron tunneling spectroscopy on individual rare-earth atoms adsorbed on metal-supported graphene reveals an element-dependent excitation, with energy between 30 and 170 meV, linearly increasing with the spin angular momentum of the $4f$ shell. This observation is possible owing to the strong spin polarization of the outer shells, characteristic of rare-earth adatoms on graphene. This polarization gives rise to a giant magnetoresistance of up to 75% observed for Dy on $\mathrm{graphene}/\mathrm{Ir}(111)$ single-atom magnets. Density functional theory calculations of the $6s5d$ shell spin polarizations and of their intra-atomic exchange constants with the $4f$ shell yield exchange energies in agreement with the experimental values. These results prove that the description of the spin dynamics in RE considering only the $4f-5d$ interaction is oversimplified. A more realistic treatment requires us to consider a multishell intra-atomic exchange in which both $6s$ and $5d$ shells are taken into account, with the $4f-6s$ contribution possibly prevailing over the $4f-5d$ one. Our findings are important for the general understanding of magnetism in rare earths, whether they are in bulk compounds or as surface adsorbed atoms and clusters. The results presented here also push for a revision of the description of the spin dynamics in rare-earth-based systems.

We study the effects of finite temperature on normal state properties of a metal near a quantum critical point to an antiferromagnetic or Ising-nematic state. At $T=0$, bosonic and fermionic self-energies are traditionally computed within Eliashberg theory, and they obey scaling relations with characteristic power laws. Corrections to Eliashberg theory break these power laws but only at very small frequencies. Quantum Monte Carlo (QMC) simulations have shown that, already at much larger frequencies, there are strong systematic deviations from these predictions, casting doubt on the validity of the theoretical analysis. We extend Eliashberg theory to finite $T$ and argue that in the $T$ range accessible in the QMC simulations above the superconducting transition, the scaling forms for both fermionic and bosonic self-energies are quite different from those at $T=0$. We compare finite $T$ results with QMC data and find good agreement for both systems. We argue that this agreement resolves the key apparent contradiction between the theory and the QMC simulations.

Hund metals have attracted attention in recent years due to their unconventional superconductivity, which supposedly originates from non-Fermi-liquid (NFL) properties of the normal state. When studying Hund metals using dynamical mean-field theory, one arrives at a self-consistent “Hund impurity problem” involving a multiorbital quantum impurity with nonzero Hund coupling interacting with a metallic bath. If its spin and orbital degrees of freedom are screened at different energy scales, $T_{\mathrm{sp}}<T_{\text{orb}}$, the intermediate energy window is governed by a novel NFL fixed point, whose nature had not yet been clarified. We resolve this problem by providing an analytical solution of a paradigmatic example of a Hund impurity problem, involving two spin and three orbital degrees of freedom. To this end, we combine a state-of-the-art implementation of the numerical renormalization group, capable of exploiting non-Abelian symmetries, with a generalization of Affleck and Ludwig’s conformal field theory (CFT) approach for multichannel Kondo models. We characterize the NFL fixed point of Hund metals in detail for a Kondo model with an impurity forming an $\mathrm{SU}(2)\times \mathrm{SU}(3)$ spin-orbital multiplet, tuned such that the NFL energy window is very wide. The impurity’s spin and orbital susceptibilities then exhibit striking power-law behavior, which we explain using CFT arguments. We find excellent agreement between CFT predictions and numerical renormalization group results. Our main physical conclusion is that the regime of spin-orbital separation, where orbital degrees of freedom have been screened but spin degrees of freedom have not, features anomalously strong local spin fluctuations: the impurity susceptibility increases as ${\chi }_{\mathrm{sp}}^{\text{imp}}\sim {\omega }^{-\gamma }$, with $\gamma >1$.

We report a probable observation of the dc Josephson effect in mesoscopic junctions of three and four superconductors. The devices are fabricated in a top-down fashion from a hybrid semiconductor-superconductor $\mathrm{InAs}/\mathrm{Al}$ epitaxial heterostructure. In general, the critical current of an $N$-terminal junction is an ($N-1$)-dimensional hypersurface in the space of bias currents, which can be reduced to a set of critical current contours. The geometry of critical current contours exhibits nontrivial responses to electrical gating, magnetic field, and phase bias, and it can be reproduced by the scattering formulation of the Josephson effect generalized to the case of $N>2$. Besides establishing solid ground beneath a host of recent theory proposals, our experiment accomplishes an important step toward creating trijunctions of topological superconductors, essential for braiding operations.

Ultrafast phase transitions induced by femtosecond light pulses present a new opportunity for manipulating the properties of materials. Understanding how these transient states are different from, or similar to, their thermal counterparts is key to determining how materials can exhibit properties that are not found in equilibrium. In this paper, we reexamine the case of the light-induced insulator-metal phase transition in the prototypical, strongly correlated material ${\mathrm{VO}}_2$, for which a nonthermal Mott-Hubbard transition has been claimed. Here, we show that heat, even on the ultrafast timescale, plays a key role in the phase transition. When heating is properly accounted for, we find a single phase-transition threshold corresponding to the thermodynamic structural insulator-metal phase transition, and we find no evidence of a hidden transient Mott-Hubbard nonthermal phase. The interplay between the initial thermal state and the ultrafast transition may have implications for other transient states of matter.

The Jahn-Teller effect is one of the most fundamental phenomena important not only for physics but also for chemistry and material science. Solving the Jahn-Teller problem and taking into account strong electron correlations we show that quantum entanglement of the spin and orbital degrees of freedom via spin-orbit coupling strongly affects this effect. Depending on the number of $d$ electrons, it may quench (electronic configurations $t_{2g}^2$, $t_{2g}^4$, and $t_{2g}^5$), partially suppress ($t_{2g}^1$), or, in contrast, induce ($t_{2g}^3$) Jahn-Teller distortions. Moreover, in certain situations, interplay between the Jahn-Teller effect and spin-orbit coupling promotes formation of the “Mexican hat” energy surface facilitating various quantum phenomena.

The spectral gap problem—determining whether the energy spectrum of a system has an energy gap above ground state, or if there is a continuous range of low-energy excitations—pervades quantum many-body physics. Recently, this important problem was shown to be undecidable for quantum-spin systems in two (or more) spatial dimensions: There exists no algorithm that determines in general whether a system is gapped or gapless, a result which has many unexpected consequences for the physics of such systems. However, there are many indications that one-dimensional spin systems are simpler than their higher-dimensional counterparts: For example, they cannot have thermal phase transitions or topological order, and there exist highly effective numerical algorithms such as the density matrix renormalization group—and even provably polynomial-time ones—for gapped 1D systems, exploiting the fact that such systems obey an entropy area law. Furthermore, the spectral gap undecidability construction crucially relied on aperiodic tilings, which are not possible in 1D. So does the spectral gap problem become decidable in 1D? In this paper, we prove this is not the case by constructing a family of 1D spin chains with translationally invariant nearest-neighbor interactions for which no algorithm can determine the presence of a spectral gap. This not only proves that the spectral gap of 1D systems is just as intractable as in higher dimensions, but it also predicts the existence of qualitatively new types of complex physics in 1D spin chains. In particular, it implies there are 1D systems with a constant spectral gap and nondegenerate classical ground state for all systems sizes up to an uncomputably large size, whereupon they switch to a gapless behavior with dense spectrum.

We study the energy and entanglement dynamics of $(1+1)\mathrm{D}$ conformal field theories (CFTs) under a Floquet drive with the sine-square deformed (SSD) Hamiltonian. Previous work has shown that this model supports both a nonheating and a heating phase. Here, we analytically establish several robust and “superuniversal” features of the heating phase which rely on conformal invariance but not on the details of the CFT involved. First, we show the energy density is concentrated in two peaks in real space, a chiral and an antichiral peak, which leads to an exponential growth in the total energy. The peak locations are set by fixed points of the Möbius transformation. Second, all of the quantum entanglement is shared between these two peaks. In each driving period, a number of Bell pairs are generated, with one member pumped to the chiral peak and the other member pumped to the antichiral peak. These Bell pairs are localized, accumulate at these two peaks, and can serve as a source of quantum entanglement. Third, in both the heating and nonheating phases, we find that the total energy is related to the half system entanglement entropy by a simple relation $E(t)\propto c\exp [(6/c)S(t)]$ with $c$ being the central charge. In addition, we show that the nonheating phase, in which the energy and entanglement oscillate in time, is unstable to small fluctuations of the driving frequency in contrast to the heating phase. Finally, we point out an analogy to the periodically driven harmonic oscillator which allows us to understand global features of the phases and introduce a quasiparticle picture to explain the spatial structure, which can be generalized to setups beyond the SSD construction.

The high kinetic inductance offered by granular aluminum (grAl) has recently been employed for linear inductors in superconducting high-impedance qubits and kinetic inductance detectors. Because of its large critical current density compared to typical Josephson junctions, its resilience to external magnetic fields, and its low dissipation, grAl may also provide a robust source of nonlinearity for strongly driven quantum circuits, topological superconductivity, and hybrid systems. Having said that, can the grAl nonlinearity be sufficient to build a qubit? Here we show that a small grAl volume ($10\times 200\times 500{\mathrm{nm}}^3$) shunted by a thin film aluminum capacitor results in a microwave oscillator with anharmonicity $\alpha$ two orders of magnitude larger than its spectral linewidth ${\mathrm{\Gamma }}_{01}$, effectively forming a transmon qubit. With increasing drive power, we observe several multiphoton transitions starting from the ground state, from which we extract $\alpha =2\pi \times 4.48\mathrm{MHz}$. Resonance fluorescence measurements of the $|0⟩\to |1⟩$ transition yield an intrinsic qubit linewidth $\gamma =2\pi \times 10\mathrm{kHz}$, corresponding to a lifetime of $16\mu \mathrm{s}$, as confirmed by pulsed time-domain measurements. This linewidth remains below $2\pi \times 150\mathrm{kHz}$ for in-plane magnetic fields up to $\sim 70\mathrm{mT}$.

The properties of organic conductors are often tuned by the application of chemical or external pressure, which change orbital overlaps and electronic bandwidths while leaving the molecular building blocks virtually unperturbed. Here, we show that, unlike any other method, light can be used to manipulate the local electronic properties at the molecular sites, giving rise to new emergent properties. Targeted molecular excitations in the charge-transfer salt $\kappa \text{−}{(\mathrm{BEDT}-\mathrm{TTF})}_2\mathrm{Cu}[\mathrm{N}{(\mathrm{CN})}_2]\mathrm{Br}$ induce a colossal increase in carrier mobility and the opening of a superconducting optical gap. Both features track the density of quasiparticles of the equilibrium metal and can be observed up to a characteristic coherence temperature $T^{*}\simeq 50\mathrm{K}$, far higher than the equilibrium transition temperature $T_{\mathit{C}}=12.5\mathrm{K}$. Notably, the large optical gap achieved by photoexcitation is not observed in the equilibrium superconductor, pointing to a light-induced state that is different from that obtained by cooling. First-principles calculations and model Hamiltonian dynamics predict a transient state with long-range pairing correlations, providing a possible physical scenario for photomolecular superconductivity.

We show that any Sachdev-Ye-Kitaev- (SYK) like model with finite-body interactions among local degrees of freedom, e.g., bosons or spins, has a fundamental difference from the standard fermionic model: The former model fails to be described by an annealed free energy at low temperature. In this respect, such models more closely resemble spin glasses. We demonstrate this by two means: first, a general theorem proving that the annealed free energy is divergent at low temperature in any model with a tensor product Hilbert space, and second, a replica treatment of two prominent examples which exhibit phase transitions from an “annealed” phase to a “nonannealed” phase as a function of the temperature. We further show that this effect appears only at $O(N)$th order in a $1/N$ expansion, even though lower-order terms misleadingly seem to converge. Our results prove that the nonbosonic nature of the particles in the SYK model is an essential ingredient for its physics, highlight connections between local models and spin glasses, and raise important questions as to the role of fermions and/or glassiness in holography.