Understanding and protecting the coherence of individual quantum systems is a central challenge in quantum science and technology. Over the past decades, a rich variety of methods to extend coherence have been developed. A complementary approach is to look for naturally occurring systems that are inherently protected against decoherence. Here, we show that pairs of identical nuclear spins in solids form intrinsically long-lived qubits. We study three carbon-13 pairs in diamond and realize high-fidelity measurements of their quantum states using a single nitrogen-vacancy center in their vicinity. We then reveal that the spin pairs are robust to external perturbations due to a combination of three phenomena: a decoherence-free subspace, a clock transition, and a variant on motional narrowing. The resulting inhomogeneous dephasing time is $T_2^{*}=1.9(3)\min$, the longest reported for individually controlled qubits. Finally, we develop complete control and realize an entangled state between two spin pairs through projective parity measurements. These long-lived qubits are abundantly present in diamond and other solids and provide new opportunities for ancilla-enhanced quantum sensing and for robust memory qubits for quantum networks.

We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multiscale entanglement renormalization Ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than ${10}^4$ parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for the 1D and 2D Heisenberg and 1D Fermi-Hubbard models. We find quantum circuit tensor networks to be substantially more expressive than other quantum circuits for these problems, and that they can even be more compact than standard tensor networks. Extrapolating to circuit depths which can no longer be emulated classically, this suggests a region of advantage in quantum expressiveness in the representation of physical ground states.

Quantum embedding methods have become powerful tools to overcome the deficiencies of traditional quantum modeling in materials science. However, while these are systematically improvable in principle, in practice it is rarely possible to achieve rigorous convergence and often necessary to employ empirical parameters. Here, we formulate a quantum embedding theory, building on the methods of density-matrix embedding theory combined with local correlation approaches from quantum chemistry, to ensure the ability to systematically converge properties of real materials with accurate correlated wave-function methods controlled by a single, rapidly convergent parameter. By expanding supercell size, basis set, and the resolution of the fluctuation space of an embedded fragment, we show that the systematic improvability of the approach yields accurate structural and electronic properties of realistic solids without empirical parameters, even across changes in geometry. The results are presented in insulating, semimetallic, and more strongly correlated regimes, finding state-of-the-art agreement with experimental data.

The extension of many-body quantum dynamics to the nonunitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time, on one hand, and unitarity and nonunitarity, on the other, can be used to realize steady-state phases of nonunitary dynamics that exhibit a rich variety of behavior in their entanglement scaling with subsystem size—from logarithmic to extensive to fractal. We show how these outcomes in nonunitary circuits (that are “spacetime dual” to unitary circuits) relate to the growth of entanglement in time in the corresponding unitary circuits, and how they differ, through an exact mapping to a problem of unitary evolution with boundary decoherence, in which information gets “radiated away” from one edge of the system. In spacetime duals of chaotic unitary circuits, this mapping allows us to analytically derive a nonthermal volume-law entangled phase with a universal logarithmic correction to the entropy, previously observed in unitary-measurement dynamics. Notably, we also find robust steady-state phases with fractal entanglement scaling, $S(\ell )\sim {\ell }^{\alpha }$ with tunable $0<\alpha <1$ for subsystems of size $\ell$ in one dimension. We present an experimental protocol for preparing these novel steady states with only a vanishing density of postselected measurements via a type of “teleportation” between spacelike and timelike slices of quantum circuits.

Many two-dimensional physical systems ranging from atomic-molecular condensates to low-dimensional superconductors and liquid-crystal films are described by coupled XY models. The interplay of topology and competing interactions in these XY systems drives new kinds of emergent behavior relevant in both quantum and classical settings. Such coupled U(1) systems further introduce rich physics, bringing topology into contact with fractionalization and deconfinement. Motivated by a hidden-order phase transition in isotropic liquid-crystal 54COOBC films, we study the finite-temperature phase diagram of a minimalist hexatic-nematic XY model. We identify a small region of composite Potts order above the vortex-binding transition; this phase is characterized by relative hexatic-nematic ordering though both variables are disordered. We propose that the Potts order results from a confinement of fractional vortices into extended nematic defects and discuss the broader implications of fractional vortices and composite ordering in the wider class of coupled XY condensates.

We report measurements of the Seebeck effect in both the $ab$ plane ($S_a$) and along the $c$ axis ($S_c$) of the cuprate superconductor ${\mathrm{La}}_{1.6-x}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (Nd-LSCO), performed in magnetic fields large enough to suppress superconductivity down to low temperature. We use the Seebeck coefficient as a probe of the particle-hole asymmetry of the electronic structure across the pseudogap critical doping $p^{\star }=0.23$. Outside the pseudogap phase, at $p=0.24>p^{\star }$, we observe a positive and essentially isotropic Seebeck coefficient as $T\to 0$. That $S>0$ at $p=0.24$ is at odds with expectations given the electronic band structure of Nd-LSCO above $p^{\star }$ and its known electronlike Fermi surface. We can reconcile this observation by invoking an energy-dependent scattering rate with a particle-hole asymmetry, possibly rooted in the non-Fermi-liquid nature of cuprates just above $p^{\star }$. Inside the pseudogap phase, for $p<p^{\star }$, $S_a$ is seen to rise at low temperature as previously reported, consistent with the drop in carrier density $n$ from $n\simeq 1+p$ to $n\simeq p$ across $p^{\star }$ as inferred from other transport properties. In stark contrast, $S_c$ at low temperature becomes negative below $p^{\star }$, a novel signature of the pseudogap phase. The sudden drop in $S_c$ reveals a change in the electronic structure of Nd-LSCO upon crossing $p^{\star }$. We can exclude a profound change of the scattering across $p^{\star }$ and conclude that the change in the out-of-plane Seebeck coefficient originates from a transformation of the Fermi surface.

A particle in an Anderson-localized system, if launched in any direction, should, on average, return to its starting point and stay there. Despite the central role played by Anderson localization in the modern understanding of condensed matter, this “quantum boomerang” effect, an essential feature of the localized state, was only recently theoretically predicted. We report the experimental observation of the quantum boomerang effect. Using a degenerate gas and a phase-shifted pair of optical lattices, we not only confirm the predicted dependence of the boomerang effect on Floquet gauge but also elucidate the crucial role of initial-state symmetries. Highlighting the key role of localization, we observe that as stochastic kicking destroys dynamical localization, the quantum boomerang effect also disappears. Measured dynamics are in agreement with numerical models and with predictions of an analytical theory we present which clarifies the connection between time-reversal symmetry and boomerang dynamics. These results showcase a unique experimental probe of the underlying quantum nature of Anderson localized matter.

Recent theoretical studies inspired by experiments on the Kitaev magnet $\alpha \text{−}{\mathrm{RuCl}}_3$ highlight the nontrivial impact of phonons on the thermal Hall conductivity of chiral topological phases. Here, we introduce mixed mesoscopic-macroscopic devices that allow refined thermal-transport probes of non-Abelian spin liquids with Ising topological order. These devices feature a quantum-coherent region with quantized or negligible phonon conductance, flanked by macroscopic lobes that facilitate efficient thermalization between chiral Majorana edge modes and bulk phonons. We show that our devices enable (i) accurate determination of the quantized thermal Hall conductivity, (ii) identification of non-Abelian Ising anyons via the temperature dependence of the thermal conductance, and, most interestingly, (iii) single-anyon detection through heat-based anyon interferometry. Analogous results apply broadly to phonon-coupled chiral topological orders.

Topological materials have drawn increasing attention owing to their rich quantum properties, as highlighted by a large intrinsic anomalous Hall effect (AHE) in Weyl and nodal-line semimetals. However, the practical applications for topological electronics have been hampered by the difficulty in the external control of their band topology. Here, we demonstrate a magnetic-field-induced switching of band topology in $\alpha \text{−}{\mathrm{EuP}}_3$, a magnetic semimetal with a layered crystal structure derived from black phosphorus. When the magnetic field is applied perpendicular to the single mirror plane of the monoclinic structure, a giant AHE signal abruptly emerges at a certain threshold magnetization value, giving rise to a prominently large anomalous Hall angle of $|{\mathrm{\Theta }}_{\mathrm{AHE}}|\sim 20°$. On the other hand, when the magnetic field is applied along the interlayer direction, which breaks the mirror symmetry, the system shows a pronounced negative longitudinal magnetoresistance. Based on first-principles calculations and group-theoretic analysis, we show that such nontrivial anomalies in the magnetotransport properties are manifestations of two distinct topological phases: topological nodal-line and Weyl semimetals, respectively. Notably, the nodal-line structure is composed of bands with the same spin character and spans a wide energy range around the Fermi level. These topological phases are stabilized via the exchange coupling between localized $\mathrm{Eu}\text{−}4f$ moments and mobile carriers conducting through the phosphorus layers. Our findings provide a realistic solution for external manipulation of band topology, enriching the functional aspects of topological materials.

We experimentally study the emergence of microcanonical equilibrium states in the turbulent relaxation dynamics of a two-dimensional chiral vortex gas. Same-sign vortices are injected into a quasi-two-dimensional disk-shaped atomic Bose-Einstein condensate using a range of mechanical stirring protocols. The resulting long-time vortex distributions are found to be in excellent agreement with the mean-field Poisson Boltzmann equation for the system describing the microcanonical ensemble at fixed energy $\mathcal{H}$ and angular momentum $\mathcal{M}$. The equilibrium states are characterized by the corresponding thermodynamic variables of inverse temperature $\widehat{\beta }$ and rotation frequency $\widehat{\omega }$. We are able to realize equilibria spanning the full phase diagram of the vortex gas, including on-axis states near zero temperature, infinite temperature, and negative absolute temperatures. At sufficiently high energies, the system exhibits a symmetry-breaking transition, resulting in an off-axis equilibrium phase at negative absolute temperature that no longer shares the symmetry of the container. We introduce a point-vortex model with phenomenological damping and noise that is able to quantitatively reproduce the equilibration dynamics.

In the presence of both space and time reversal symmetries, an $s$-wave $A_{1g}$ superconducting state is usually topologically trivial. Here, we demonstrate that an exception can take place in a type of nonsymmorphic lattice structure. We specify the demonstration in a time reversal invariant system with a centrosymmetric space group $P4/nmm$, the symmetry that governs iron-based superconductors, by showing the existence of a second-order topological state protected by a mirror symmetry. The topological superconductivity is featured by $2\mathcal{Z}$ degenerate Dirac cones on the (10) edge and $\mathcal{Z}$ pairs of Majorana modes at the intersection between the (11) and $(1\overline{1})$ edges. The topological invariance and Fermi surface criterion for the topological state are provided. Moreover, we point out that the previously proposed $s$-wave state in iron-based superconductors, which features a sign-changed superconducting order parameter between two electron pockets, is such a topological state. Thus, these results not only open a new route to pursue topological superconductivity, but also establish a measurable quantity to settle one long-lasting debate on the pairing nature of iron-based superconductors.

There is growing interest in using ultrafast light pulses to drive functional materials into nonequilibrium states with novel properties. The conventional wisdom is that above-gap photoexcitation behaves similarly to raising the electronic temperature and lacks the desired selectivity in the final state. Here, we report a novel nonthermal lattice instability induced by ultrafast above-gap excitation in SnSe, a representative of the $IV-VI$ class of semiconductors that provides a rich platform for tuning material functionality with ultrafast pulses due to their multiple lattice instabilities. The new lattice instability is accompanied by a drastic softening of the lowest-frequency $A_g$ phonon. This mode has previously been identified as the soft mode in the thermally driven phase transition to a $Cmcm$ structure. However, by a quantitative reconstruction of the atomic displacements from time-resolved x-ray diffraction for multiple Bragg peaks and excitation densities, we show that ultrafast photoexcitation with near-infrared (1.55 eV) light induces a distortion toward a different structure with $Immm$ symmetry. The $Immm$ structure of SnSe is an orthorhombic distortion of the rocksalt structure and does not occur in equilibrium. Density functional theory calculations reveal that the photoinduced $Immm$ lattice instability arises from electron excitation from the Se $4p$- and Sn $5s$-derived bands deep below the Fermi level that cannot be excited thermally. The results have implications for optical control of the thermoelectric, ferroelectric, and topological properties of the monochalcogenides and related materials. More generally, the results emphasize the need for ultrafast structural probes to reveal distinct atomic-scale dynamics that are otherwise too subtle or invisible in conventional spectroscopies.

Giant and tunneling magnetoresistance are physical phenomena used for reading information in commercial spintronic devices. The effects rely on a conserved spin current passing between a reference and a sensing ferromagnetic electrode in a multilayer structure. Recently, we have proposed that these fundamental spintronic effects can be realized in unconventional collinear antiferromagnets with nonrelativistic alternating spin-momentum coupling. Here, we elaborate on the proposal by presenting archetype model mechanisms for the giant and tunneling magnetoresistance effects in multilayers composed of these unconventional collinear antiferromagnets. The models are based, respectively, on anisotropic and valley-dependent forms of the alternating spin-momentum coupling. Using first-principles calculations, we link these model mechanisms to real materials and predict an approximately 100% scale for the effects. We point out that, besides the giant or tunneling magnetoresistance detection, the alternating spin-momentum coupling can allow for magnetic excitation by the spin-transfer torque.

Resistive switching is of the key phenomena for applications such as nonvolatile memories or neuromorphic computing. ${\mathrm{V}}_3{\mathrm{O}}_5$, a compound of the vanadium oxide Magnéli series, is one of the rare materials to exhibit an insulator-metal transition above room temperature ($T_c\sim 415\mathrm{K}$). The switching mechanisms in this material are still not clear. Here, we demonstrate both static dc volatile resistive switching and fast oscillatory spiking regimes in ${\mathrm{V}}_3{\mathrm{O}}_5$ devices at room temperature (120 K below the phase transition temperature) by applying an electric field. We couple electrical measurements, operando optical imaging, and infrared measurements to track the reflectivity change and the temperature of a device during the resistive switching. We find that the resistive switching starts via thermal runaway deep in the insulating state and triggers the phase transition with the formation of a filament of the high-temperature phase. Furthermore, we capture optically and thermally the spiking oscillations that we link to the negative differential resistance regime and find the filament forms and dissolves via a periodic spatiotemporal instability that we describe by numerical simulations. Our studies play an important role in understanding the volatile resistive switching mechanisms and demonstrate that ${\mathrm{V}}_3{\mathrm{O}}_5$ can be a key vanadium oxide for neuromorphic computing.

Higgs and Goldstone modes, well known in high-energy physics, have been realized in a number of condensed matter physics contexts, including superconductivity and magnetism. The Goldstone-Higgs concept is also applicable to and gives rise to new insight on structural phase transitions. Here, we show that the Leggett mode, a collective mode observed in multiband superconductors, also has an analog in crystallographic phase transitions. Such structural Leggett modes can occur in the phase channel as in the original work of Leggett [Prog. Theor. Phys. 36, 901 (1966)]. That is, they are antiphase Goldstone modes (antiphasons). In addition, a new collective mode can also occur in the amplitude channel, an out-of phase (antiphase) Higgs mode, that should be observable in multiband superconductors as well. We illustrate the existence and properties of these structural Leggett modes using the example of the pyrochlore relaxor ferroelectric ${\mathrm{Cd}}_2{\mathrm{Nb}}_2{\mathrm{O}}_7$.

${\mathrm{CeRh}}_2{\mathrm{As}}_2$ has recently been reported to be a rare case of a multiphase unconventional superconductor close to a quantum critical point (QCP). Here, we present a comprehensive study of its normal-state properties and of the phase (I) below $T_0\approx 0.4\mathrm{K}$ which preempts superconductivity at $T_c=0.26\mathrm{K}$. The second-order phase transition at $T_0$ presents signatures in specific heat and thermal expansion but none in magnetization and ac susceptibility, indicating a nonmagnetic origin of phase I. In addition, an upturn of the in-plane resistivity at $T_0$ points to a gap opening at the Fermi level in the basal plane. Thermal expansion indicates a strong-positive-pressure dependence of $T_0$, $d{T}_0/dp=1.5\mathrm{K}/\mathrm{GPa}$, in contrast to the strong-negative-pressure coefficient observed for magnetic order in Ce-based Kondo lattices close to a QCP. Similarly, an in-plane magnetic field shifts $T_0$ to higher temperatures and transforms phase I into another nonmagnetic phase (II) through a first-order phase transition at about 9 T. Using renormalized band-structure calculations, we find that the Kondo effect ($T_K\approx 30\mathrm{K}$) leads to substantial mixing of the excited crystalline-electric-field states into the ground state. This allows quadrupolar degrees of freedom in the resulting heavy bands at the Fermi level which are prone to nesting. The huge sensitivity of the quadrupole moment on hybridization together with nesting causes an unprecedented case of phase transition into a quadrupole-density-wave state at a temperature $T_0\ll T_K$, which explains the nature of phases I and II.

In the local or itinerant extreme, magnetic excitations can be described by the Heisenberg model which treats electron spins as localized moments, or by the itinerant-electron model where the exchange interaction between electrons leads to unequal numbers of electrons with up and down spins. However, the nature of the magnetic excitations has been elusive when both local moments and itinerant electrons are present in the intermediate range. Using inelastic neutron scattering, we provide direct spectroscopic evidence on the coexistence of and interplay between local moments and itinerant electrons in a van der Waals metallic ferromagnet ${\mathrm{Fe}}_{2.72}{\mathrm{GeTe}}_2$, which can sustain tunable room-temperature ferromagnetism down to the monolayer limit. We find that there exist ferromagnetic spin-wave excitations dispersing from the zone center at low energies resulting from local moments and a columnlike broad continuum at the zone boundary at high energies up to over 100 meV resulting from itinerant electrons. Unlike the two-dimensional crystal structure, the low-energy mode exhibits a three-dimensional nature, and the high-energy mode also has an out-of-plane dependence. Both modes persist well above the Curie temperature of 160 K. Our neutron spectroscopic data reveal that the low-energy spin waves at 100 K are more coherent than those at 4 K, which is evidence of the weakening of the Kondo screening at high temperatures. These results unambiguously demonstrate the coexistence of local moments and itinerant electrons and the Kondo effect between these two components in ${\mathrm{Fe}}_{2.72}{\mathrm{GeTe}}_2$. Such behaviors are generally expected in heavy-fermion systems with heavy $f$ electrons but are rarely clearly observed in materials with light $d$ electrons. These findings shed light on the understanding of magnetism in transition-metal compounds.

Determination of the symmetry property of superconducting gaps has been a central issue in studies to understand the mechanisms of unconventional superconductivity. Although it is often difficult to completely achieve the aforementioned goal, the existence of superconducting nodes, one of the few important experimental signatures of unconventional superconductivity, plays a vital role in exploring the possibility of unconventional superconductivity. The interplay between superconducting nodes and topology has been actively investigated, and intensive research in the past decade has revealed various intriguing nodes out of the scope of the pioneering work to classify superconducting order parameters based on the point groups. However, a systematic and unified description of superconducting nodes for arbitrary symmetry settings is still elusive. In this paper, we develop a systematic framework to comprehensively classify superconducting nodes pinned to any line in momentum space. While most previous studies are based on the homotopy theory, our theory is on the basis of the symmetry-based analysis of band topology, which enables systematic diagnoses of nodes in all nonmagnetic and magnetic space groups. Furthermore, our framework can readily provide a highly effective scheme to detect nodes in a given superconductor by using density-functional theory and assuming symmetry properties of Cooper pairs (called pairing symmetries). There are two main advantages of our method. One is that, while the symmetry-indicator theory cannot be directly applied to systems violating compatibility conditions, our diagnostic scheme focuses on such systems, which results in a complement of the symmetry-indicator theory. The other is that, although our method does not predict any pairing symmetry itself, our framework can diagnose not only the positions but also the dimensions of nodes such as line or surface nodes, which can reduce candidates of pairing symmetries. We substantiate the power of our method through the time-reversal broken and noncentrosymmetric superconductor CaPtAs. Our work establishes a unified theory for understanding superconducting nodes and facilitates determining superconducting gaps in materials combined with experimental observations.

Angle-resolved photoemission spectroscopy (ARPES) is the most powerful technique to investigate the electronic band structure of crystalline solids. To completely characterize the electronic structure of topological materials, one needs to go beyond band structure mapping and access information about the momentum-resolved Bloch wave function, namely, orbitals, Berry curvature, and topological invariants. However, because phase information is lost in the process of measuring photoemission intensities, retrieving the complex-valued Bloch wave function from photoemission data has yet remained elusive. We introduce a novel measurement methodology and associated observable in extreme ultraviolet angle-resolved photoemission spectroscopy, based on continuous modulation of the ionizing radiation polarization axis. Tracking the energy- and momentum-resolved amplitude and phase of the photoemission intensity modulation upon polarization axis rotation allows us to retrieve the circular dichroism in photoelectron angular distributions (CDAD) without using circular photons, providing direct insights into the phase of photoemission matrix elements. In the case of two relevant bands, it is possible to reconstruct the orbital pseudospin (and thus the Bloch wave function) with moderate theory input, as demonstrated for the prototypical, layered, semiconducting, transition metal dichalcogenide $2\mathrm{H}\text{−}{\mathrm{WSe}}_2$. This novel measurement methodology in ARPES, which is articulated around the manipulation of the photoionization transition dipole matrix element, in combination with a simple tight-binding theory, is general and adds a new dimension to obtaining insights into the orbital pseudospin, Berry curvature, and Bloch wave functions of many relevant crystalline solids.

The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic of many-body quantum chaos. In addition, partial spectral form factors (PSFFs) can be defined which refer to subsystems of the many-body system. They provide unique insights into energy eigenstate statistics of many-body systems, as we show in an analysis on the basis of random matrix theory and of the eigenstate thermalization hypothesis. We propose a protocol that allows the measurement of the SFF and PSFFs in quantum many-body spin models, within the framework of randomized measurements. Aimed to probe dynamical properties of quantum many-body systems, our scheme employs statistical correlations of local random operations which are applied at different times in a single experiment. Our protocol provides a unified test bed to probe many-body quantum chaotic behavior, thermalization, and many-body localization in closed quantum systems which we illustrate with numerical simulations for Hamiltonian and Floquet many-body spin systems.