The high-pressure (HP) behavior of dioxides is of interest due to their extensive polymorphism and role as analogs for ${\mathrm{SiO}}_2$, a phase expected to be important in the deep mantles of Earth and terrestrial exoplanets. Here we report on dynamic ramp compression of quartz-type germanium dioxide ${\mathrm{GeO}}_2$ to stresses up to 882 GPa, a higher peak stress than previous studies by a factor of 5. X-ray diffraction data show that $\mathrm{HP}\text{−}{\mathrm{PdF}}_2$-type ${\mathrm{GeO}}_2$ occurs under ramp loading from 154 to 440 GPa, and this phase persists to higher pressure than predicted by theory. Above 440 GPa, we observe evidence for transformation to a new phase of ${\mathrm{GeO}}_2$. Based on the diffraction data, the best candidate for this new phase is the cotunnite-type structure which has been predicted to be a stable phase of ${\mathrm{GeO}}_2$ above 300 GPa. The $\mathrm{HP}\text{−}{\mathrm{PdF}}_2$-type and cotunnite-type structures are important phases in a wide range of $A{X}_2$ compounds, including ${\mathrm{SiO}}_2$, at multihundred GPa stresses. Our results demonstrate that ramp compression can be an effective technique for synthesizing and characterizing such phases in oxides. In addition, we show that pulsed x-ray diffraction under ramp compression can be used to examine lower-symmetry phases in oxide materials.

Couplings between topological edge channels open electronic phases possessing nontrivial eigenmodes far beyond the noninteracting-edge picture. However, inelastic scatterings mask the eigenmodes’ inherent features, often preventing us from identifying the phases, as is the case for the quintessential Landau-level filling factor $\nu =2/3$ edge composed of the counterpropagating $\nu =1/3$ and 1 ($1/3–1$) channels. Here, we study the coherent-incoherent crossover of the $1/3–1$ channels by tuning the channel length in situ using a new device architecture comprising a junction of $\nu =1/3$ and 1 systems, the particle-hole conjugate of the $2/3$ edge. We successfully observed the concurrence of the fluctuating electrical conductance and the quantized thermal conductance in the crossover regime, the definitive hallmark of the eigenmodes in the disorder-dominated edge phase left experimentally unverified.

XY* transitions represent one of the simplest examples of unconventional quantum criticality, in which fractionally charged excitations condense into a superfluid and display novel features that combine quantum criticality and fractionalization. Nevertheless, their experimental realization is challenging. Here we propose to study the XY* transition in quantum Hall bilayers at filling $({\nu }_1,{\nu }_2)=(\frac{1}{3},\frac{2}{3})$ where the exciton condensate (EC) phase plays the role of the superfluid. Supported by exact diagonalization calculation, we argue that there is a continuous transition between an EC phase at small bilayer separation to a pair of decoupled fractional quantum Hall states at large separation. The transition is driven by condensation of a fractional exciton, a bound state of a Laughlin quasiparticle and quasihole, and is in the XY* universality class. The fractionalization is manifested by unusual properties including a large anomalous exponent and fractional universal conductivity, which can be conveniently measured through interlayer tunneling and counterflow transport, respectively. We also show that the edge is likely to realize the newly predicted extraordinary log boundary criticality. Our work highlights the promise of quantum Hall bilayers as an ideal platform for exploring exotic bulk and boundary critical behaviors that are amenable to immediate experimental exploration in dual-gated bilayer systems. The XY* critical theory can be generalized to a bilayer system with an arbitrary Abelian state in one layer and its particle-hole partner in the other layer. Therefore, we anticipate many distinct XY* transitions corresponding to the different Laughlin states and Jain sequences in the single-layer case.

We perform a systematic symmetry classification of many-body Lindblad superoperators describing general (interacting) open quantum systems coupled to a Markovian environment. Our classification is based on the behavior of the many-body Lindbladian under antiunitary symmetries and unitary involutions. We find that Hermiticity preservation reduces the number of symmetry classes, while trace preservation and complete positivity do not, and that the set of admissible classes depends on the presence of additional unitary symmetries: in their absence or in symmetry sectors containing steady states, many-body Lindbladians belong to one of ten non-Hermitian symmetry classes; if however, there are additional symmetries and we consider non-steady-state sectors, they belong to a different set of 19 classes. In both cases, it does not include classes with Kramers degeneracy. Remarkably, our classification admits a straightforward generalization to the case of non-Markovian, and even non-trace-preserving, open quantum dynamics. While the abstract classification is completely general, we then apply it to general (long-range, interacting, spatially inhomogeneous) spin-$1/2$ chains. We explicitly build examples in all ten classes of Lindbladians in steady-state sectors, describing standard physical processes such as dephasing, spin injection and absorption, and incoherent hopping, thus illustrating the relevance of our classification for practical physics applications. Finally, we show that the examples in each class display unique random-matrix correlations. To fully resolve all symmetries, we employ the combined analysis of bulk complex spacing ratios and the overlap of eigenvector pairs related by symmetry operations. We further find that statistics of levels constrained onto the real and imaginary axes or close to the origin are not universal due to spontaneous breaking of Lindbladian $PT$ symmetry.

Symmetry-protected topological (SPT) phases are many-body quantum states that are topologically nontrivial as long as the relevant symmetries are unbroken. In this work we show that SPT phases are also well defined for average symmetries, where quenched disorders locally break the symmetries, but restore the symmetries upon disorder averaging. An example would be crystalline SPT phases with imperfect lattices. Specifically, we define the notion of average SPT phase for disordered ensembles of quantum states. We then classify and characterize a large class of average SPT phases using a decorated domain wall approach, in which domain walls (and more general defects) of the average symmetries are decorated with lower-dimensional topological states. We then show that if the decorated domain walls have dimension higher than $(0+1)\mathrm{D}$, then the boundary states of such average SPT phases will almost certainly be long-range entangled, with probability approaching 1 as the system size approaches infinity. This generalizes the notion of t’Hooft anomaly to average symmetries, which we dub “average anomaly.” The average anomaly can also manifest as constraints on lattice systems similar to the Lieb-Schultz-Mattis theorems, but with only average lattice symmetries. We also generalize our problem to “quantum disorders” that can admit short-range entanglement on their own, and develop a theory of such generalized average SPT phases purely based on density matrices and quantum channels. Our results indicate that topological quantum phenomena associated with average symmetries can be at least as rich as those with ordinary exact symmetries.

Explaining quantum many-body dynamics is a long-held goal of physics. A rigorous operator algebraic theory of dynamics in locally interacting systems in any dimension is provided here in terms of time-dependent equilibrium (Gibbs) ensembles. The theory explains dynamics in closed, open, and time-dependent systems, provided that relevant pseudolocal quantities can be identified, and time-dependent Gibbs ensembles unify wide classes of quantum nonergodic and ergodic systems. The theory is applied to quantum many-body scars, continuous, discrete, and dissipative time crystals, Hilbert space fragmentation, lattice gauge theories, and disorder-free localization, among other cases. Novel pseudolocal classes of operators are introduced in the process: projected-local, which are local only for some states, cryptolocal, whose locality is not manifest in terms of any finite number of local densities, and transient ones, that dictate finite-time relaxation dynamics. An immediate corollary is proving saturation of the Mazur bound for the Drude weight. This proven theory is intuitively the rigorous algebraic counterpart of the weak eigenstate thermalization hypothesis and has deep implications for thermodynamics: Quantum many-body systems “out of equilibrium” are actually always in a time-dependent equilibrium state for any natural initial state. The work opens the possibility of designing novel out-of-equilibrium phases, with the newly identified scarring and fragmentation phase transitions being examples.

High harmonic generation (HHG) has developed in recent years as a promising tool for ultrafast materials spectroscopy. At the forefront of these advancements, several works proposed using HHG as an all-optical probe for topology of quantum matter by identifying its signatures in the emission spectra. However, it remains unclear if such spectral signatures are indeed a robust and general approach for probing topology. To address this point, we perform a fully ab initio study of HHG from prototypical two-dimensional topological insulators in the Kane-Mele quantum spin-Hall and anomalous-Hall phases. We analyze the spectra and previously proposed topological signatures by comparing HHG from the topological and trivial phases and across the phase transition. We demonstrate and provide detailed microscopic explanations of why, in these systems, none of the observables proposed thus far uniquely and universally probes material topology. Specifically, we find that the (i) HHG helicity, (ii) anomalous HHG ellipticity, (iii) HHG elliptical dichroism, and (iv) temporal delays in HHG emission are all unreliable signatures of topological phases. Our results suggest that extreme care must be taken when interpreting HHG spectra for topological signatures and that contributions from the crystal symmetries and chemical nature might be dominant over those from topology. They hint that a truly universal topological signature in nonlinear optics is unlikely and raise important questions regarding possible utilization and detection of topology in out-of-equilibrium systems.

Electronic nematicity is the spontaneous loss of rotational symmetry in a metal, without breaking translational symmetry. In the cuprate superconductors, there is experimental evidence for nematicity, but its origin remains unclear. Here we investigate the onset of nematicity in the transport of charge by means of electric and thermoelectric measurements in underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$, performed by passing the current (electrical or thermal) first along the $a$ axis then the $b$ axis of the orthorhombic structure in the same crystal, with a hole doping $p=0.12$. Upon cooling, we observe no additional in-plane anisotropy—beyond the background anisotropy due to the CuO chains—in either the resistivity $\rho$ or the Seebeck coefficient $S$ as the temperature $T^{\star }$ for the onset of the pseudogap phase is crossed. We conclude that the pseudogap phase of cuprates is not nematic. However, at temperatures much lower than $T^{\star }$, a strong additional anisotropy is observed, most clearly in the Peltier coefficient $\alpha =S/\rho$. We interpret it as nematicity associated with the development of charge order.

Understanding topological matter is an outstanding challenge across several disciplines of physical science. Programmable quantum simulators have emerged as a powerful approach to studying such systems. While quantum spin liquids of paradigmatic toric code type have recently been realized in the laboratory, controlled exploration of topological phases with non-Abelian excitations remains an open problem. We introduce and analyze a new approach to simulating topological matter based on periodic driving. Specifically, we describe a model for a so-called Floquet spin liquid, obtained through a periodic sequence of parallel quantum gate operations that effectively simulates the Hamiltonian of the non-Abelian spin liquid in Kitaev’s honeycomb model. We show that this approach, including the toolbox for preparation, control, and readout of topological states, can be efficiently implemented in state-of-the-art experimental platforms. One specific implementation scheme is based on Rydberg atom arrays and utilizes recently demonstrated coherent qubit transport combined with controlled-phase gate operations. We describe methods for probing the non-Abelian excitations, and the associated Majorana zero modes, and simulate possible fusion and braiding experiments. Our analysis demonstrates the potential of programmable quantum simulators for exploring topological phases of matter. Extensions including simulation of Kitaev materials and lattice gauge theories are also discussed.

We show how to define a quantized many-body charge polarization $\overrightarrow{𝒫}$ for $(2+1)\mathrm{D}$ topological phases of matter, even in the presence of nonzero Chern number and magnetic field. For invertible topological states, $\overrightarrow{𝒫}$ is a ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$, ${\mathbb{Z}}_3$, ${\mathbb{Z}}_2$, or ${\mathbb{Z}}_1$ topological invariant in the presence of ($M=2$, 3, 4, or 6)-fold rotational symmetry, lattice (magnetic) translational symmetry, and charge conservation. $\overrightarrow{𝒫}$ manifests in the bulk of the system as (i) a fractional quantized contribution of $\overrightarrow{𝒫}·\overrightarrow{b}\text{mod}1$ to the charge bound to lattice disclinations and dislocations with Burgers vector $\overrightarrow{b}$, (ii) a linear momentum for magnetic flux, and (iii) an oscillatory system size dependent contribution to the effective 1D polarization on a cylinder. We study $\overrightarrow{𝒫}$ in lattice models of spinless free fermions in a magnetic field. We derive predictions from topological field theory, which we match to numerical calculations for the effects (i)–(iii), demonstrating that these can be used to extract $\overrightarrow{𝒫}$ from microscopic models in an intrinsically many-body way. We show how, given a high symmetry point o, there is a topological invariant, the discrete shift ${𝒮}_{\mathrm{o}}$, such that $\overrightarrow{𝒫}$ specifies the dependence of ${𝒮}_{\mathrm{o}}$ on o. We derive colored Hofstadter butterflies, corresponding to the quantized value of $\overrightarrow{𝒫}$, which further refine the colored butterflies from the Chern number and discrete shift.

Femtosecond core-level transient absorption spectroscopy is utilized to investigate photoinduced dynamics of the charge density wave in $1T\text{−}{\mathrm{TiSe}}_2$ at the Ti $M_{2,3}$ edge (32–50 eV). Photoexcited carriers and phonons are found to primarily induce spectral redshifts of core-level excitations, and a carrier relaxation time and phonon heating time of approximately 360 fs and 1.0 ps are extracted, respectively. Pronounced oscillations in delay-dependent absorption spectra are assigned to coherent excitations of the optical $A_{1g}$ phonon (6.0 THz) and the $A_{1g}^{*}$ charge density wave amplitude mode (3.3 THz). By comparing the measured spectra with time-dependent density functional theory simulations, we determine the directions of the momentary atomic displacements of both coherent modes and estimate their amplitudes. Interestingly, the spectral fingerprint of the amplitude mode can be associated with many-body electron screening, strengthening the importance of electron-electron and simultaneous electron-phonon interaction for the stability of the charge density wave. In addition, we find that 10% and 13% of the absorbed energy is stored in the $A_{1g}$ and $A_{1g}^{*}$ coherent modes, respectively. This work presents a first look on charge density wave excitations with tabletop core-level transient absorption spectroscopy, enabling simultaneous access to electronic and lattice excitation and relaxation.

We study theoretically how local measurements performed on critical quantum ground states affect long-distance correlations. These states are highly entangled and feature algebraic correlations between local observables. As a consequence, local measurements can have highly nonlocal effects. Our focus is on Tomonaga-Luttinger liquid ground states, a continuous family of critical states in one dimension whose structure is characterized by a Luttinger parameter $K$. We show that arbitrarily weak local measurements, performed over extended regions of space, can conspire to drive transitions in long-distance correlations. Conditioning first on a translation-invariant set of measurement outcomes, we show that there is a transition in the character of the postmeasurement quantum state for $K<1$, and highlight a formal analogy with the effect of a static defect on transport through a Tomonaga-Luttinger liquid. To investigate the full ensemble of measurement outcomes, we consider averages of physical quantities which are necessarily nonlinear in the system density matrix. We show how their behavior can be understood within a replica field theory, and for the measurements that we consider we find that the symmetry of the theory under exchange of replicas is broken for $K<1/2$. A well-known barrier to experimentally observing the collective effects of multiple measurements has been the need to postselect on random outcomes. Here we resolve this problem by introducing cross-correlations between experimental measurement results and classical simulations, which act as resource-efficient probes of the transition. The phenomena we discuss are, moreover, robust to local decoherence.

Traditionally, x-ray scattering techniques have been used to detect the breaking of the structural symmetry of the lattice, which accompanies a periodic displacement of the atoms associated with charge density wave (CDW) formation in the cuprate pseudogap states. Similarly, spectroscopic imaging scanning tunneling microscopy (STM) has visualized the short-range CDW. However, local coupling of electrons to the lattice in the form of a short-range CDW has been a challenge to visualize; thus, a link between these measurements has been missing. Here, we introduce a novel STM-based technique to visualize the local bond-length variations obtained from topographic imaging with picometer precision. Application of this technique to the high-$T_c$ cuprate superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ reveals a high-fidelity local lattice distortion of the BiO lattice as large as 2%. In addition, analysis of local breaking of rotational symmetry associated with the bond lengths reveals modulations around four-unit-cell periodicity in both $B_1$ and $E$ representations in the $C_{4v}$ group of the lattice, which coincides with the unidirectional $d$-symmetry CDW ($d\mathrm{CDW}$) previously identified within the ${\mathrm{CuO}}_2$ planes, thus providing direct evidence of electron-lattice coupling in the pseudogap state and a link between the x-ray scattering and STM measurements. Overall, our results suggest that the periodic lattice displacements in $E$ representations correspond to a locally frozen version of the soft phonons identified by the x-ray scattering measurements, and a fluctuation of the bond length is reflected by the fluctuation of the $d\mathrm{CDW}$ formation near the quantum critical point.

We report the experimental observation of the spin-wave moiré edge and cavity modes using Brillouin light scattering spectromicroscopy in a nanostructured magnetic moiré lattice consisting of two twisted triangle antidot lattices based on an yttrium iron garnet thin film. Spin-wave moiré edge modes are detected at an optimal twist angle and with a selective excitation frequency. At a given twist angle, the magnetic field acts as an additional degree of freedom for tuning the chiral behavior of the magnon edge modes. Micromagnetic simulations indicate that the edge modes emerge within the original magnonic band gap and at the intersection between a mini flatband and a propagation magnon branch. Our theoretical estimate for the Berry curvature of the magnon-magnon coupling suggests a nontrivial topology for the chiral edge modes and confirms the key role played by the dipolar interaction. Our findings shed light on the topological nature of the magnon edge mode for emergent moiré magnonics.

The correlation functions of quantum systems—central objects in quantum field theories—are defined in high-dimensional space-time domains. Their numerical treatment thus suffers from the curse of dimensionality, which hinders the application of sophisticated many-body theories to interesting problems. Here, we propose a multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains (QTTs), “qubits” describing exponentially different length scales. The ansatz then assumes a separation of length scales by decomposing the resulting high-dimensional tensors into tensor trains (also known as matrix product states). We numerically verify the ansatz for various equilibrium and nonequilibrium systems and demonstrate compression ratios of several orders of magnitude for challenging cases. Essential building blocks of diagrammatic equations, such as convolutions or Fourier transforms, are formulated in the compressed form. We numerically demonstrate the stability and efficiency of the proposed methods for the Dyson and Bethe-Salpeter equations. The QTT representation provides a unified framework for implementing efficient computations of quantum field theories.

Orbital degrees of freedom play an essential role in metals, semiconductors, and strongly confined electronic systems. Experiments with ultracold atoms have used highly anisotropic confinement to explore low-dimensional physics, but they typically eliminate orbital degrees of freedom by preparing atoms in the motional ground states of the strongly confined directions. Here, we prepare multiband systems of spin-polarized fermionic potassium (${}^{40}\mathrm{K}$) in the quasi-one-dimensional (q1D) regime and quantify the strength of atom-atom correlations using radio-frequency spectroscopy. The activation of orbital degrees of freedom leads to a new phenomenon: a low-energy scattering channel that has even particle-exchange parity along the q1D axis, as if the underlying interactions were $s$-wave. This emergent exchange symmetry is enabled by orbital singlet wave functions in the strongly confined directions, which also confer high-momentum components to low-energy q1D collisions. We measure both the q1D odd-wave and even-wave “contact” parameters for the first time and compare them to theoretical predictions of one-dimensional many-body models. The strength and spatial symmetry of interactions are tuned by a $p$-wave Feshbach resonance and by transverse confinement strength. Near resonance, the even-wave contact approaches its theoretical unitary value, whereas the maximum observed odd-wave contact remains several orders of magnitude below its unitary limit. Low-energy scattering channels of multi-orbital systems, such as those found here, may provide new routes for the exploration of universal many-body phenomena.

Since the discovery of magic-angle twisted bilayer graphene, flat bands in Dirac materials have become a prominent platform for realizing strong correlation effects in electronic systems. Here we show that the symmetry group protecting the Dirac cone in such materials determines whether a Dirac band may be flattened by the tuning of a small number of parameters. We devise a criterion that, given a symmetry group, allows for the calculation of the number of parameters required to make the Dirac velocity vanish. This criterion is employed to study band flattening in twisted bilayer graphene and in surface states of 3D topological insulators. Following this discussion, we identify the symmetries under which the vanishing of the Dirac velocity implies the emergence of perfectly flat bands. Our analysis allows us to construct additional model Hamiltonians that display perfectly flat bands at certain points in the space of parameters: the first is a toy model of two coupled 3D topological insulator surfaces, and the second is a quasicrystalline generalization of the chiral model of twisted bilayer graphene.

The 3D Ising transition, the most celebrated and unsolved critical phenomenon in nature, has long been conjectured to have emergent conformal symmetry, similar to the case of the 2D Ising transition. Yet, the emergence of conformal invariance in the 3D Ising transition has rarely been explored directly, mainly due to unavoidable mathematical or conceptual obstructions. Here, we design an innovative way to study the quantum version of the 3D Ising phase transition on spherical geometry, using the “fuzzy (noncommutative) sphere” regularization. We accurately calculate and analyze the energy spectra at the transition, and explicitly demonstrate the state-operator correspondence (i.e., radial quantization), a fingerprint of conformal field theory. In particular, we identify13 parity-even primary operators within a high accuracy and two parity-odd operators that were not known before. Our result directly elucidates the emergent conformal symmetry of the 3D Ising transition, a conjecture made by Polyakov half a century ago. More importantly, our approach opens a new avenue for studying 3D conformal field theories by making use of the state-operator correspondence and spherical geometry.

Alkali-doped fullerides are strongly correlated organic superconductors that exhibit high transition temperatures, exceptionally large critical magnetic fields, and a number of other unusual properties. The proximity to a Mott insulating phase is thought to be a crucial ingredient of the underlying physics and may also affect precursors of superconductivity in the normal state above $T_c$. We report on the observation of a sizable magneto-thermoelectric (Nernst) effect in the normal state of ${\mathrm{K}}_3{\mathrm{C}}_{60}$, which displays the characteristics of superconducting fluctuations. This nonquasiparticle Nernst effect emerges from an ordinary quasiparticle background below a temperature of 80 K, far above $T_c=20\mathrm{K}$. At the lowest fields and close to $T_c$, the scaling of the effect is captured by a model based on Gaussian fluctuations. The behavior at higher magnetic fields displays a symmetry between the magnetic length and the correlation length of the system. The temperature up to which we observe fluctuations is exceptionally high for a three-dimensional isotropic system, where fluctuation effects are expected to be suppressed.

Recent years have seen remarkable development in open quantum systems effectively described by non-Hermitian Hamiltonians. A unique feature of non-Hermitian topological systems is the skin effect, anomalous localization of an extensive number of eigenstates driven by nonreciprocal dissipation. Despite its significance for non-Hermitian topological phases, the relevance of the skin effect to quantum entanglement and critical phenomena has remained unclear. Here, we find that the skin effect induces a nonequilibrium quantum phase transition in the entanglement dynamics. We show that the skin effect gives rise to a macroscopic flow of particles and suppresses the entanglement propagation and thermalization, leading to the area law of the entanglement entropy in the nonequilibrium steady state. Moreover, we reveal an entanglement phase transition induced by the competition between the unitary dynamics and the skin effect even without disorder or interactions. This entanglement phase transition accompanies nonequilibrium quantum criticality characterized by a nonunitary conformal field theory whose effective central charge is extremely sensitive to the boundary conditions. We also demonstrate that it originates from an exceptional point of the non-Hermitian Hamiltonian and the concomitant scale invariance of the skin modes localized according to the power law. Furthermore, we show that the skin effect leads to the purification and the reduction of von Neumann entropy even in Markovian open quantum systems described by the Lindblad master equation. Our work opens a way to control the entanglement growth and establishes a fundamental understanding of phase transitions and critical phenomena in open quantum systems far from thermal equilibrium.