Understanding the nature of the excitation spectrum in quantum spin liquids is of fundamental importance, in particular for the experimental detection of candidate materials. However, current theoretical and numerical techniques have limited capabilities, especially in obtaining the dynamical structure factor, which gives a crucial characterization of the ultimate nature of the quantum state and may be directly assessed by inelastic neutron scattering. In this work, we investigate the low-energy properties of the $S=1/2$ Heisenberg model on the triangular lattice, including both nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ superexchanges, by a dynamical variational Monte Carlo approach that allows accurate results on spin models. For $J_2=0$, our calculations are compatible with the existence of a well-defined magnon in the whole Brillouin zone, with gapless excitations at $K$ points (i.e., at the corners of the Brillouin zone). The strong renormalization of the magnon branch (also including rotonlike minima around the $M$ points, i.e., midpoints of the border zone) is described by our Gutzwiller-projected state, where Abrikosov fermions are subject to a nontrivial magnetic $\pi$ flux threading half of the triangular plaquettes. When increasing the frustrating ratio $J_2/J_1$, we detect a progressive softening of the magnon branch at $M$, which eventually becomes gapless within the spin-liquid phase. This feature is captured by the band structure of the unprojected wave function (with two Dirac points for each spin component). In addition, we observe an intense signal at low energies around the $K$ points, which cannot be understood within the unprojected picture and emerges only when the Gutzwiller projection is considered, suggesting the relevance of gauge fields for the low-energy physics of spin liquids.

We study the electronic structures and topological properties of ($M+N$)-layer twisted graphene systems. We consider the generic situation that $N$-layer graphene is placed on top of the other $M$-layer graphene and is twisted with respect to each other by an angle $\theta$. In such twisted multilayer graphene systems, we find that there exist two low-energy flat bands for each valley emerging from the interface between the $M$ layers and the $N$ layers. These two low-energy bands in the twisted multilayer graphene system possess valley Chern numbers that are dependent on both the number of layers and the stacking chiralities. In particular, when the stacking chiralities of the $M$ layers and $N$ layers are opposite, the total Chern number of the two low-energy bands for each valley equals $\pm (M+N-2)$ (per spin). If the stacking chiralities of the $M$ layers and the $N$ layers are the same, then the total Chern number of the two low-energy bands for each valley is $\pm (M-N)$ (per spin). The valley Chern numbers of the low-energy bands are associated with large, valley-contrasting orbital magnetizations, suggesting the possible existence of orbital ferromagnetism and anomalous Hall effect once the valley degeneracy is lifted either externally by a weak magnetic field or internally by Coulomb interaction through spontaneous symmetry breaking. Such an orbital ferromagnetic state is characterized by chiral current loops circulating around the $AA$ region of the moiré pattern, which can be experimentally detected.

We report a combined experimental and theoretical investigation that reveals a new mechanism responsible for the enhancement of electron-phonon coupling in doped semiconductors in which multiple inequivalent valleys are simultaneously populated. Using Raman spectroscopy on ionic-liquid-gated monolayer and bilayer ${\mathrm{MoS}}_2$, ${\mathrm{WS}}_2$, and ${\mathrm{WSe}}_2$ over a wide range of electron and hole densities, we find that phonons with a dominant out-of-plane character exhibit strong softening upon electron accumulation while remaining unaffected upon hole doping. This unexpected—but very pronounced—electron-hole asymmetry is systematically observed in all monolayers and bilayers. By performing first-principles simulations, we show that the phonon softening occurs when multiple inequivalent valleys are populated simultaneously. Accordingly, the observed electron-hole asymmetry originates from the much larger energy separation between valleys in the valence bands—as compared to the conduction band—that prevents the population of multiple valleys upon hole accumulation. We infer that the enhancement of the electron-phonon coupling occurs because the population of multiple valleys acts to strongly reduce the efficiency of electrostatic screening for those phonon modes that cause the energy of the inequivalent valleys to oscillate out of phase. This robust mechanism is likely to play an important role in several physical phenomena, possibly including the occurrence of superconductivity in different transition metal dichalcogenides.

We define dynamical universality classes for many-body systems whose unitary evolution is punctuated by projective measurements. In cases where such measurements occur randomly at a finite rate $p$ for each degree of freedom, we show that the system has two dynamical phases: “entangling” and “disentangling.” The former occurs for $p$ smaller than a critical rate $p_c$ and is characterized by volume-law entanglement in the steady state and “ballistic” entanglement growth after a quench. By contrast, for $p>p_c$ the system can sustain only area-law entanglement. At $p=p_c$ the steady state is scale invariant, and in $1+1\mathrm{D}$, the entanglement grows logarithmically after a quench. To obtain a simple heuristic picture for the entangling-disentangling transition, we first construct a toy model that describes the zeroth Rényi entropy in discrete time. We solve this model exactly by mapping it to an optimization problem in classical percolation. The generic entangling-disentangling transition can be diagnosed using the von Neumann entropy and higher Rényi entropies, and it shares many qualitative features with the toy problem. We study the generic transition numerically in quantum spin chains and show that the phenomenology of the two phases is similar to that of the toy model but with distinct “quantum” critical exponents, which we calculate numerically in $1+1\mathrm{D}$. We examine two different cases for the unitary dynamics: Floquet dynamics for a nonintegrable Ising model, and random circuit dynamics. We obtain compatible universal properties in each case, indicating that the entangling-disentangling phase transition is generic for projectively measured many-body systems. We discuss the significance of this transition for numerical calculations of quantum observables in many-body systems.

Knowledge of the behavior of hydrogen in metal hydrides is the key for understanding their electronic properties. Here, we present an ${}^1\mathrm{H}\text{−}\mathrm{NMR}$ study of cubic FeH up to 202 GPa. We observe a distinct deviation from the ideal metallic behavior between 64 and 110 GPa that suggests pressure-induced H-H interactions. Accompanying ab initio calculations support this result, as they reveal the formation of an intercalating sublattice of electron density, which enhances the hydrogen contribution to the electronic density of states at the Fermi level. This study shows that pressure-induced H-H interactions can occur in metal hydrides at much lower compression and larger H-H distances than previously thought and stimulates an alternative pathway in the search for novel high-temperature superconductors.

The propagation of information in nonrelativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance $r$ as a power law, $1/r^{\alpha }$. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al., FOCS’18. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when $\alpha >3D$ (where $D$ is the number of dimensions).

We report the coexistence of ferroelectricity and a spin liquid state in hexagonal ${\mathrm{TbInO}}_3$ with quasi-two-dimensional triangular spin lattice. Geometrical ferroelectricity associated with In trimerization accompanies topological ferroelectric structural defects. Magnetic susceptibility data show in-plane magnetic anisotropy of Tb spins without any long-range order above 1.8 K, and we also confirm no trace of any phase transition down to 0.15 K from a specific heat measurement, which indicates that this system is highly frustrated and may host a spin liquid ground state. By analyzing the Schottky anomaly in the specific heat results, we propose a model where crystal-field levels are different in each Tb sites, and only one of them has a magnetic ground state and forms a unique honeycomb spin lattice. These observations put forward an interesting possibility where spin liquid and ferroelectric behaviors coexist, and the atomically sharp ferroelectric domain walls may host new magnetic edge states or local spin excitations.

We study a two-dimensional tight-binding model of a topological crystalline insulator (TCI) protected by rotation symmetry. The model is built by stacking two Chern insulators with opposite Chern numbers which transform under conjugate representations of the rotation group, e.g., $p_{\pm }$ orbitals. Despite its apparent similarity to the Kane-Mele model, it does not host stable gapless surface states. Nevertheless, the model exhibits topological responses including the appearance of quantized fractional charge bound to rotational defects (disclinations) and the pumping of angular momentum in response to threading an elementary magnetic flux, which are described by a mutual Chern-Simons coupling between the electromagnetic gauge field and an effective gauge field corresponding to the rotation symmetry. In addition, we show that although the filled bands of the model do not admit a symmetric Wannier representation, this obstruction is removed upon the addition of appropriate atomic orbitals, which implies “fragile” topology. As a result, the response of the model can be derived by representing it as a superposition of atomic orbitals with positive and negative integer coefficients. Following the analysis of the model, which serves as a prototypical example of 2D TCIs protected by rotation, we show that all TCIs protected by point group symmetries which do not have protected surface states are either atomic insulators or fragile phases. Remarkably, this implies that gapless surface states exist in free-electron systems if and only if there is a stable Wannier obstruction. We then use dimensional reduction to map the problem of classifying 2D TCIs protected by rotation to a zero-dimensional problem which is then used to obtain the complete noninteracting classification of such TCIs as well as the reduction of this classification in the presence of interactions.

The improper ferroelectricity in ${\mathrm{YMnO}}_3$ and other related multiferroic hexagonal manganites is known to cause topologically protected ferroelectric domains that give rise to rich and diverse physical phenomena. The local structure and structural coherence across the ferroelectric transition, however, were previously not well understood. Here, we reveal the evolution of the local structure with temperature in ${\mathrm{YMnO}}_3$ using neutron total scattering techniques, and we interpret them with the help of first-principles calculations and with a first-principles-based effective Hamiltonian. The results show that, at room temperature, the local and average structures are consistent with the established ferroelectric $P{6}_{3}cm$ symmetry. On heating, both local and average structural analyses show striking anomalies from about 800 K up to the Curie temperature and signatures of a locally more preserved structure than on average, consistent with increasing fluctuations of the order-parameter angle. These fluctuations result in an unusual local symmetry lowering into a continuum of structures on heating. This local symmetry breaking persists into the high-symmetry nonpolar phase, constituting an unconventional type of order-disorder transition, and we pinpoint it as the reason for the anomalous behavior near the phase transition. The hidden disorder revealed in ${\mathrm{YMnO}}_3$ by total scattering is expected to find analogies in other materials with structural frustration or characteristic energy barriers of different magnitudes.

Unconventional superconductors are often characterized by numerous competing and even intertwined orders in their phase diagrams. The fluctuations associated with these orders may provide the exotic pairing glue that underlies their high-temperature superconductivity. Helimagnet MnP, the first Mn-based superconductor under pressure, lacks high rotational symmetry. However, our resonant soft x-ray scattering experiment discovers novel helical orbital density wave (ODW) orders in MnP and reveals intertwined ordering phenomena. In particular, an ODW forms with half the period of the spin order and fully develops slightly above the spin ordering temperature, which resembles the behaviors of the nematic phase of the iron-based superconductors. Moreover, we find that their domains develop simultaneously, yet the spin order domains are larger than those of the ODW; and they cooperatively produce another ODW with $1/3$ the period of the spin order. These observations provide a comprehensive picture of the intertwined orders in this three-dimensional, low-symmetry system and shed light on the understanding of its superconducting mechanism.

Topological mechanics has been studied intensively in periodic lattices in the past a few years, leading to the discovery of topologically protected boundary floppy modes in Maxwell lattices. In this paper, we extend this concept to two-dimensional quasicrystalline parallelogram tilings, and we use the Penrose tiling as our example to demonstrate that topological boundary floppy modes can arise from a small geometric perturbation to the tiling. The same construction can also be applied to disordered parallelogram tilings to generate topological boundary floppy modes. We find that a topological polarization can be defined for quasicrystalline structures as a bulk topological invariant. Remarkably, due to the unusual orientational symmetry of quasicrystals, the resulting topological polarization can exhibit orientational symmetries not allowed in periodic lattices. We prove the existence of these topological boundary floppy modes using a duality theorem which relates floppy modes and states of self-stress in parallelogram tilings and fiber networks, which are Maxwell reciprocal diagrams to one another. Our result reveals new physics about the interplay between topological states and quasicrystalline order and leads to novel designs of quasicrystalline topological mechanical metamaterials.

Quasiparticles and collective modes are two fundamental aspects that characterize quantum matter in addition to its ground-state features. For example, the low-energy physics for Fermi-liquid phase in He-III is featured not only by fermionic quasiparticles near the chemical potential but also by fruitful collective modes in the long-wave limit, including several different sound waves that can propagate through it under different circumstances. On the other hand, it is very difficult for sound waves to be carried by electron liquid in ordinary metals due to the fact that long-range Coulomb interaction among electrons will generate a plasmon gap for ordinary electron density oscillation and thus prohibits the propagation of sound waves through it. In the present paper, we propose a unique type of acoustic collective mode in Weyl semimetals under magnetic field called chiral zero sound. Chiral zero sound can be stabilized under the so-called “chiral limit,” where the intravalley scattering time is much shorter than the intervalley one and propagates only along an external magnetic field for Weyl semimetals with multiple pairs of Weyl points. The sound velocity of chiral zero sound is proportional to the field strength in the weak field limit, whereas it oscillates dramatically in the strong field limit, generating an entirely new mechanism for quantum oscillations through the dynamics of neutral bosonic excitation, which may manifest itself in the thermal conductivity measurements under magnetic field.

Density-functional perturbation theory (DFPT) is nowadays the method of choice for the accurate computation of linear and nonlinear-response properties of materials from first principles. A notable advantage of DFPT over alternative approaches is the possibility of treating incommensurate lattice distortions with an arbitrary wave vector $\mathbf{q}$ at essentially the same computational cost as the lattice-periodic case. Here we show that $\mathbf{q}$ can be formally treated as a perturbation parameter and used in conjunction with the established results of perturbation theory (e.g., the “$2n+1$” theorem) to perform a long-wave expansion of an arbitrary response function in powers of the wave-vector components. This procedure provides a powerful general framework to access a wide range of spatial dispersion effects that were formerly difficult to calculate by means of first-principles electronic structure methods. In particular, the physical response to the spatial gradient of any external field can now be calculated at negligible cost by using the response functions to uniform perturbations (electric, magnetic, or strain fields) as the only input. We demonstrate our method by calculating the flexoelectric and dynamical quadrupole tensors of selected crystalline insulators and model systems.

We explore the interplay of electron-electron correlations and spin-orbit coupling in the model Fermi liquid ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ using laser-based angle-resolved photoemission spectroscopy. Our precise measurement of the Fermi surface confirms the importance of spin-orbit coupling in this material and reveals that its effective value is enhanced by a factor of about 2, due to electronic correlations. The self-energies for the $\beta$ and $\gamma$ sheets are found to display significant angular dependence. By taking into account the multi-orbital composition of quasiparticle states, we determine self-energies associated with each orbital component directly from the experimental data. This analysis demonstrates that the perceived angular dependence does not imply momentum-dependent many-body effects but arises from a substantial orbital mixing induced by spin-orbit coupling. A comparison to single-site dynamical mean-field theory further supports the notion of dominantly local orbital self-energies and provides strong evidence for an electronic origin of the observed nonlinear frequency dependence of the self-energies, leading to “kinks” in the quasiparticle dispersion of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$.

The properties of the isotropic incompressible $\nu =5/2$ fractional quantum Hall (FQH) state are described by a paired state of composite fermions in zero (effective) magnetic field, with a uniform $p_x+i{p}_y$ pairing order parameter, which is a non-Abelian topological phase with chiral Majorana and charge modes at the boundary. Recent experiments suggest the existence of a proximate nematic phase at $\nu =5/2$. This finding motivates us to consider an inhomogeneous paired state—a $p_x+i{p}_y$ pair-density wave (PDW)—whose melting could be the origin of the observed liquid-crystalline phases. This state can viewed as an array of domain and antidomain walls of the $p_x+i{p}_y$ order parameter. We show that the nodes of the PDW order parameter, the location of the domain walls (and antidomain walls) where the order parameter changes sign, support a pair of symmetry-protected counterpropagating Majorana modes. The coupling behavior of the domain-wall Majorana modes crucially depends on the interplay of the Fermi energy $E_F$ and the PDW pairing energy $E_{\mathrm{P}\mathrm{D}\mathrm{W}}$. The analysis of this interplay yields a rich set of topological states: (1) In the weak-coupling regime ($E_F>E_{\mathrm{P}\mathrm{D}\mathrm{W}}$), the hybridization of domain walls leads to a Majorana Fermi surface (MFS), which is protected by inversion and particle-hole symmetries. (2) As the MFS shrinks towards degenerate Dirac points, lattice effects render it unstable towards an Abelian stripe phase with two copropagating Majorana modes at the boundary. (3) A uniform component of the order parameter, which breaks inversion symmetry, gaps the MFS and causes the system to enter a non-Abelian FQH state supporting a chiral Majorana edge state. (4) In the strong-coupling regime, $E_F<E_{\mathrm{P}\mathrm{D}\mathrm{W}}$, the bulk fermionic spectrum becomes gapped; this is a trivial phase with no chiral Majorana edge states, which is in the universality class of an Abelian Halperin paired state. The pair-density-wave order state in a paired FQH system provides a fertile setting to study Abelian and non-Abelian FQH phases—as well as transitions thereof—tuned by the strength of the paired liquid crystalline order.

The effects of uniaxial compressive stress on the normal state ${}^{17}\mathrm{O}$ nuclear-magnetic-resonance properties of the unconventional superconductor ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ are reported. The paramagnetic shifts of both planar and apical oxygen sites show pronounced anomalies near the nominal $\mathbf{a}$-axis strain ${ϵ}_{aa}\equiv {ϵ}_v$ that maximizes the superconducting transition temperature $T_c$. The spin susceptibility weakly increases on lowering the temperature below $T\simeq 10\mathrm{K}$, consistent with an enhanced density of states associated with passing the Fermi energy through a van Hove singularity. Although such a Lifshitz transition occurs in the $\gamma$ band formed by the Ru $d_{xy}$ states hybridized with in-plane O $p_{\pi }$ orbitals, the large Hund’s coupling renormalizes the uniform spin susceptibility, which, in turn, affects the hyperfine fields of all nuclei. We estimate this “Stoner” renormalization $S$ by combining the data with first-principles calculations and conclude that this is an important part of the strain effect, with implications for superconductivity.

We study a large-$N$ tensor model with $O(N{)}^3$ symmetry containing two flavors of Majorana fermions, ${\psi }_1^{abc}$ and ${\psi }_2^{abc}$. We also study its random counterpart consisting of two coupled Sachdev-Ye-Kitaev (SYK) models, each containing $N_{\mathrm{SYK}}$ Majorana fermions. In these models, we assume tetrahedral quartic Hamiltonians which depend on a real coupling parameter $\alpha$. We find a duality relation between two Hamiltonians with different values of $\alpha$, which allows us to restrict the model to the range of $-1\le \alpha \le 1/3$. The scaling dimension of the fermion number operator $Q=i{\psi }_1^{abc}{\psi }_2^{abc}$ is complex and of the form $1/2+if(\alpha )$ in the range $-1\le \alpha <0$, indicating an instability of the conformal phase. Using Schwinger-Dyson equations to solve for the Green functions, we show that in the true low-temperature phase this operator acquires an expectation value, which demonstrates the breaking of an antiunitary particle-hole symmetry and other discrete symmetries. We also calculate spectra of the coupled SYK models for values of $N_{\mathrm{SYK}}$ where exact diagonalizations are possible. For negative $\alpha$, we find a gap separating the two lowest energy states from the rest of the spectrum, leading to an exponential decay of the zero-temperature correlation functions. For $N_{\mathrm{SYK}}$ divisible by 4, the two lowest states have a small splitting. They become degenerate in the large-$N_{\mathrm{SYK}}$ limit, as expected from the spontaneous breaking of a ${\mathbb{Z}}_2$ symmetry.

We present a theoretical method to generate a highly accurate time-independent Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which renormalization-group–like flow equations are derived to produce the effective Hamiltonian. Our tractable method has a range of validity reaching into frequency—and drive strength—regimes that are usually inaccessible via high-frequency $\omega$ expansions in the parameter $h/\omega$, where $h$ is the upper limit for the strength of local interactions. We demonstrate exact properties of our approach on a simple toy model and test an approximate version of it on both interacting and noninteracting many-body Hamiltonians, where it offers an improvement over the more well-known Magnus expansion and other high-frequency expansions. For the interacting models, we compare our approximate results to those found via exact diagonalization. While the approximation generally performs better globally than other high-frequency approximations, the improvement is especially pronounced in the regime of lower frequencies and strong external driving. This regime is of special interest because of its proximity to the resonant regime where the effect of a periodic drive is the most dramatic. Our results open a new route towards identifying novel nonequilibrium regimes and behaviors in driven quantum many-particle systems.

Continuous quantum phase transitions beyond the conventional paradigm of fluctuations of a symmetry-breaking order parameter are challenging for theory. These phase transitions often involve emergent deconfined gauge fields at the critical points as demonstrated in phase transitions between different broken-symmetry states of $2+1$-dimensional quantum magnets, as well as those between symmetry-protected topological (SPT) phases. In this paper, we present several examples of deconfined quantum critical points between SPT phases in $3+1$-D for both bosonic and fermionic systems. These critical theories can be formulated as non-Abelian gauge theories either in the infrared-free regime or in the conformal window when they flow to the Banks-Zaks fixed points. We explicitly demonstrate several interesting quantum critical phenomena. We describe situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points. We exhibit the possibility—which we dub “unnecessary quantum critical points”—of stable generic continuous phase transitions within the same phase. We present examples of interaction-driven, band-theory-forbidden, continuous phase transitions between two distinct band insulators. The understanding we develop leads us to suggest an interesting possible $3+1$-D field theory duality between $SU(2)$ gauge theory coupled to one massless adjoint Dirac fermion and the theory of a single massless Dirac fermion augmented by a decoupled topological field theory.

The spreading of entanglement in out-of-equilibrium quantum systems is currently at the center of intense interdisciplinary research efforts involving communities with interests ranging from holography to quantum information. Here we provide a constructive and mathematically rigorous method to compute the entanglement dynamics in a class of “maximally chaotic,” periodically driven, quantum spin chains. Specifically, we consider the so-called “self-dual” kicked Ising chains initialized in a class of separable states and devise a method to compute exactly the time evolution of the entanglement entropies of finite blocks of spins in the thermodynamic limit. Remarkably, these exact results are obtained despite the maximally chaotic models considered: Their spectral correlations are described by the circular orthogonal ensemble of random matrices on all scales. Our results saturate the so-called “minimal cut” bound and are in agreement with those found in the contexts of random unitary circuits with infinite-dimensional local Hilbert space and conformal field theory. In particular, they agree with the expectations from both the quasiparticle picture, which accounts for the entanglement spreading in integrable models, and the minimal membrane picture, recently proposed to describe the entanglement growth in generic systems. Based on a novel “duality-based” numerical method, we argue that our results describe the entanglement spreading from any product state at the leading order in time when the model is nonintegrable.