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The entanglement entropy in many gapless quantum systems receives a contribution from the corners in the entangling surface in 2+1d, which is characterized by a universal function α(θ) depending on the opening angle θ, and contains pertinent low energy information. For conformal field theories (CFTs), the leading expansion coefficient in the smooth limit θ → &#960 yields the stress tensor two-point function coefficient CT. Little is known about α(θ) beyond that limit. Here, we show that the next term in the smooth limit expansion contains information beyond the two- and three-point correlators of the stress tensor. We conjecture that it encodes four-point data, making it much richer. Further, we establish strong constraints on this and higher-order smooth-limit coefficients. We also show that α(θ) is lower-bounded by a nontrivial function multiplied by the central charge CT, e.g., α(π/2) &#8937 (π²ln2)CT/6. This bound for 90-degree corners is nearly saturated by all known results, including recent numerics for the interacting Wilson-Fisher quantum critical points (QCPs). A bound is also given for the Rényi entropies. We illustrate our findings using O(N) QCPs, free boson and Dirac fermion CFTs, strongly coupled holographic ones, and other models. Exact results are also given for Lifshitz quantum critical points, and for conical singularities in 3 + 1d. [ABSTRACT FROM AUTHOR]

Quantum critical (QC) phase transitions generally lead to the absence of quasiparticles. The resulting correlated quantum fluid, when thermally excited, displays rich universal dynamics. We establish nonperturbative constraints on the linear-response dynamics of conformal QC systems at finite temperature, in spatial dimensions above 1. Specifically, we analyze the large frequency or momentum asymptotics of observables, which we use to derive powerful sum rules and inequalities. The general results are applied to the O(N) Wilson-Fisher fixed point, describing the QC Ising model when N = 1. We focus on the order parameter and scalar susceptibilities, and the dynamical shear viscosity. Connections to simulations, experiments, and gauge theories are made. [ABSTRACT FROM AUTHOR]

Weyl semimetals (WSMs) constitute a 3D phase with linearly dispersing Weyl excitations at low energy, which lead to unusual electrodynamic responses and open Fermi arcs on boundaries. We derive a simple criterion to identify and characterize WSMs in an interacting setting using the exact electronic Green's function at zero frequency, which defines a topological Bloch Hamiltonian. We apply this criterion by numerically analyzing, via cluster and other methods, interacting lattice models with and without time-reversal symmetry. We identify various mechanisms for how interactions move and renormalize Weyl fermions. Our methods remain valid in the presence of long-ranged Coulomb repulsion. Finally, we introduce a WSM-like phase for which our criterion breaks down due to fractionalization: the charge-carrying Weyl quasiparticles are orthogonal to the electron. [ABSTRACT FROM AUTHOR]

We extend the range of possibilities for the charge response in the quantum critical regime in 2 + ID using holography, and compare them with field theory and recent quantum Monte Carlo results. We show that a family of (infinitely many) higher derivative terms in the gravitational bulk leads to behavior far richer than what was previously obtained. For example, we prove that the conductivity becomes unbounded, undermining previously obtained constraints. We further find a nontrivial and infinite set of theories that have a self-dual conductivity. Particle-vortex or S duality plays a key role; notably, it maps theories with a finite number of bulk terms to ones with an infinite number. Many properties, such as sum rules and stability conditions, are proven. [ABSTRACT FROM AUTHOR]

We study the charge response of conformal field theories (CFTs) at nonzero temperature in 2+1 dimensions using the anti-de Sitter (AdS)/CFT correspondence. A central role is played by the quasinormal modes (QNMs), specifically, the poles and zeros of the current correlators. We generalize our recent study of the QNMs of the ac charge conductivity to include momentum dependence. This sheds light on the various excitations in the CFT. We begin by discussing the R-current correlators of the N=8 SU(Nc) super-Yang-Mills theory at its conformal fixed point using holography. For instance, transitions in the QNM spectrum as a function of momentum clearly identify "hydrodynamic-to-relativistic" crossovers. We then extend our study to include four-derivative terms in the gravitational description allowing us to study more generic charge response as well as the role of the S duality, which plays a central role in understanding the correlators. The presence of special purely damped QNMs can lead to new behavior, distinct from what occurs in the aforementioned gauge theory. We also extend previous conductivity sum rules to finite momentum and discuss their interpretation in the gravity picture. A comparison is finally made with the conformal fixed point of the vector O(N) model in the large-N limit. [ABSTRACT FROM AUTHOR]

We study the finite temperature and magnetic-field phase diagram of electrons on the pyrochlore lattice subject to a local repulsion as a model for the pyrochlore iridates. We provide the most general symmetry-allowed Hamiltonian, including next-nearest-neighbor hopping, and relate it to a Slater-Koster-based Hamiltonian for the iridates. It captures Lifshitz and/or thermal transitions among several phases, such as metals, semimetals, topological insulators and Weyl semimetals, and gapped antiferromagnets with different orders. Our results on the charge conductivity, both dc and optical, Hall coefficient, magnetization, and susceptibility show good agreement with recent experiments and provide new predictions. As such, our effective model sheds light on the pyrochlore iridates in a unified way. [ABSTRACT FROM AUTHOR]

We discuss the universal-transport signatures near a zero-temperature continuous Mott transition between a Fermi liquid and a quantum spin liquid in two spatial dimensions. The correlation-driven transition occurs at fixed filling and involves fractionalization of the electron: upon entering the spin liquid, a Fermi surface of neutral spinons coupled to an internal gauge field emerges. We present a controlled calculation of the value of the zero-temperature universal resistivity jump predicted to occur at the transition. More generally, the behavior of the universal scaling function that collapses the temperature- and pressure-dependent resistivity is derived, and is shown to bear a strong imprint of the emergent gauge fluctuations. We further predict a universal jump of the thermal conductivity across the Mott transition, which derives from the breaking of conformal invariance by the damped gauge field, and leads to a violation of the Wiedemann-Franz law in the quantum critical region. A connection to the quasitriangular organic salts is made, where such a transition might occur. Finally, we present some transport results for the pure rotor O(N) conformal field theory. [ABSTRACT FROM AUTHOR]

We study charge transport of quantum critical points described by conformal field theories in 2 + 1 space-time dimensions. The transport is described by an effective field theory on an asymptotically anti-de Sitter space-time, expanded to fourth order in spatial and temporal gradients. The presence of a horizon at nonzero temperatures implies that this theory has quasinormal modes with complex frequencies. The quasinormal modes determine the poles and zeros of the conductivity in the complex frequency plane, and so fully determine its behavior on the real frequency axis, at frequencies both smaller and larger than the absolute temperature. We describe the role of particle-vortex or S duality on the conductivity, specifically how it maps poles to zeros and vice versa. These analyses motivate two sum rules obeyed by the quantum critical conductivity: the holographic computations are the first to satisfy both sum rules, while earlier Boltzmann-theory computations satisfy only one of them. Finally, we compare our results with the analytic structure of the O(N) model in the large-N limit, and other CFTs. [ABSTRACT FROM AUTHOR]

Topological phases of quantum matter defy characterization by conventional order parameters but can exhibit a quantized electromagnetic response and/or protected surface states. We examine such phe-nomena in a model for three-dimensional correlated complex oxides, the pyrochlore iridates. The model realizes interacting topological insulators, with and without time-reversal symmetry, and topological Weyl semimetals. We use cellular dynamical mean-field theory, a method that incorporates quantum many-body effects and allows us to evaluate the magnetoelectric topological response coefficient in correlated systems. This invariant is used to unravel the presence of an interacting axion insulator absent within a simple mean-field study. We corroborate our bulk results by studying the evolution of the topological boundary states in the presence of interactions. Consequences for experiments and for the search for correlated materials with symmetry-protected topological order are given. [ABSTRACT FROM AUTHOR]

We construct a model for interacting electrons with strong spin-orbit coupling in the pyrochlore iridates. We establish the importance of the direct hopping process between the Ir atoms, and use the relative strength of the direct and indirect hopping as a generic tuning parameter to study the correlation effects across the iridates family. We predict quantum phase transitions between conventional and/or topologically nontrivial phases. At weak coupling, we find topological insulator and metallic phases. As one increases the interaction strength. various magnetic orders emerge. The topological Weyl semimetal phase is found to be realized in these different orders, one of them being the all-in/all-out pattern. Our findings establish the possible magnetic ground states for the iridates and suggest the generic presence of the Weyl semimetal phase in correlated magnetic insulators on the pyrochlore lattice. We discuss the implications for existing and future experiments. [ABSTRACT FROM AUTHOR]

The entanglement entropy (EE) has emerged as an important window into the structure of complex quantum states of matter. We analyze the universal part of the EE for gapless systems on tori in 2D and 3D, denoted by χ. Focusing on scale-invariant systems, we derive general nonperturbative properties for the shape dependence of χ and reveal surprising relations to the EE associated with corners in the entangling surface. We obtain closed-form expressions for χ in 2D and 3D within a model that arises in the study of conformal field theories (CFTs), and we use them to obtain Ansätze without fitting parameters for the 2D and 3D free boson CFTs. Our numerical lattice calculations show that the Ansätze are highly accurate. Finally, we discuss how the torus EE can act as a fingerprint of exotic states such as gapless quantum spin liquids, e.g., Kitaev's honeycomb model. [ABSTRACT FROM AUTHOR]

We compute the entanglement entropy of the Wilson-Fisher conformal field theory (CFT) in 2+1 dimensions with O(N) symmetry in the limit of large N for general entanglement geometries. We show that the leading large-N result can be obtained from the entanglement entropy of N Gaussian scalar fields with their mass determined by the geometry. For a few geometries, the universal part of the entanglement entropy of the Wilson-Fisher CFT equals that of a CFT of N massless scalar fields. However, in most cases, these CFTs have a distinct universal entanglement entropy even at N=∞. Notably, for a semi-infinite cylindrical region it scales as N0 in the Wilson-Fisher theory, in stark contrast to the N-linear result of the Gaussian fixed point. [ABSTRACT FROM AUTHOR]

Topological states of electrons present new avenues to explore the rich phenomenology of correlated quantum matter. Topological insulators (TIs) in particular offer an experimental setting to study novel quantum critical points (QCPs) of massless Dirac fermions, which exist on the sample's surface. Here, we obtain exact results for the zero- and finite-temperature optical conductivity at the semimetal-superconductor QCP for these topological surface states. This strongly interacting QCP is described by a scale invariant theory with emergent supersymmetry, which is a unique symmetry mixing bosons and fermions. We show that supersymmetry implies exact relations between the optical conductivity and two otherwise unrelated properties: the shear viscosity and the entanglement entropy. We discuss experimental considerations for the observation of these signatures in TIs. [ABSTRACT FROM AUTHOR]

We study the contribution to the entanglement entropy of (2+1)-dimensional conformal field theories (CFTs) coming from a sharp corner in the entangling surface. This contribution is encoded in a function a(θ) of the corner opening angle, and was recently proposed as a measure of the degrees of freedom in the underlying CFT. We show that the ratio a(θ)/CT, where CT is the central charge in the stress tensor correlator, is an almost universal quantity for a broad class of theories including various higher-curvature holographic models, free scalars, and fermions, and Wilson-Fisher fixed points of the O(N) models with N=1,2,3. Strikingly, the agreement between these different theories becomes exact in the limit θ→π, where the entangling surface approaches a smooth curve. We thus conjecture that the corresponding ratio is universal for general CFTs in three dimensions. [ABSTRACT FROM AUTHOR]

Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultracold atoms. We investigate such nontrivial quantum dynamics in a different setting: a spin-1 bilinear-biquadratic chain. It has a solvable entangled ground state, but a gapless excitation spectrum that is poorly understood. By using large-scale density matrix renormalization group simulations, we find that the lowest excitations have a dynamical exponent z that varies from 2 to 3.2 as we vary a coupling in the Hamiltonian. We find an additional gapless mode with a continuously varying exponent 2≤z<2.7, which establishes the presence of multiple dynamics. In order to explain these striking properties, we construct a continuum wave function for the ground state, which correctly describes the correlations and entanglement properties. We also give a continuum parent Hamiltonian, but show that additional ingredients are needed to capture the excitations of the chain. By using an exact mapping to the nonequilibrium dynamics of a classical spin chain, we find that the large dynamical exponent is due to subdiffusive spin motion. Finally, we discuss the connections to other spin chains and to a family of quantum critical models in two dimensions. [ABSTRACT FROM AUTHOR]

We compute the nonzero temperature conductivity of conserved flavor currents in conformal field theories (CFTs) in 2+1 space-time dimensions. At frequencies much greater than the temperature, ℏω≫kBT, the ω dependence can be computed from the operator product expansion (OPE) between the currents and operators, which acquire a nonzero expectation value at T>0. Such results are found to be in excellent agreement with quantum Monte Carlo studies of the O(2) Wilson-Fisher CFT. Results for the conductivity and other observables are also obtained in vector 1/N expansions. We match these large ω results to the corresponding correlators of holographic representations of the CFT: the holographic approach then allows us to extrapolate to small ℏω/(kBT). Other holographic studies implicitly only used the OPE between the currents and the energy-momentum tensor, and this yields the correct leading large ω behavior for a large class of CFTs. However, for the Wilson-Fisher CFT, a relevant “thermal” operator must also be considered, and then consistency with the Monte Carlo results is obtained without a previously needed ad hoc rescaling of the T value. We also establish sum rules obeyed by the conductivity of a wide class of CFTs. [ABSTRACT FROM AUTHOR]

We study high-frequency response functions, notably the optical conductivity, in the vicinity of quantum critical points (QCPs) by allowing for both detuning from the critical coupling and finite temperature. We consider general dimensions and dynamical exponents. This leads to a unified understanding of sum rules. In systems with emergent Lorentz invariance, powerful methods from quantum field theory allow us to fix the high-frequency response in terms of universal coefficients. We test our predictions analytically in the large-N O(N) model and using the gauge-gravity duality and numerically via quantum Monte Carlo simulations on a lattice model hosting the interacting superfluid-insulator QCP. In superfluid phases, interacting Goldstone bosons qualitatively change the high-frequency optical conductivity and the corresponding sum rule. [ABSTRACT FROM AUTHOR]

A quantum critical (QC) fluid exhibits universal subleading corrections to the area law of its entanglement entropies. In two dimensions, when the partition involves a corner of angle θ, the subleading term is logarithmic with coefficient aα(θ) for the α-Rényi entropy. In the smooth limit θ→π,a1(θ) yields the central charge of the stress tensor when the QC point is described by a conformal field theory (CFT). For general Rényi indices and angles, aα(θ) is richer and few general results exist. We study aα(θ) focusing on two benchmark CFTs, the free Dirac fermion and boson. We perform numerical lattice calculations to obtain high precision results in θ,α regimes hitherto unexplored. We derive field theory estimates for aα(θ), including exact results, and demonstrate an excellent quantitative match with our numerical calculations. We also develop and test strong lower bounds, which apply to both free and interacting QC systems. Finally, we comment on the near collapse of aα(θ) for various theories, including interacting O(N) models. [ABSTRACT FROM AUTHOR]

The entanglement entropy (EE) encodes key properties of quantum many-body systems. It is usually calculated for subregions of finite volume (or area in 2D). Here, we study the EE of skeletal regions that have no volume, such as a line in 2D. We show that skeletal entanglement displays new behavior compared with its bulk counterpart, and leads to distinct universal quantities. We provide nonperturbative bounds for the skeletal area-law coefficient of a large family of quantum states. We then explore skeletal scaling for the toric code, conformal bosons and Dirac fermions, Lifshitz critical points, and Fermi liquids. We discover signatures including skeletal topological EE, novel corner terms, and strict area-law scaling for metals. These findings suggest that skeletal entropy serves as a measure for the range of entanglement. Finally, we outline open questions relating to other systems and measures such as the logarithmic negativity.