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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.

Understanding the fluctuations of observables is one of the main goals in science, be it theoretical or experimental, quantum or classical. We investigate such fluctuations in a subregion of the full system, focusing on geometries with sharp corners. We report that the angle dependence is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We exemplify our findings with fractional quantum Hall states, topological insulators, scale invariant quantum critical theories, and metals. We suggest experimental tests, and anticipate that our findings can be generalized to other spatial dimensions or geometries. In addition, we highlight the similarities of the fluctuation shape dependence with findings relating to quantum entanglement measures., (© 2022. The Author(s).)

The experimental discovery of the fractional Hall conductivity in two-dimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange statistics. These anyons are usually studied deep inside an insulating topological phase. It is natural to ask whether such fractionalization can be detected more broadly, say near a phase transition from a conventional to a topological phase. To answer this question, we study a strongly correlated quantum phase transition between a topological state, called a [Formula: see text] quantum spin liquid, and a conventional superfluid using large-scale quantum Monte Carlo simulations. Our results show that the universal conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. Moreover, a dynamically self-dual optical conductivity emerges at low temperatures above the transition point, indicating the presence of the elusive vison particles. Our study opens the door for the experimental detection of anyons in a broader regime, and has ramifications in the study of quantum materials, programmable quantum simulators, and ultra-cold atomic gases. In the latter case, we discuss the feasibility of measurements in optical lattices using current techniques., (© 2021. The Author(s).)

Quantum spin liquids (QSLs) are exotic phases of matter that host fractionalized excitations. It is difficult for local probes to characterize QSL, whereas quantum entanglement can serve as a powerful diagnostic tool due to its nonlocality. The kagome antiferromagnetic Heisenberg model is one of the most studied and experimentally relevant models for QSL, but its solution remains under debate. Here, we perform a numerical Aharonov-Bohm experiment on this model and uncover universal features of the entanglement entropy. By means of the density matrix renormalization group, we reveal the entanglement signatures of emergent Dirac spinons, which are the fractionalized excitations of the QSL. This scheme provides qualitative insights into the nature of kagome QSL and can be used to study other quantum states of matter. As a concrete example, we also benchmark our methods on an interacting quantum critical point between a Dirac semimetal and a charge-ordered phase.

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.

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.

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.

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)/C(T), where C(T) 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.

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.

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.

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 phenomena 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.