The systematic diagnosis of band topology enabled by the method of “symmetry indicators” underlies the recent advances in the search for new materials realizing topological crystalline insulators. Such an efficient method has been missing for superconductors because the quasiparticle spectrum in the superconducting phase is not usually available. In this work, we establish symmetry indicators for weak-coupling superconductors that detect nontrivial topology based on the representations of the metallic band structure in the normal phase, assuming a symmetry property of the gap function. We demonstrate the applications of our formulas using examples of tight-binding models and density-functional-theory band structures of realistic materials.

Upcoming searches for the stochastic background of inflationary gravitational waves (GWs) offer the exciting possibility to probe the evolution of our Universe prior to big bang nucleosynthesis. In this spirit, we explore the sensitivity of future GW observations to a broad class of beyond-the-standard-model scenarios that lead to a nonstandard expansion history. We consider a new scalar field whose coherent oscillations dominate the energy density of the Universe at very early times, resulting in a scalar era prior to the standard radiation-dominated era. The imprint of this scalar era on the primordial GW spectrum provides a means to probe well-motivated yet elusive models of particle physics. Our work highlights the complementarity of future GW observatories across the entire range of accessible frequencies.

$\mathrm{MnB}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_4$ has recently been established as an intrinsic antiferromagnetic (AFM) topological insulator—an ideal platform to create quantum anomalous Hall insulator and axion insulator states. We performed comprehensive studies on the structure, nontrivial surface state, and magnetotransport properties of this material. Our results reveal an intrinsic anomalous Hall effect arising from a noncollinear spin structure for the magnetic field parallel to the $c$ axis. We observed negative magnetoresistance under arbitrary field orientation below and above the Néel temperature $\left(T_{\mathrm{N}}\right)$, providing clear evidence for strong spin fluctuation-driven spin scattering in both the AFM and paramagnetic states. Furthermore, we found that the nontrivial surface state opens a large gap $(\sim 85\mathrm{meV})$ even far above $T_{\mathrm{N}}$. Our findings demonstrate that the bulk band structure of $\mathrm{MnB}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_4$ is strongly coupled with the magnetic property and that a net Berry curvature in momentum space can be created in the canted AFM state. In addition, our results imply that the gap opening in the surface states is intrinsic, likely caused by the strong spin fluctuations in this material.

Fracton topological phases host fractionalized topological quasiparticles with restricted mobility, with promising applications to fault-tolerant quantum computation. While a variety of exactly solvable fracton models have been proposed, there is a need for platforms to realize them experimentally. We show that a rich set of fracton phases emerges in interacting Majorana band models whose building blocks are within experimental reach. Specifically, our Majorana constructions overcome a principal obstacle, namely, the implementation of the complicated spin cluster interactions underlying fracton stabilizer codes. The basic building blocks of the proposed constructions include Coulomb blockaded Majorana islands and weak interisland Majorana hybridizations. This setting produces a wide variety of fracton states and promises numerous opportunities for probing and controlling fracton phases experimentally. Our approach also reveals the relation between fracton phases and Majorana fermion codes and further generates a hierarchy of fracton spin liquids.

We study the vibrational spectra and the specific heat of disordered systems using an effective hydrodynamic framework. We consider the contribution of diffusive modes, i.e., the “diffusons,” to the density of states and the specific heat. We prove analytically that these modes provide a constant term to the vibrational density of states $g\left(\omega \right)$. This contribution is dominant at low frequencies, with respect to the Debye propagating modes. We compare our results with numerical simulations data and random matrix theory. Finally, we compute the specific heat and we show the existence of a linear in $T$ scaling $C\left(T\right)\sim cT$ at low temperatures due to the diffusive modes. We analytically derive the coefficient $c$ in terms of the diffusion constant $D$ of the quasilocalized modes and we obtain perfect agreement with numerical data. The linear in $T$ behavior in the specific heat is stronger as the modes are more localized and crosses over to a $T^3$ (Debye) regime at a temperature $T^{*}\sim \sqrt{v^3/D}$, where $v$ is the speed of sound. Our results suggest that the anomalous properties of glasses and disordered systems can be understood effectively within a hyrodynamic approach, which accounts for diffusive quasilocalized modes generated via disorder-induced scattering.

A recent experimental realization of a quantum degenerate gas of ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$ molecules opens up prospects of exploring strong dipolar Fermi gases and many-body phenomena arising in that regime. Here, we derive a mean-field variational approach based on the Wigner function for the description of the ground-state properties of such systems. We show that the stability of dipolar fermions in a general harmonic trap is universal as it only depends on the trap aspect ratios and the dipoles' orientation. We calculate the species-independent stability diagram and the deformation of the Fermi surface (FS) for polarized molecules, whose electric dipoles are oriented along a preferential direction. Compared to atomic magnetic species, the stability of a molecular electric system turns out to strongly depend on its geometry and the FS deformation significantly increases.

The smectic phase shows a layered structure, which is the most fundamental and universal order found in soft materials. However, previous technical limitations made it difficult to fully and microscopically observe the interlayer molecular motions in the smectic phase. We were able to directly measure the interlayer molecular motions by quasielastic scattering spectroscopy using Mössbauer gamma rays for $4^{\prime }-n$-octyl-4-cyanobiphenyl (8CB). From the measured motions, we evaluated the order parameter of the layer structure and explain the macroscopic diffusion coefficient in the microscopic viewpoint. Our methodology can be applied broadly to determine the layer order parameter of various soft materials.

Quantum entanglement may have various origins ranging from solely interaction-driven quantum correlations to single-particle effects. Here, we explore the dependence of entanglement on time-dependent single-particle basis transformations in fermionic quantum many-body systems, thus aiming at isolating single-particle sources of entanglement growth in quench dynamics. Using exact diagonalization methods, for paradigmatic nonintegrable models we compare to the standard real-space cut various physically motivated bipartitions. Moreover, we search for a minimal entanglement basis using local optimization algorithms, which at short to intermediate postquench times yields a significant reduction of entanglement beyond a dynamical Hartree-Fock solution. In the long-time limit, we identify an asymptotic universality of entanglement for weakly interacting systems, as well as a crossover from dominant real-space to momentum-space entanglement in Hubbard models undergoing an interaction quench. Finally, we discuss the relevance of our findings for the development of tensor-network-based algorithms for quantum dynamics.

Percolation on complex networks is used both as a model for dynamics $\mathit{on}$ networks, such as network robustness or epidemic spreading, and as a benchmark for our models $\mathit{of}$ networks, where our ability to predict percolation measures our ability to describe the networks themselves. In many applications, correctly identifying the phase transition of percolation on real-world networks is of critical importance. Unfortunately, this phase transition is obfuscated by the finite size of real systems, making it hard to distinguish finite-size effects from the inaccuracy of a given approach that fails to capture important structural features. Here, we borrow the perspective of smeared phase transitions and argue that observed discrepancies may be due to the complex mesoscopic structure of real networks rather than to finite-size effects only. We support and illustrate this claim by studying real and synthetic networks through the lens of local order parameters, message passing, and local susceptibility. Our results not only shed light on the nature of the percolation transition in complex networks but also provide two important insights on the numerical and analytical tools we use to study them. First, we propose a measure of local susceptibility to better detect both clean and smeared phase transitions by looking at the topological variability of the order parameter. Second, we discuss a shortcoming in state-of-the-art analytical approaches such as message passing, which can detect smeared transitions but not characterize their nature.

The detection of gravitational waves has established a new and very exciting field of astronomy in the past few years. To increase the number of detections and allow observation of a wider range of sources, several future gravitational wave detectors will operate at cryogenic temperatures. Recent investigations of a mirror in one of the cryostats of the Japanese KAGRA detector showed a decrease in reflectivity due to ice growth, induced by residual water molecules moving from the warm to the cold sections of the detector's vacuum system. Based on the optical measurements made in KAGRA, in this paper we calculate the implications of an ice layer on coating thermal noise for the planned European Einstein Telescope. We find coating thermal noise to oscillate, due to periodic reflectivity changes as the ice layer grows. The average coating thermal noise increases significantly over a time of one year with a larger increase at higher temperatures.

A complex conjugation of unitary quantum map is a second-order map (supermap) that maps a unitary operator $U$ to its complex conjugate $U^{*}$. First, we present a deterministic quantum protocol that universally implements the complex conjugation supermap when we are given a blackbox quantum circuit, guaranteed to implement some unitary operation, whose only known description is its dimension. We then discuss the complex conjugation supermap in the context of entanglement theory and derive a conjugation-based expression of the $G$ concurrence. Finally, we present a physical process involving identical fermions from which the complex conjugation protocol is derived as a simulation of the process using qudits.

In quantum computing, the indirect measurement of unitary operators such as the Hadamard test plays a significant role in many algorithms. However, in certain cases, the indirect measurement can be reduced to the direct measurement, where a quantum state is destructively measured. Here, we investigate under what conditions such a replacement is possible and develop a general methodology for trading an indirect measurement with sequential direct measurements. The results can be applied to construct quantum circuits to evaluate the analytical gradient, metric tensor, Hessian, and even higher order derivatives of a parametrized quantum state. Also, we propose a method to measure the out-of-time-order correlator based on the presented protocol. Our protocols can significantly reduce the depth of a quantum circuit by making the controlled operation unnecessary, and thus are suitable for quantum-classical hybrid algorithms on near-term quantum computers.

In this paper we calculate the optical forces and torques caused by the presence of a sizable magneto-optical effect. We find a conservative force proportional to the gradient of the spin density of the light field and an extinction force proportional to the helicity of the light field. The conservative interaction allows for a spin-selective, magnetic field based Stern-Gerlach experiment, capable of differentiating between right and left circular polarizations. We also prove that by using a spinless linearly polarized plane wave, the magneto-optical effect allows for the existence of a permanent nonreciprocal torque, proportional to the intensity of the light field.

The impressive progress in fabricating and controlling superconducting devices for quantum information processing has reached a level where reliable theoretical predictions need to account for quantum correlations that are not captured by the conventional modeling of contemporary quantum computers. This applies particularly to the qubit initialization as the process which crucially limits typical operation times. Here, we employ numerically exact methods to study realistic implementations of a transmon qubit embedded in electromagnetic environments focusing on the most important system-reservoir correlation effects such as the Lamb shift and entanglement. For the qubit initialization we find a fundamental trade-off between speed and accuracy which sets intrinsic constraints in the optimization of future reset protocols. Instead, the fidelities of quantum logic gates can be sufficiently accurately predicted by standard treatments. Our results can be used to accurately predict the performance of specific setups and also to guide future experiments in probing low-temperature properties of qubit reservoirs.

The soft ferroelectric phonon in ${\mathrm{SrTiO}}_3$ observed with optical spectroscopy has an extraordinarily strong spectral weight which is much stronger than expected in the limit of a perfectly ionic compound. This “charged phonon” effect in ${\mathrm{SrTiO}}_3$ is caused by the close-to-covalent character of the Ti-O ionic bond and implies a strong coupling between the soft ferroelectric phonon and the interband transitions across the 3-eV gap of ${\mathrm{SrTiO}}_3$. We demonstrate that this coupling leads, in addition to the charged phonon effect, to a pairing interaction involving the exchange of two transverse optical phonons. This process owes its relevance to the strong electron-phonon coupling and to the fact that the interaction mediated by a single transverse optical phonon vanishes at low electron density. We use the experimental soft phonon spectral weight to calculate the strength of the biphonon mediated pairing interaction in the electron-doped material and show that it is of the correct magnitude when compared to the experimental value of the superconducting critical temperature. Biphonon exchange is therefore an important pairing mechanism at low doping, and may be the key to understanding the occurrence of superconductivity in doped ${\mathrm{SrTiO}}_3$ and other low electron density materials.

We show that the mesoscopic incommensurate ${\mathbb{Z}}_2$ vortex crystals proposed for layered triangular anisotropic magnets can be most saliently identified by two distinctive signatures in dynamical spin response experiments: the presence of pseudo-Goldstone phononlike modes at low frequencies $\omega$, associated with the collective vibrations of the vortex cores, and a characteristic multiscattered intensity profile at higher $\omega$, arising from a large number of Bragg reflections and magnon band gaps. These are direct fingerprints of the large vortex sizes and magnetic unit cells and the solitonic spin profile around the vortex cores.

We introduce a complete physical model for the single-particle electronic structure of twisted bilayer graphene (TBLG), which incorporates the crucial role of lattice relaxation. Our model, based on $k·p$ perturbation theory and openly available, combines the accuracy of density functional theory calculations through effective tight-binding Hamiltonians with the computational efficiency and complete control of the twist angle offered by continuum models. The inclusion of relaxation significantly changes the band structure at the first magic-angle twist corresponding to flat bands near the Fermi level (the “low-energy” states), and eliminates the appearance of a second magic-angle twist. We show that minimal models for the low-energy states of TBLG can be easily modified to capture the changes in electronic states as a function of twist angle.

In a weakly collisional, low-electron-beta plasma, large-scale Alfvén turbulence transforms into inertial kinetic-Alfvén turbulence at scales smaller than the ion microscale (gyroscale or inertial scale). We propose that at such kinetic scales, the nonlinear dynamics tends to organize turbulent eddies into thin current sheets, consistent with the existence of two conserved integrals of the ideal equations, energy and helicity. The formation of strongly anisotropic structures is arrested by the tearing instability that sets a critical aspect ratio of the eddies at each scale $a$ in the plane perpendicular to the guide field. This aspect ratio is defined by the balance of the eddy turnover rate and the tearing rate, and varies from ${(d_e/a)}^{1/2}$ to $d_e/a$ depending on the assumed profile of the current sheets. The energy spectrum of the resulting turbulence varies from $k^{-8/3}$ to $k^{-3}$, and the corresponding spectral anisotropy with respect to the strong background magnetic field from $k_z\lesssim k_{\perp }^{2/3}$ to $k_z\lesssim k_{\perp }$.

We present femtosecond hard x-ray diffraction experiments that study the effect of photodoping on the perovskite ${\mathrm{EuTiO}}_3$. We observe an ultrafast transient increase of reflection intensities that are directly related to the antiferrodistortive rotation of the oxygen octahedra. This increase relates directly to an increase of the order parameter associated with a purely structural phase transition that is opposite to the behavior of increasing the materials temperature. First-principles calculations show that the creation of electron-hole pairs leads to changes in the vibrational potential that is consistent with an increase of the order parameter. The order parameter increase can be understood from an ultrafast charge-transfer-induced reduction of the Goldschmidt tolerance factor, which is a fundamental control parameter for the properties of perovskites.

Magnetic energy transfer from small to large scales due to successive magnetic island coalescence is investigated. A solvable analytical model is introduced and shown to correctly capture the evolution of the main quantities of interest, as borne out by direct numerical simulations. Magnetic reconnection is identified as the key mechanism enabling the inverse transfer, and setting its properties: Magnetic energy decays as ${\tilde{t}}^{-1}$, where $\tilde{t}$ is time normalized to the (appropriately defined) reconnection timescale, and the correlation length of the field grows as ${\tilde{t}}^{1/2}$. The magnetic energy spectrum is self-similar, and evolves as $\propto {\tilde{t}}^{-3/2}{k}^{-2}$, where the $k$ dependence is imparted by the formation of thin current sheets.