We present a study of the magnetic-flux evolution in the magnetic superconductor $\mathrm{RbEuF}{\mathrm{e}}_4\mathrm{A}{\mathrm{s}}_4$ performed using magneto-optical imaging and magnetization measurements during field cooling and warming and magnetic field cycling at temperatures above and below the magnetic transition point, $T_m$. The vortex patterns emerging at $T\lesssim T_m$ reveal that the Eu-spin subsystem serves as an internal pump of the magnetic flux while the superconducting critical current controls the delivery of magnetic-flux quanta into the bulk. The interplay of magnetic susceptibility amplifying the magnetic induction and vortex pinning attenuating the magnetic-flux entry results in a field- and temperature-dependent critical state that emulates a paramagnetic Meissner effect. The observed vortex dynamics corresponds to a nontrivial spatial current distribution and yields a self-consistent inhomogeneous enhancement of the sample magnetization.

We consider the class of dual-unitary quantum circuits in $1+1$ dimensions and introduce a notion of “solvable” matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size $\ell$ reaches infinite temperature after a time $t\propto \ell$, irrespective of the presence of conserved quantities, the light cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of nonsolvable initial mixed states depending on one real parameter $\beta$, which, as $\beta$ is varied from zero to infinity, interpolate between the infinite-temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of $\beta$, and highlight the differences from the case of solvable MPSs.

We present microscopic definitions of both the $F$ symbol and $R$ symbol—two pieces of algebraic data that characterize anyon excitations in $\left(2+1\right)$-dimensional systems. An important feature of our definitions is that they are operational; that is, they provide concrete procedures for computing these quantities from microscopic models. In fact, our definitions, together with known results, provide a way to extract a complete set of anyon data from a microscopic model, at least in principle. We illustrate our definitions by computing the $F$ symbol and $R$ symbol in several exactly solvable lattice models and edge theories. We also show that our definitions of the $F$ symbol and $R$ symbol satisfy the pentagon and hexagon equations, thereby providing a microscopic derivation of these fundamental constraints.

We measure the magnetoconductance through a micron-sized quantum dot hosting about 500 electrons in the quantum Hall regime. In the Coulomb blockade, when the island is weakly coupled to source and drain contacts, edge reconstruction at filling factors between 1 and 2 in the dot leads to the formation of two compressible regions tunnel coupled via an incompressible region of filling factor $\nu =1$. We interpret the resulting conductance pattern in terms of a phase diagram of stable charge in the two compressible regions. Increasing the coupling of the dot to source and drain, we realize a Fabry-Pérot quantum Hall interferometer, which shows an interference pattern strikingly similar to the phase diagram in the Coulomb blockade regime. We interpret this experimental finding using an empirical model adapted from the Coulomb-blockaded to the interferometer case. The model allows us to relate the observed abrupt jumps of the Fabry-Pérot interferometer phase to a change in the number of bulk quasiparticles. This opens up an avenue for the investigation of phase shifts due to (fractional) charge redistributions in future experiments on similar devices.

We present an extension of the tunneling theory for scanning tunneling microscopy (STM) to include different types of electron-vibrational couplings responsible for inelastic contributions to the tunnel current in the strong-coupling limit. It allows for a better understanding of more complex scanning tunneling spectra of molecules on a metallic substrate in separating elastic and inelastic contributions. The starting point is the exact solution of the spectral functions for the electronically active local orbitals in the absence of the STM tip. This includes electron-phonon coupling in the coupled system comprising the molecule and the substrate to arbitrary order including the antiadiabatic strong-coupling regime as well as the Kondo effect on a free-electron spin of the molecule. The tunneling current is derived in second order of the tunneling matrix element which is expanded in powers of the relevant vibrational displacements. We use the results of an ab initio calculation for the single-particle electronic properties as an adapted material-specific input for a numerical renormalization group approach for accurately determining the electronic properties of a 1,4,5,8-naphthalene-tetracarboxylic acid dianhydride molecule on Ag(111) as a challenging sample system for our theory. Our analysis shows that the mismatch between the ab initio many-body calculation of the tunnel current in the absence of any electron-phonon coupling to the experimental scanning tunneling spectra can be resolved by including two mechanisms: (i) a strong unconventional Holstein term on the local substrate orbital leads to the reduction of the Kondo temperature and (ii) a further electron-vibrational coupling to the tunneling matrix element is responsible for inelastic steps in the $dI/dV$ curve at finite frequencies.

We report on thermal and optically driven transitions between the commensurate (C) and incommensurate (IC) charge-density wave (CDW) phases of $1T-\mathrm{TaS}{\mathrm{e}}_2$. Optical excitation results in suppression of the C-CDW on a subpicosecond timescale. The optically driven C to IC transition involves a short-lived (∼1 ps) unreconstructed phase. Nucleation of an IC phase stacking order is observed already at ∼4 ps following photoexcitation. The short timescales involved in establishing the stacking order implies that the nucleation of the IC phase is influenced by the local geometry of the adjacent layers such that the stacking direction of the C phase determines the stacking direction of the IC phase. From this follows that the nucleation of the IC-CDW is inherently three dimensional (3D). We observe the activation of a coherent shear mode in the optically driven transitions to the transiently stabilized unreconstructed phase. The activation mechanism starts with a rapid lifting of the periodic lattice distortions (PLD) of the Ta sublattice which results in formation of local transient velocity disparities in the Se sublattice. The local differences in Se-phonon amplitudes result in noncompensated shear forces between the layers. This is an example of a multistep coherent launching mechanism. The energy of the optically excited electronic state dissipates energy into modes of the PLD through strong electron-phonon coupling. The rapid suppression of the PLD launches the third step, a coherent vibrational shear mode with low dissipation. The results highlight the importance in considering the 3D nature of the CDWs in the analysis of both structure and dynamics in transition-metal dichalcogenides.

Large electromechanical effects in relaxor ferroelectrics are generally attributed to the collective response of an ensemble of correlated, nanometer-sized polar structures induced by chemical and charge disorder. Here, we study finite-size effects on such polar order (i.e., how it evolves when sample dimensions approach the polarization correlation length) in 7–70-nm-thick films of the relaxor ferroelectric ${\text{PbSc}}_{\text{0}.5}{\text{Ta}}_{\text{0}.5}{\text{O}}_{\text{3}}$. Temperature-dependent polarization studies reveal a linear suppression of the polarization and nonlinearity associated with relaxor order as the film thickness decreases to $\approx 30$ nm. Below this thickness, however, the suppression rapidly accelerates, and polarization is completely absent by film thicknesses of $\approx 7$ nm, despite the continued observation of a broad peak in dielectric permittivity and frequency dispersion. Diffuse-scattering measurements reveal the diffuse-scattering symmetry, and analysis suggests the films have a polarization correlation length of $\approx 23$ nm. Taken together, it is apparent that reduction of sample size and the resulting distribution of polar structures drive suppression and eventual quenching of the electrical response of relaxors, which may be attributed to increasing dipole-dipole and dipole-interface interactions.

We present a theory of the entanglement transition tuned by measurement strength in qudit chains evolved by random unitary circuits and subject to either weak or random projective measurements. The transition can be understood as a nonanalytic change in the amount of information extracted by the measurements about the initial state of the system, quantified by the Fisher information. To compute the von Neumann entanglement entropy $S$ and the Fisher information $\mathcal{F}$, we apply a replica method based on a sequence of quantities ${\tilde{S}}^{\left(n\right)}$ and ${\mathcal{F}}^{\left(n\right)}$ that depend on the $n\mathrm{th}$ moments of density matrices and reduce to $S$ and $\mathcal{F}$ in the limit $n\to 1$. These quantities with $n\ge 2$ are mapped to free energies of a classical spin model with $n!$ internal states in two dimensions with specific boundary conditions. In particular, ${\tilde{S}}^{\left(n\right)}$ is the excess free energy of a domain wall terminating on the top boundary, and ${\mathcal{F}}^{\left(n\right)}$ is related to the magnetization on the bottom boundary. Phase transitions occur as the spin models undergo ordering transitions in the bulk. Taking the limit of large local Hilbert space dimension $q$ followed by the replica limit $n\to 1$, we obtain the critical measurement probability $p_c=1/2$ and identify the transition as a bond percolation in the 2D square lattice in this limit. Finally, we show there is no phase transition if the measurements are allowed in an arbitrary nonlocal basis, thereby highlighting the relation between the phase transition and information scrambling. We establish an explicit connection between the entanglement phase transition and the purification dynamics of a mixed state evolution and discuss implications of our results to experimental observations of the transition and simulability of quantum dynamics.

We investigate the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. Using a replica approach, we map the calculation of the entanglement entropies in such circuits onto a two-dimensional statistical-mechanics model. In this language, the area- to volume-law entanglement transition can be interpreted as an ordering transition in the statistical-mechanics model. We derive the general scaling properties of the entanglement entropies and mutual information near the transition using conformal invariance. We analyze in detail the limit of infinite on-site Hilbert space dimension in which the statistical-mechanics model maps onto percolation. In particular, we compute the exact value of the universal coefficient of the logarithm of subsystem size in the $n\mathrm{th}$ Rényi entropies for $n\ge 1$ in this limit using relatively recent results for the conformal field theory describing the critical theory of two-dimensional (2D) percolation, and we discuss how to access the generic transition at finite on-site Hilbert space dimension from this limit, which is in a universality class different from 2D percolation. We also comment on the relation to the entanglement transition in random tensor networks, studied previously in Vasseur et al. [Phys. Rev. B 100, 134203 (2019)].

Wigner crystals are prime candidates for the realization of regular electron lattices under minimal requirements on external control and electronics. However, several technical challenges have prevented their detailed experimental investigation and applications to date. We propose an implementation of two-dimensional electron lattices for quantum simulation of Ising spin systems based on self-assembled Wigner crystals in transition-metal dichalcogenides. We show that these semiconductors allow for minimally invasive all-optical detection schemes of charge ordering and total spin. For incident light with optimally chosen beam parameters and polarization, we predict a strong dependence of the transmitted and reflected signals on the underlying lattice periodicity, thus revealing the charge order inherent in Wigner crystals. At the same time, the selection rules in transition-metal dichalcogenides provide direct access to the spin degree of freedom via Faraday rotation measurements.

Recently, we proposed a way to engineer a flexible acoustomechanical coupling between the center-of-mass motion of an isolated micromagnet and one of its internal acoustic phonons by using a magnon as a passive mediator [C. Gonzalez-Ballestero, J. Gieseler, and O. Romero-Isart, Phys. Rev. Lett. 124, 093602 (2020)]. In our approach, the coupling is enabled by the strong magnetoelastic interaction between magnons and acoustic phonons which originates from the small particle size. Here, we substantially extend our previous work. First, we provide the full theory of the quantum acoustomagnonic interaction in small micromagnets and analytically calculate the magnon-phonon coupling rates. Second, we fully derive the acoustomechanical Hamiltonian presented in Gonzalez-Ballestero et al. Finally, we extend our previous results for the fundamental acoustic mode to higher-order modes. Specifically, we show the cooling of the center-of-mass motion with a range of internal acoustic modes. Additionally, we derive the power spectral densities of the center-of-mass motion which allow us to probe the same acoustic modes.

The pyrochlore iridate ${\mathrm{In}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ is a $J_{\mathrm{eff}}=\frac{1}{2}$ Mott insulator with frustrated magnetism. Despite the large trigonal distortion, only a small admixture of $J_{\mathrm{eff}}=\frac{3}{2}$ component in the $J_{\mathrm{eff}}=\frac{1}{2}$ bands is observed as compared with other pyrochlore iridates $A_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ ($A$ = trivalent cation). We argue that the reduced intersite hopping between the $J_{\mathrm{eff}}=\frac{1}{2}$ and the $J_{\mathrm{eff}}=\frac{3}{2}$ manifold, due to the large trigonal distortion and the covalent character of In-O bonds, plays a predominant role in the distinct behavior of ${\mathrm{In}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$. Such effect of the intersite hopping should not be dismissed in the local physics of $J_{\mathrm{eff}}=\frac{1}{2}$ Mott insulators.

When nanometric metal structures are illuminated with light, large optical near fields arise. These fields are even further enhanced when two nanometer-sized structures are brought in nanometric distance. Then the individual near fields of the structures couple. Measuring the coupled optical near fields directly is hard. Here we demonstrate an scanning tunneling microscope–based setup which allows us to probe the coupling of optical near fields from two nanometer-sharp metal needles facing each other. By measuring the emitted photocurrent as a function of the gap distance, we retrieve the peak fields at the tip apices. The comparison to optical near-field simulations shows that large field enhancement of 15.9 is present at the tip apex. This is an enhancement 4-times larger compared to the individual nanotip. The demonstrated sensitivity of the coupling on the gap size is of large interest for future applications in ultrafast near-field microscopy.

High coercivity magnets are an important resource for renewable energy, electric vehicles, and memory technologies. Most hard magnetic materials incorporate rare earths such as neodymium and samarium, but concerns about the environmental impact and supply stability of these materials are prompting research into alternatives. Here, we present a hybrid bilayer of cobalt and the nanocarbon molecule ${\text{C}}_{60}$ which exhibits significantly enhanced coercivity with minimal reduction in magnetization. We demonstrate how this anisotropy enhancing effect cannot be described by existing models of molecule-metal magnetic interfaces. We outline a form of anisotropy, arising from asymmetric magnetoelectric coupling in the metal-molecule interface. Because this phenomenon arises from $\pi \text{−}d$ hybrid orbitals, we propose calling this effect $\pi$-anisotropy. While the critical temperature of this effect is currently limited by the rotational degree of freedom of the chosen molecule, ${\text{C}}_{60}$, we describe how surface functionalization would allow for the design of room-temperature, carbon-based hard magnetic films.

Most of the $\mathrm{Y}$-type hexaferrite materials family hosts a variety of magnetic structures as a ground state, and a multiferroic phase, termed the FE3 phase, can be stabilized by applying a magnetic ($H$) field. This phase has recently been found to persist even after removing the $H$ field. The magnetoelectric properties of $\mathrm{Y}$-type hexaferrites are dominated mainly by the FE3 phase via the spin-driven electric polarization ($P$). In the present study, the stability of the competing magnetic phases was investigated in $\mathrm{Y}$-type hexaferrite compounds ${\mathrm{Ba}}_{2-y}{\mathrm{Sr}}_y{\mathrm{Co}}_2{\mathrm{Fe}}_{12-x}{\mathrm{Al}}_x{\mathrm{O}}_{22}$ ($x=0.9$) with Sr-doping levels of $y=0.8$, 1.0, and 1.2. Combining the measurements of magnetization ($M$), $P$, and neutron diffraction, we revealed the $H-T$ magnetic phase diagrams. It was found that the stability of the multiferroic FE3 phase is greatly improved in the Sr-rich compound. At room temperature, the FE3 phase in the Ba-rich compound is fragile against the removal of the $H$ field, while it is robust in the Sr-rich compound, even for zero-field cooling. We also investigated the interplay between $P$ and $M$ in the FE3 phase in the presence of both the high electric ($E$) and $H$ fields, and we found that the coupling between $P$ and $M$ depends on the energy barrier separating the two magnetoelectric states. The energy barrier gradually decreases as the temperature is increased, leading to a reduction of the $P-M$ coupling.

Motivated by the recent observation of superconductivity in strontium-doped ${\mathrm{NdNiO}}_2$, we study the superconducting instabilities in this system from various vantage points. Starting with first-principles calculations, we construct two distinct tight-binding models, a simpler single-orbital as well as a three-orbital model, both of which capture the key low-energy degrees of freedom to varying degrees of accuracy. We study superconductivity in both models using the random phase approximation. We then analyze the problem at stronger coupling, and study the dominant pairing instability in the associated $t-J$ model limit. In all instances, the dominant pairing tendency is in the $d_{x^2-y^2}$ channel, analogous to the cuprate superconductors.

We study superconductivity of twisted bilayer graphene with local and nonlocal attractive interactions. We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for microscopic tight-binding and low-energy continuum models. We predict qualitative differences between local and nonlocal interaction schemes which could be distinguished experimentally. In the flat-band limit where the pair potential exceeds the band width we show that the superfluid weight and BKT temperature are determined by multiband processes and quantum geometry of the band.

We analyze the ground-state energy, local spin correlation, impurity spin polarization, impurity-induced magnetization, and corresponding zero-field susceptibilities of the symmetric single-impurity Kondo model on a tight-binding chain with bandwidth $W=2\mathcal{D}$ where a spin-$\frac{1}{2}$ impurity at the chain center interacts with coupling strength $J_{\mathrm{K}}$ with the local spin of the bath electrons. We compare perturbative results and variational upper bounds from Yosida, Gutzwiller, and first-order Lanczos wave functions to the numerically exact extrapolations obtained from the density-matrix renormalization group (DMRG) method and from the numerical renormalization group (NRG) method performed with respect to the inverse system size and Wilson parameter, respectively. In contrast to the Lanczos and Yosida wave functions, the Gutzwiller variational approach becomes exact in the strong-coupling limit $J_{\mathrm{K}}\gg W$, and reproduces the ground-state properties from DMRG and NRG for large couplings $J_{\mathrm{K}}\gtrsim W$, with a high accuracy. For weak coupling, the Gutzwiller wave function describes a symmetry-broken state with an oriented local moment, in contrast to the exact solution. We calculate the impurity spin polarization and its susceptibility in the presence of magnetic fields that are applied globally or only locally to the impurity spin. The Yosida wave function provides qualitatively correct results in the weak-coupling limit. In DMRG, chains with about ${10}^3$ sites are large enough to describe the susceptibilities down to $J_{\mathrm{K}}/\mathcal{D}\approx 0.6$. For smaller Kondo couplings, only the NRG provides reliable results for a general host-electron density of states ${\rho }_0\left(\epsilon \right)$. To compare with results from Bethe ansatz that become exact in the wide-band limit, we study the impurity-induced magnetization and zero-field susceptibility. For small Kondo couplings, the zero-field susceptibilities at zero temperature approach ${\chi }_0(J_{\mathrm{K}}\ll \mathcal{D})/{\left(g{\mu }_{\mathrm{B}}\right)}^2\approx exp[1/({\rho }_0\left(0\right)J_{\mathrm{K}})]/\left[2C\mathcal{D}\sqrt{\pi e{\rho }_0\left(0\right)J_{\mathrm{K}}}\right]$, where $ln\left(C\right)$ is the regularized first inverse moment of the density of states. Using NRG, we determine the universal subleading corrections up to second order in ${\rho }_0\left(0\right)J_{\mathrm{K}}$.

This paper studies the two-channel Kondo lattice in the large-$N$ limit at half-filling. In this model, the continuous channel-symmetry is spontaneously broken, forming a channel-ferromagnet in which one conduction channel forms a Kondo insulator, while the other remains conducting. The paper discusses how this ground state can be understood using the concept of order fractionalization, in which the channel magnetization breaks up into an emergent spinor order parameter. By integrating out the fermions, we derive an effective action that describes this symmetry breaking and its emergent collective modes. A remarkable observation is that topological defects in the order parameter carry a U(1) flux, manifested in the Aharonov-Bohm phase picked by electrons that orbit the defect. By studying the effective action, we argue that the phase diagram contains a nonmagnetic transition between a large and a small Fermi surface.

We report ferromagnetic resonance in the normal configuration of an electrically insulating magnetic bilayer consisting of two yttrium iron garnet (YIG) films epitaxially grown on both sides of a 0.5-mm-thick nonmagnetic gadolinium gallium garnet (GGG) slab. An interference pattern is observed and it is explained as the strong coupling of the magnetization dynamics of the two YIG layers either in phase or out of phase by the standing transverse sound waves, which are excited through a magnetoelastic interaction. This coherent mediation of angular momentum by circularly polarized phonons through a nonmagnetic material over macroscopic distances can be useful for future information technologies.