The recently introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement this method in the framework of a continuous-time Monte Carlo method with an auxiliary field in quantum impurity models. We introduce and train a diagram generating function (DGF) to model the probability distribution of auxiliary field configurations in continuous imaginary time, at all orders of diagrammatic expansion. By using DGF to propose global moves in configuration space, we show that the self-learning continuous-time Monte Carlo method can significantly reduce the computational complexity of the simulation.

The spin Seebeck effect (SSE) is observed in magnetic insulator|heavy metal bilayers as an inverse spin Hall effect voltage under a temperature gradient. The SSE can be detected nonlocally as well, viz. in terms of the voltage in a second metallic contact (detector) on the magnetic film, spatially separated from the first contact that is used to apply the temperature bias (injector). Magnon-polarons are hybridized lattice and spin waves in magnetic materials, generated by the magnetoelastic interaction. Kikkawa et al. [Phys. Rev. Lett. 117, 207203 (2016)] interpreted a resonant enhancement of the local SSE in yttrium iron garnet (YIG) as a function of the magnetic field in terms of magnon-polaron formation. Here we report the observation of magnon-polarons in nonlocal magnon spin injection/detection devices for various injector-detector spacings and sample temperatures. Unexpectedly, we find that the magnon-polaron resonances can suppress rather than enhance the nonlocal SSE. Using finite element modeling, we explain our observations as a competition between the SSE and spin diffusion in YIG. These results give unprecedented insights into the magnon-phonon interaction in a key magnetic material.

The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly interacting Majorana fermions that exhibits profound connections to quantum chaos and black holes. We propose a solid-state implementation based on a quantum dot coupled to an array of topological superconducting wires hosting Majorana zero modes. Interactions and disorder intrinsic to the dot mediate the desired random Majorana couplings, while an approximate symmetry suppresses additional unwanted terms. We use random-matrix theory and numerics to show that our setup emulates the SYK model (up to corrections that we quantify) and discuss experimental signatures.

The magnetic insulator yttrium iron garnet (YIG) with a ferrimagnetic transition temperature of $\sim 560$ K has been widely used in microwave and spintronic devices. Anomalous features in spin Seeback effect (SSE) voltages have been observed in Pt/YIG and attributed to magnon-phonon coupling. Here, we use inelastic neutron scattering to map out low-energy spin waves and acoustic phonons of YIG at 100 K as a function of increasing magnetic field. By comparing the zero and 9.1 T data, we find that instead of splitting and opening up gaps at the spin wave and acoustic phonon dispersion intersecting points, magnon-phonon coupling in YIG enhances the hybridized scattering intensity. These results are different from expectations of conventional spin-lattice coupling, calling for different paradigms to understand the scattering process of magnon-phonon interactions and the resulting magnon polarons.

We study the role of “$\theta$ terms” in the action for three-dimensional $U\left(1\right)$ symmetric tensor gauge theories, describing quantum phases of matter hosting gapless higher-spin gauge modes and gapped subdimensional particle excitations, such as fractons. In Maxwell theory, the $\theta$ term is a total derivative which has no effect on the gapless photon, but has two important, closely related consequences: attaching electric charge to magnetic monopoles (the Witten effect) and leading to a Chern-Simons theory on the boundary. We will find that a similar story holds in the higher-spin $U\left(1\right)$ gauge theories. These theories admit generalized $\theta$ terms which have no effect on the gapless gauge mode, but which bind together electric and magnetic charges (both of which are generally subdimensional) in specific combinations, in a higher-spin manifestation of the Witten effect. We derive the corresponding Witten quantization condition. We find that, as in Maxwell theory, imposing time-reversal invariance restricts $\theta$ to certain discrete values. We also find that these new $\theta$ terms imply a nontrivial boundary structure. The boundaries host fracton excitations coupled to a tensor $U\left(1\right)$ gauge field with a Chern-Simons-like action, in both chiral and nonchiral varieties. These boundary theories open a door to the study of $U\left(1\right)$ fracton phases described by tensor Chern-Simons theories, not only on boundaries of three-dimensional systems, but also in strictly two spatial dimensions. We explicitly work through three examples of bulk and boundary theories, the principles of which can be readily extended to arbitrary higher-spin theories.

Two topics of high current interest in the field of unconventional superconductivity are noncentrosymmetric superconductors and multiband superconductivity. Half-Heusler superconductors such as YPtBi exemplify both. In this paper, we study bulk and surface states in nodal superconducting phases of the half-Heusler compounds, belonging to the $A_1$ ($s+p$-like) and $T_2$ ($k_z{k}_x+i{k}_z{k}_y$-like) irreducible representations of the point group. These two phases preserve and break time-reversal symmetry, respectively. For the $A_1$ case, we find that flat surface bands persist in the multiband system. In addition, the system has dispersive surface bands with zero-energy crossings forming Fermi arcs, which are protected by mirror symmetries. For the $T_2$ case, there is an interesting coexistence of point and line nodes, known from the single-band case, with Bogoliubov Fermi surfaces (two-dimensional nodes). There are no flat-band surface states, as expected, but dispersive surface bands with Fermi arcs exist. If these arcs do not lie in high-symmetry planes, they are split by the antisymmetric spin-orbit coupling so that their number is doubled compared to the inversion-symmetric case.

The tunnel magneto-Seebeck effect is the dependence of the thermopower of magnetic tunnel junctions on the magnetic configuration. It is conventionally interpreted in terms of a thermoelectric generalization of the tunnel magnetoresistance. Here, we investigate the heat-driven electron transport in these junctions associated with electron-magnon scattering, using stochastic Landau-Lifshitz phenomenology and quantum kinetic theory. Our findings challenge the widely accepted single-electron picture of the tunneling thermopower in magnetic junctions.

We unravel theoretically a key intrinsic relaxation mechanism among the low-lying singlet and triplet donor-pair states in silicon, an important element in the fast-developing field of spintronics and quantum computation. Despite the perceived weak spin-orbit coupling (SOC) in Si, we find that our discovered relaxation mechanism, combined with the electron-phonon and interdonor interactions, drives the transitions in the two-electron states over a large range of donor coupling regimes. The scaling of the relaxation rate with interdonor exchange interaction $J$ goes from $J^5$ to $J^4$ at the low to high temperature limits. Our analytical study draws on the symmetry analysis over combined band, donor envelope, and valley configurations. It uncovers naturally the dependence on the donor-alignment direction and triplet spin orientation, and especially on the dominant SOC source from donor impurities. While a magnetic field is not necessary for this relaxation, unlike in the single-donor spin relaxation, we discuss the crossover behavior with increasing Zeeman energy in order to facilitate comparison with experiments.

Rydberg atoms have attracted considerable interest due to their huge interaction among each other and with external fields. They demonstrate characteristic scaling laws in dependence on the principal quantum number $n$ for features such as the magnetic field for level crossing or the electric field of dissociation. Recently, the observation of excitons in highly excited states has allowed studying Rydberg physics in cuprous oxide crystals. Fundamentally different insights may be expected for Rydberg excitons, as the crystal environment and associated symmetry reduction compared to vacuum give not only optical access to many more states within an exciton multiplet but also extend the Hamiltonian for describing the exciton beyond the hydrogen model. Here we study experimentally and theoretically the scaling of several parameters of Rydberg excitons with $n$, for some of which we indeed find laws different from those of atoms. For others we find identical scaling laws with $n$, even though their origin may be distinctly different from the atomic case. At zero field the energy splitting of a particular multiplet $n$ scales as $n^{-3}$ due to crystal-specific terms in the Hamiltonian, e.g., from the valence band structure. From absorption spectra in magnetic field we find for the first crossing of levels with adjacent principal quantum numbers a $B_r\propto n^{-4}$ dependence of the resonance field strength, $B_r$, due to the dominant paramagnetic term unlike for atoms for which the diamagnetic contribution is decisive, resulting in a $B_r\propto n^{-6}$ dependence. By contrast, the resonance electric field strength shows a scaling as $E_r\propto n^{-5}$ as for Rydberg atoms. Also similar to atoms with the exception of hydrogen we observe anticrossings between states belonging to multiplets with different principal quantum numbers at these resonances. The energy splittings at the avoided crossings scale roughly as $n^{-4}$, again due to crystal specific features in the exciton Hamiltonian. The data also allow us to assess the susceptibility of Rydberg excitons to the external fields: The crossover field strength in magnetic field from a hydrogenlike exciton to a magnetoexciton dominated by electron and hole Landau level quantization scales as $n^{-3}$. In electric field, on the other hand, we observe the exciton polarizability to scale as $n^7$. At higher fields, the exciton ionization can be studied with ionization voltages that demonstrate an $n^{-4}$ scaling law. Particularly interesting is the field dependence of the width of the absorption lines which remains constant before dissociation for high enough $n$, while for small $n\lesssim 12$ an exponential increase is found. These results are in excellent agreement with theoretical predictions.

We establish a scenario where fluctuations of new degrees of freedom at a quantum phase transition change the nature of a transition beyond the standard Landau-Ginzburg paradigm. To this end, we study the quantum phase transition of gapless Dirac fermions coupled to a ${\mathbb{Z}}_3$ symmetric order parameter within a Gross-Neveu-Yukawa model in 2+1 dimensions, appropriate for the Kekulé transition in honeycomb lattice materials. For this model, the standard Landau-Ginzburg approach suggests a first-order transition due to the symmetry-allowed cubic terms in the action. At zero temperature, however, quantum fluctuations of the massless Dirac fermions have to be included. We show that they reduce the putative first-order character of the transition and can even render it continuous, depending on the number of Dirac fermions $N_f$. A nonperturbative functional renormalization group approach is employed to investigate the phase transition for a wide range of fermion numbers and we obtain the critical $N_f$, where the nature of the transition changes. Furthermore, it is shown that for large $N_f$ the change from the first to second order of the transition as a function of dimension occurs exactly in the physical 2+1 dimensions. We compute the critical exponents and predict sizable corrections to scaling for $N_f=2$.

We have measured the doping and temperature dependence of lattice vibrations and magnetic excitations in the prototypical doped spin-orbit Mott insulator ${\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{IrO}}_4$ $(x=0$, 0.015, and 0.10). Our findings show that the pseudospin-lattice coupling—responsible for the renormalization of several low energy phonon modes—is preserved even when long-range magnetic order is suppressed by doping. In our most highly doped sample, the single magnon $(\mathrm{\Gamma }$ point) excitation disappears while the two-magnon mode softens and becomes heavily damped. Doping-induced electron-phonon coupling is also observed in a higher energy phonon mode. We observe two different electron-phonon interaction channels, which provide evidence of the coexistence of fluctuating magnetic moments and mobile carriers in doped iridates.

Since its experimental discovery, many phenomenological theories successfully reproduced the rapid rise of the Hall number $n_H$, going from $p$ at low doping to $1+p$ at the critical doping $p^{*}$ of the pseudogap in superconducting cuprates. Further comparison with experiments is now needed in order to narrow down candidates. In this paper, we consider three previously successful phenomenological theories in a unified formalism—an antiferromagnetic mean field (AF), a spiral incommensurate antiferromagnetic mean field (sAF), and the Yang-Rice-Zhang (YRZ) theory. We find a rapid rise in the specific heat and a rapid drop in the Seebeck coefficient for increasing doping across the transition in each of those models. The predicted rises and drops are locked, not to $p^{*}$, but to the doping where antinodal electron pockets, characteristic of each model, appear at the Fermi surface shortly before $p^{*}$. While such electron pockets are still to be found in experiments, we discuss how they could provide distinctive signatures for each model. We also show that the range of doping where those electron pockets would be found is strongly affected by the position of the van Hove singularity.

Magnetic phase separation in single-crystal dysprosium at 97–187 K was investigated using aberration-corrected Lorentz microscopy. The high-resolution Lorentz microscopy combined with the transport-of-intensity equation method successfully visualized the in-plane magnetization distribution of the coexisting magnetic phases. The onset of a phase transition from the ferromagnetic (FM) phase to helical antiferromagnetic (HAFM) phase was observed at $\sim 100\mathrm{K}$, and the two nanoscale phases coexisted up to $\sim 140\mathrm{K}$. The volume fraction of the FM phase decreased with increasing temperature, eventually resulting in the formation of static magnetic solitons, which are isolated single domains of the FM phase, at around 130 K. We also performed the in situ observation of the HAFM phase at 142 K by applying an external magnetic field normal to the helical axis. With increasing field, a distorted HAFM phase emerged and the nanoscale phase separation between the HAFM phase and the fan phase subsequently occurred from $\sim 6$ to $\sim 11\mathrm{kOe}$. It was proven that the boundaries between these nanoscale coexisting phases were perpendicular to the $z$ axis, which is the rotation axis common to the modulated magnetic structures.

Recently, entropy corrections on nonorientable manifolds such as the Klein bottle are proposed as a universal characterization of critical systems with an emergent conformal field theory (CFT). We show that entropy correction on the Klein bottle can be interpreted as a boundary effect via transforming the Klein bottle into an orientable manifold with nonlocal boundary interactions. The interpretation reveals the conceptual connection of the Klein bottle entropy with the celebrated Affleck-Ludwig entropy in boundary CFT. We propose a generic scheme to extract these universal boundary entropies from quantum Monte Carlo calculation of partition function ratios in lattice models. Our numerical results on the Affleck-Ludwig entropy and Klein bottle entropy for the $q$-state quantum Potts chains with $q=2,3$ show excellent agreement with the CFT predictions. For the quantum Potts chain with $q=4$, the Klein bottle entropy slightly deviates from the CFT prediction, which is possibly due to marginally irrelevant terms in the low-energy effective theory.

Superconducting (SC) gap symmetry and magnetic response of cubic ${\mathrm{U}}_{0.97}{\mathrm{Th}}_{0.03}{\mathrm{Be}}_{13}$ are studied by means of high-precision heat-capacity and dc magnetization measurements using a single crystal, in order to address the long-standing question of its second phase transition at $T_{\mathrm{c}2}$ in the SC state below $T_{\mathrm{c}1}$. The absence (presence) of an anomaly at $T_{\mathrm{c}2}$ in the field-cooling (zero-field-cooling) magnetization indicates that this transition is between two different SC states. There is a qualitative difference in the field variation of the transition temperatures; $T_{\mathrm{c}2}\left(H\right)$ is isotropic, whereas $T_{\mathrm{c}1}\left(H\right)$ exhibits a weak anisotropy between the [001] and [111] directions. In the low-temperature phase below $T_{\mathrm{c}2}\left(H\right)$, the angle-resolved heat capacity $C(T,H,\varphi )$ reveals that the gap is fully opened over the Fermi surface, narrowing down the possible gap symmetry.

Time crystals are proposed states of matter which spontaneously break time translation symmetry. There is no settled definition of such states. We offer a new definition which follows the traditional recipe for Wigner symmetries and order parameters. Supplementing our definition with a few plausible assumptions we find that a) systems with time-independent Hamiltonians should not exhibit time translation symmetry breaking while b) the recently studied $\pi$ spin glass/Floquet time crystal can be viewed as breaking a global internal symmetry and as breaking time translation symmetry, as befits its two names.

We investigate the scattering of a quantum particle with a two-dimensional (2D) Rashba spin-orbit coupled dispersion off of circularly symmetric potentials. As the energy of the particle approaches the bottom of the lowest spin-split band, i.e., the van Hove singularity, earlier work has shown that scattering off of an infinite circular barrier exhibits a number of features unusual from the point of view of conventional 2D scattering theory: the low-energy $S$ matrix is independent of the range of the potential, all partial waves contribute equally, the differential cross section becomes increasingly anisotropic and 1D-like, and the total cross section exhibits quantized plateaus. Via a nonperturbative determination of the $T$ matrix and an optical theorem which we prove here, we show that this behavior is universal for Rashba scattering off of any circularly symmetric, spin independent, finite-range potential. This is relevant both for impurity scattering in the noninteracting limit as well as for short-range two-particle scattering in the interacting problem.

Recent advances in the experimental growth and control of disordered thin films, heterostructures, and interfaces provide fertile ground for the observation and characterization of the collective superconducting excitations emerging below $T_c$ after breaking the $U\left(1\right)$ gauge symmetry. Here we combine THz experiments in a nanostructured granular Al thin film and theoretical calculations to demonstrate the existence of optically active phase modes, which represent the Goldstone excitations of the broken gauge symmetry. By measuring the complex transmission through the sample we identify a sizable and temperature-dependent optical subgap absorption, which cannot be ascribed to quasiparticle excitations. A quantitative modeling of this material as a disordered Josephson array of nanograins allows us to determine, with no free parameters, the structure of the spatial inhomogeneities induced by shell effects. Besides being responsible for the enhancement of the critical temperature with respect to bulk Al, already observed in the past, this spatial inhomogeneity provides a mechanism for the optical visibility of the Goldstone mode. By computing explicitly the optical spectrum of the superconducting phase fluctuations we obtain a good quantitative description of the experimental data. Our results demonstrate that nanograin arrays are a promising setting to study and control the collective superconducting excitations via optical means.

The magnetic phase diagram of magnetoelectric ${\mathrm{LiCoPO}}_4$ is established using neutron diffraction and magnetometry in fields up to $25.9\mathrm{T}$ applied along the crystallographic $b$ axis. For fields greater than $11.9\mathrm{T}$, the magnetic unit cell triples in size with propagation vector $\mathbf{Q}=(0,\frac{1}{3},0)$. A magnetized elliptic cycloid is formed with spins in the $(b,c)$ plane and the major axis oriented along $b$. Such a structure allows for the magnetoelectric effect with an electric polarization along $c$ induced by magnetic fields applied along $b$. Intriguingly, additional ordering vectors $\mathbf{Q}\approx (0,\frac{1}{4},0)$ and $\mathbf{Q}\approx (0,\frac{1}{2},0)$ appear for increasing fields in the hysteresis region below the transition field. Traces of this behavior are also observed in the magnetization. A simple model based on a mean-field approach is proposed to explain these additional ordering vectors. In the field interval $20.5–21.0\mathrm{T}$, the propagation vector $\mathbf{Q}=(0,\frac{1}{3},0)$ remains but the spins orient differently compared to the cycloid phase. Above $21.0\mathrm{T}$ and up until saturation, a commensurate magnetic structure exists with a ferromagnetic component along $b$ and an antiferromagnetic component along $c$.

${\mathrm{Na}}_2{\mathrm{IrO}}_3$ was one of the first materials proposed to feature the Kane-Mele-type topological insulator phase. Contemporaneously it was claimed that the very same material is in a Mott insulating phase which is described by the Kitaev-Heisenberg (KH) model. First experiments indeed revealed Mott insulating behavior in conjunction with antiferromagnetic long-range order. Further refined experiments established antiferromagnetic order of zigzag type which is not captured by the KH model. Since then several extensions and modifications of the KH model were proposed in order to describe the experimental findings. Here we suggest that adding charge fluctuations to the KH model represents an alternative explanation of zigzag antiferromagnetism. Moreover, a phenomenological three-band Hubbard model unifies all the pieces of the puzzle: topological insulator physics for weak and KH model for strong electron-electron interactions as well as a zigzag antiferromagnet at intermediate interaction strength.