The dynamic behaviors of magnetic domain walls have significant implications for developing advanced spintronic devices. In this study, we investigate the intriguing resonance phenomenon within the magnetic domain wall structure, focusing on the dissipation mechanism and its impact on domain wall dynamic motion. By applying a static external magnetic field, we observe a remarkable amplification of domain wall velocity through the resonant excitations of the flexure modes. The resonance of the flexure mode exerts an indirect influence on the domain wall velocity through energy dissipation, leading to a significant enhancement from the predictions of the one-dimensional Walker model. We establish a robust model platform rooted in energy dissipation allows comprehensive understanding the dramatic enhancement of domain wall velocity observed during width-directional flexure mode resonance. By directly quantifying energy dissipation, our approach provides highly effective and accurate estimates of domain wall velocity, surpassing previous methods that focus solely on the instantaneous dynamics of the domain wall structure. These findings offer crucial insights into the fundamental mechanisms governing the dynamics of domain walls and other magnetic systems, such as magnetic skyrmions, bubbles, and magnetic vortices, paving the way for development and optimization of next-generation spintronic devices.

Supersolid is an exotic quantum state of matter that spontaneously hosts the features of both solid and superfluid, which breaks the translation and U(1) gauge symmetries. Here we study the spin dynamics in the triangular-lattice compound ${\mathrm{Na}}_2\mathrm{BaCo}{\left({\mathrm{PO}}_4\right)}_2$, which is revealed in [Xiang et al., Nature (London) 625, 270 (2024)] as a quantum magnetic analog of supersolid. We simulate the easy-axis Heisenberg model with tensor network approach and uncover unique dynamic traits. These features are manifested in two branches of excitations that can be associated with the spin solidity and superfluidity, respectively. One branch contains the U(1) Goldstone and roton modes, while the other comprises pseudo-Goldstone and roton modes. The gapless Goldstone modes of the in-plane superfluid order are confirmed by our inelastic neutron scattering measurements. Together with the evident out-of-plane solid order indicated by the magnetic Bragg peaks, our findings provide spectroscopic evidence for spin supersolidity in this easy-axis antiferromagnet. Akin to the role of phonon-roton modes—Landau elementary excitations—in shaping the helium superfluid thermodynamics, the intriguing double magnon-roton dispersion here determines the low-temperature thermodynamics of spin supersolids down to sub-Kelvin regime, explaining the recently observed giant magnetocaloric effect in ${\mathrm{Na}}_2\mathrm{BaCo}{\left({\mathrm{PO}}_4\right)}_2$.

Chiral superconductors are theorized to exhibit spontaneous edge currents. Here, we found magnetic fields at the edges of ${\mathrm{UTe}}_2$, a candidate odd-parity chiral superconductor, that seem to agree with predictions for a chiral order parameter. However, we did not detect the chiral domains that would be expected, and recent polar Kerr and muon spin relaxation data in nominally clean samples argue against chiral superconductivity. Our results show that hidden sources of magnetism must be carefully ruled out when using spontaneous edge currents to identify chiral superconductivity.

Trapped ions in a periodic potential are a paradigm of a frustrated Wigner crystal. The dynamics are captured by a long-range Frenkel-Kontorova model. We show that the classical ground state can be mapped to the one of a long-range Ising spin chain in a magnetic field, whose strength is determined by the mismatch between the chain's and substrate lattice's periodicity. The mapping is exact when the substrate potential is a piecewise harmonic potential and holds for any two-body interaction decaying as $1/r^{\alpha }$ with the distance $r$. The ground state is a devil's staircase of regular, periodic structures as a function of the mismatch and of the interaction exponent $\alpha$. While the staircase is well defined in the thermodynamic limit for $\alpha >1$, for Coulomb interactions, $\alpha =1$, we argue that it disappears and the sliding-to-pinned transition becomes a crossover, with a convergence to the thermodynamic limit scaling logarithmically with the chain's size. Due to this slow convergence, fractal properties can be observed even in chains of hundreds of ions at laser cooling temperatures. These dynamics are a showcase of the versatility of trapped-ion platforms for exploring the interplay between frustration and interactions.

Chiral Spin Liquids (CSL) are quantum spin analogs of electronic Fractional Chern Insulators. Their realizations on ultracold-atom or Rydberg-atom platforms remain very challenging. Recently, a setup of time-periodic modulations of nearest-neighbor Heisenberg couplings applied on an initial genuine spin liquid state on the square lattice has been proposed to stabilize a (Abelian) ${\mathbb{Z}}_2$ CSL phase. In the high-frequency limit, it was shown that time evolution can be described in terms of a static effective chiral Hamiltonian. Here we revisit this proposal and consider drives at lower frequency in a regime where the high-frequency Magnus expansion fails. We show that a Dynamical CSL (DCSL) is nevertheless stabilized in a finite range of frequency. The topological nature of this dynamical phase, as well as its instability below a critical frequency, is connected to specific features of the Floquet pseudo-energy spectrum. We also show that the DCSL can be represented faithfully by a two-dimensional time-periodic tensor network and, as in the static case, topological order is associated to a tensor gauge symmetry (${\mathbb{Z}}_2$ in that case).

Designing systems with large magnetic anisotropy energy (MAE) is desirable and critical for nanoscale magnetic devices. A recent breakthrough achieved the theoretical limit of the MAE for $3d$ transition metal atoms by placing a single Co atom on a MgO(100) surface, a result not replicated by standard first-principles simulations. Our paper, incorporating Hubbard-$U$ correction and spin-orbit coupling, successfully reproduces and explains the high MAE of a Co adatom on a MgO (001) surface. We go further by exploring ways to enhance MAE in $3d$ transition metal adatoms through different structural geometries of $3d-\mathrm{O}$ molecules on MgO. One promising structure, with molecules perpendicular to the surface, enhances MAE while reducing substrate interaction, minimizing spin fluctuations, and boosting magnetic stability. Additionally, we demonstrate significant control over MAE by precisely placing $3d-\mathrm{O}$ molecules on the substrate at the atomic level.

Chirality is pivotal in magnonics, particularly for achieving spin-wave nonreciprocity which is critical in advancing spin-wave-based communication and logic operations. In general, chirality in magnetic systems is realized through the interfacial antisymmetric exchange interaction, namely, the Dzyaloshinskii-Moriya interaction, which is an intrinsic phenomenon occurring at the buried interface of a ferromagnet and heavy metal. In this work, using micromagnetic simulations, we present a different route to achieve spin-wave nonreciprocity using an engineered chiral magnonic crystal, where we artificially created in-plane twisted spin textures by imposing certain handedness in the structural geometry. The manipulation of the relative arrangement of these chiral enantiomers led to spin-wave nonreciprocity, which could be tuned by selecting different channels within the crystal, with additional versatility in the resonant mode frequency. Further adjustment of the external magnetic field strength confirms that the spin-wave directionality originates from the spin texture. This enables additional control over the band gap and mode propagation characteristics by external field tuning. Our work provides an innovative route to simultaneously access opposite spin-wave directions in consecutive channels, which makes this system competent for a real on-chip magnonic diode, with predefined paths for counterpropagating information.

Crossed Andreev reflection (CAR) is a process that creates entanglement between spatially separated electrons and holes. Such entangled pairs have potential applications in quantum information processing, and it is therefore relevant to determine how the probability for CAR can be increased. CAR competes with another nonlocal process called elastic cotunneling (EC), which does not create entanglement. In conventional normal metal/superconductor/normal metal heterostructures, earlier theoretical work predicted that EC dominates over CAR. Nevertheless, we show numerically that when the Keldysh-Usadel equations are solved self-consistently in the superconductor, CAR can dominate over EC. Self-consistency is necessary both for the conversion from a quasiparticle current to a supercurrent and to describe the spatial variation of the order parameter correctly. A requirement for the CAR probability to surpass the EC probability is that the inverse proximity effect be small. Otherwise, the subvoltage density of states becomes large and EC is strengthened by quasiparticles flowing through the superconductor. Therefore, CAR becomes dominant in the nonlocal transport with increasing interface resistance and length of the superconducting region. Our results show that even the simplest possible experimental setup with easily accessible normal metals and superconductors can provide dominant CAR by designing the experimental parameters correctly. We also find that spin splitting in the superconductor increases the subvoltage density of states, and thus always favors EC over CAR. Finally, we tune the chemical potential in the leads such that transport is governed by electrons of one spin type. This can increase the CAR probability at finite values of the spin splitting compared to using a spin-degenerate voltage bias, and provides a way to control the spin of the conduction electrons electrically.

The energy levels of quasiparticles in superconductors experience Doppler shifts due to the influence of a finite current flow. The influence of the Doppler shift is particularly pronounced in unconventional superconductors with gap nodes. In the case of a normal/insulator/superconductor junction of a $d$-wave superconductor, a zero-bias conductance peak exhibits a peak shift in an applied magnetic field. Although the shifts have been detected in past experiments, the shifts showed different field responses depending on each experiment. In this paper, we evaluate the magnitudes of the shift based on realistic junction shapes to elucidate the origin of the variability in experimental Doppler shifts. We find that the peak shift depends on the junction shape; the splitting is significantly suppressed when the junction is formed at a protruding position. Also, the shifts are suppressed by the penetration of magnetic flux quanta, resulting in nonlinear responses to the applied field. The present results explain the origin of the variability in experimental Doppler shifts.

In this work, we study the scaling relation of energy and length scales in the two-dimensional (2D) random singlet (RS) state in the random $Q$ model. To investigate the intrinsic energy scale of the spinon subsystem arising from the model, we develop a constrained subspace update algorithm within the framework of the stochastic series expansion method to extract the singlet-triplet gap of the system. The 2D RS state exhibits scaling behavior similar to the infinite-randomness fixed point, at least within the length scales that we simulate. Furthermore, by rescaling the system size according to the strength of randomness, we observe that the data for the excitation gap and the width of the gap distribution collapse onto a single curve. This implies that a model with different strengths of randomness may correspond to the same fixed point.

A quantum state for being an eigenstate of some local Hamiltonian should be constrained by zero energy variance and consequently, the constraint is rather strong that a single eigenstate may uniquely determine the Hamiltonian. For non-Hermitian systems, it is natural to expect that determining the Hamiltonian requires a pair of both left and right eigenstates. Here, we observe that it can be sufficient to determine a non-Hermitian Hamiltonian from a single right or left eigenstate. Our approach is based on the quantum covariance matrix, where the solution of Hamiltonian corresponds to the complex null vector. Our scheme favors non-Hermitian Hamiltonian learning on experimental quantum systems, as only the right eigenstates there can be accessed. Furthermore, we use numerical simulations to examine the effects of measurement errors and show the stability of our scheme.

Andreev reflection at a normal-superconductor interface may be accompanied with an anomalous spatial shift. The studies so far are limited to the top incidence configuration. Here, we investigate this effect in the side incidence configuration, with the interface parallel to the principal axis of superconductor. We find that the shift exhibits rich behaviors reflecting the character of pair potential. It has two contributions: one from the $k$-dependent phase of pair potential, and the other from the evanescent mode. For chiral $p$-wave pairing, the pairing phase contribution is proportional to the chirality of pairing and is independent of excitation energy, whereas the evanescent mode contribution is independent of chirality and is nonzero only for excitation energy below the gap. The two contributions also have opposite parity with respect to the incident angle. For $d_{x^2-y^2}$-wave pairing, only the evanescent mode contribution exists, and the shift exhibits suppressed zones in incident angles, manifesting the superconducting nodes. The dependence of the shift on other factors, such as the angle of incident plane and Fermi surface anisotropy, are discussed.

A mobile impurity immersed in a noninteracting Fermi sea is dressed by the gapless particle-hole excitations of the fermionic medium. This conventional Fermi-polaron setting is well described by the so-called ladder approximation, which consists of neglecting impurity-hole scattering processes. In this work, we analyze polaron formation in the context of insulating states of matter, considering increasing levels of correlation in the medium: band insulators originating from external periodic potentials, spontaneously formed charge density waves, and a Fermi-Hubbard system undergoing a metal-Mott insulator transition. The polaron spectral function is shown to exhibit striking signatures of the underlying fermionic background, such as the single-particle band gap, particle-hole symmetry and the transition to the Mott state. These signatures are identified within the framework of the Chevy ansatz, i.e., upon restricting the Hilbert space to single particle-hole excitations. Interestingly, we find that the ladder approximation is inaccurate in these band systems, due to the fact that the particle and hole scattering phase spaces are comparable. Our results provide a step forward in the understanding of polaron formation in correlated many-body media, which are relevant to both cold-atom and semiconductor experiments.

We present here a theory of excitonic complexes in gated ${\text{WSe}}_{\text{2}}$ quantum dots (QDs). The QD gate potential causes type-II band alignment, i.e., electrostatically confines holes and repels electrons, or vice versa. Hence, the confinement of excitons involves a delicate balance of the repulsion of electrons by the gate potential with the attraction by the Coulomb potential of the hole localized in the QD. We present a theory of neutral excitonic complexes within a gated ${\text{WSe}}_{\text{2}}$ QD, considering spin, valley, electronic orbitals, and many-body interactions. We analyze how the electron-hole attraction depends on a range of parameters, such as screened Coulomb interaction, strength of confinement of holes, and repulsion of electrons. Using an atomistic tight-binding model, we compute valence and conduction band states within a computational box comprising over 1 million atoms with applied gate potential. The gate potential is split into a fictitious type-I potential which attracts both the electron and hole and a correction repelling the electron only. The atomistic wave functions are then used to calculate direct and exchange Coulomb matrix elements for a fictitious type-I QD and to obtain a spectrum of interacting electron-hole pairs. Next, the effect of repulsive potential, pulling away the electron from the valence hole, is included in the excitonic basis. This allows us to determine whether electron-hole pairs are sufficiently attracted to overcome electron repulsion by the confinement potential. Finally, we compute the dipole transition between hole and electron states to obtain the absorption spectrum.

Magnetic adatoms on $s$-wave superconductors induce bound states inside the superconducting gap, called Yu-Shiba-Rusinov (YSR) states. The anisotropy of the Fermi surface determines the spatial extension of bound states in a quasi-two-dimensional superconductor. This is especially important in the diluted impurity limit since the orbital overlap determines the coupling of YSR states of neighboring atoms and the formation of the collective YSR system. Here, we build diluted arrays of Mn atoms with different dimensionalities on the (100) surface of $\beta \text{−}{\mathrm{Bi}}_2\mathrm{Pd}$ and measure the evolution of their YSR spectra with the structure. We detect the coupling as a split of YSR peaks in subgap spectra and find that the split size increases with the number of atoms. The orientation of the structures along different directions of the $\beta \text{−}{\mathrm{Bi}}_2\mathrm{Pd}$ substrate modulates the split and particle-hole asymmetry of the YSR states due to the anisotropic character of the Fermi surface, captured by the Green's function model. With the aid of the model, we found multiple YSR excitations in an extended 2D array of 25 Mn atoms, and we identified that their spatial distribution reflects a chiral local density of states.

Entanglement properties of purified quantum states are of key interest for two reasons. First, in quantum information theory, minimally entangled purified states define the entanglement of purification as a fundamental measure for the complexity of the corresponding physical mixed state. Second, dynamical entanglement growth in purified states represents the main bottleneck for calculating dynamical physical properties on classical computers in the framework of tensor network states. Here, we demonstrate how geometric methods, including parallel transport, may be harnessed to reduce such dynamical entanglement growth, and how to obtain a general prescription for maintaining (locally) optimal entanglement entropy when time-evolving a purified state. Adapting and extending by higher-order skew corrections the notion of Uhlmann geometric phases, we reveal the relation between dynamical entanglement growth and the geometry of the Hilbert-Schmidt bundle as the mathematical foundation of purified states. With benchmarks on a nonintegrable spin chain model, we compare the computational performance of matrix product state algorithms based on our present geometric disentangling method to previous approaches for taming entanglement growth in purified states. Our findings provide numerical evidence that geometric disentanglers are a powerful approach, superior in various aspects to known methods for disentangling purified states in a range of physically relevant computational scenarios. To exclude the effect of algorithmic imperfections, we also provide a numerically exact analysis for systems of moderate size.

The effect of Hubbard and Kondo interactions on the edge states in the half-filled Su-Schrieffer-Heeger chain of electrons is investigated by studying the behavior of charge quasiparticles using Kumar representation and the density matrix renormalization group method. For any finite dimerization of hopping, by increasing the Hubbard interaction, the edge states are found to transmigrate from the physical charge gap to a high energy gap through an intermediate phase without the edge states. The extent of this phase with no edge states shrinks smoothly upon increasing the dimerization. The transmigration of edge states from the charge gap to the high energy gap is also found to occur with Kondo interaction, but through an intermediate phase which itself changes from having no edge states for weak dimerization to having the edge states in the physical as well as the high energy gaps coexisting from moderate to strong dimerization.

Correlated systems represent a class of materials that are difficult to describe through traditional electronic structure methods. The computational cost of simulating the structural dynamics of such systems, with correlation effects considered, is substantial. Here, we investigate the structural dynamics of $f$- and $d$-electron correlated systems by integrating quantum embedding techniques with interatomic potentials derived from graph neural networks. For cerium, a prototypical correlated $f$-electron system, we use density functional theory with the Gutzwiller approximation to generate training data due to efficiency with which correlation effects are included for large multiorbital systems. For nickel oxide, a prototypical correlated $d$-electron system, advancements in computational capabilities now permit the use of full dynamical mean field theory to obtain energies and forces. We train neural networks on these data to create a model of the potential energy surface, enabling rapid and effective exploration of structural dynamics. Utilizing these potentials, we delineate transition pathways between the $\alpha$, ${\alpha }^{\prime }$, and ${\alpha }^{″}$ phases of cerium and predict the melting curve of nickel oxide. Our results demonstrate the potential of machine learning potentials to accelerate the study of strongly correlated systems, offering a scalable approach to explore and understand the complex physics governing these materials.

Quantum spin Hall insulators, which possess a nontrivial ${\mathbb{Z}}_2$ topological phase, have attracted great attention for two decades. It is generally believed that when an even number of layers of the quantum spin Hall insulators are stacked, the ${\mathbb{Z}}_2$ topological phase becomes unstable due to the ${\mathbb{Z}}_2$ nature. While the counterexamples of the instability were observed in several papers, there is no systematic understanding. In this work, we provide a systematic understanding of the robust ${\mathbb{Z}}_2$ topological phase in a Hermitian system with chiral symmetry against stacking. We clarify that the robustness generally originates from level repulsion in the corresponding non-Hermitian system derived from Hermitization. We demonstrate this by treating a class DIII superconductor in 1D with ${\mathbb{Z}}_2$ topology and the corresponding non-Hermitian 1D system in class ${\mathrm{AII}}^{†}$ with ${\mathbb{Z}}_2$ point-gap topology.

From lattice-regularized models, devoid of any non-Hermitian (NH) skin effects, here we compute the electrical (${\sigma }_{xy}$), thermal (${\kappa }_{xy}$), and spin (${\sigma }_{xy}^{sp}$) Hall, and the electrical ($G_{xx}$) and thermal ($G_{xx}^{th}$) longitudinal conductivities for appropriate NH planar topological insulators and superconductors related to all five nontrivial Altland-Zirbauer symmetry classes in their Hermitian limits. These models feature real eigenvalues over an extended NH parameter regime, only where the associated topological invariants remain quantized. In this regime, the NH quantum anomalous and spin Hall insulators show quantized ${\sigma }_{xy}$ and $G_{xx}$, respectively, the NH $p+ip$ ($p\pm ip$) pairing shows half-quantized ${\kappa }_{xy}$ ($G_{xx}^{th}$), while the NH $d+id$ pairing shows quantized ${\kappa }_{xy}$ and ${\sigma }_{xy}^{sp}$ in the clean and weak disorder (due to random pointlike charge impurities) regimes. We compute these quantities in experimentally realizable suitable six-terminal setups using the Kwant software package. But, in the strong disorder regime, all these topological responses vanish and with the increasing non-Hermiticity in the system this generic phenomenon occurs at weaker disorder.