We report a comprehensive study of spin dynamics in the ${\left({\mathrm{Mo}}_{2/3}{\mathrm{Tb}}_{1/3}\right)}_2\mathrm{AlC} i$-MAX compound using ac susceptibility measurements across a range of magnetic fields. Unique behaviors were observed, including spin dynamics in the kHz range between ${\mu }_{0}H\approx 0.2T-6T$, indicating a nontrivial superparamagnetic state, suggesting that the compound acts as a transitional system within the $i$-MAX family, bridging stable spin-dynamic materials and fluctuation-dominated ones. Field- and frequency-dependent magnetic phase transitions, coupled with relaxation behaviors, reveal complex interactions between spin density waves and superparamagnetic components. These findings, corroborated by $\mu \mathrm{SR}$ studies, deepen our understanding of magnetic phase diagrams and field-induced phenomena in $i$-MAX systems, laying the groundwork for further exploration of their unique properties and applications.

We consider spin chain models with local Hamiltonians that display weak ergodicity breaking. In these models, the majority of the eigenstates are thermal, but there is a distinguished subspace of the Hilbert space in which ergodicity is broken. We achieve such a weak breaking by embedding selected integrable models into larger Hilbert spaces of otherwise chaotic models. The integrable subspaces do not have a tensor product structure with respect to any spatial bipartition, therefore our constructions differ from certain trivial embeddings. We consider multiple mechanisms for such an embedding, and we also review previous examples in the literature. Curiously, all our examples can be seen as perturbations of models with Hilbert space fragmentation, such that the perturbed models are not fragmented anymore.

Recently, tight-binding models on hyperbolic lattices (discretized anti–de Sitter space) have gained significant attention, leading to hyperbolic band theory and non-Abelian Bloch states. In this paper, we investigate these quantum systems from the perspective of quantum information, focusing particularly on the scaling of entanglement entropy (EE) that has been regarded as a powerful quantum-information probe into exotic phases of matter. It is known that on a $d$-dimensional translation-invariant Euclidean lattice, the EE of band insulators scales as an area law ($\sim L^{d-1}$, where $L$ is the linear size of the boundary between two subsystems). Meanwhile, the EE of metals [with a finite density of state (DOS)] scales as the renowned Gioev-Klich-Widom scaling law ($\sim L^{d-1}lnL$). The appearance of logarithmic divergence, as well as the analytic form of the coefficient $c$, is mathematically controlled by the Widom conjecture of asymptotic behavior of Toeplitz matrices and can be physically understood via the Swingle's argument. However, the hyperbolic lattice, which generalizes translational symmetry, results in the inapplicability of these analytic approaches and the potential nontrivial behavior of the EE. Here we make an initial attempt through numerical simulation. Remarkably, we find that both cases adhere to the area law, indicating the effect of background hyperbolic geometry that influences quantum entanglement. To achieve the results, we first apply the vertex-inflation method to generate a hyperbolic lattice on the Poincaré disk, and then apply the Haydock recursion method to compute the DOS. Finally, we study the scaling of the EE for different bipartitions via exact diagonalization and perform finite-size scaling. We also investigate how the coefficient of the area law is correlated to the bulk gap in the gapped case and to the DOS in the gapless case, respectively. Future directions are discussed.

Topology is a powerful tool for categorizing magnetization textures by defining a topological index in both two-dimensional (2D) systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D nanomagnetism, both volume and surface topological numbers must be considered, requiring the identification of a proper global topological invariant to support categorization. Here we consider domain walls in cylindrical nanowires as an excellent playground for 3D nanomagnetic systems, excited by a charge current, that generates an Œrsted field. We first provide experimental evidence of previously unreported domain-wall transformations of topology occurring at the nanosecond timescale. We investigate these transformations with micromagnetic simulations, tracking both bulk and surface topological signatures. We demonstrate a topological invariant combining both signatures, while the topological charge varies from bulk to surface during the dynamics. The experimental change of topology is reproduced when the pulse duration matches the timescale of the internal transformations of the wall, and the current is switched off before the transformation is complete. We expect that the topological categorization and dynamical exploitation apply to any 3D nanomagnetic system.

We present an application of quantics tensor trains (QTTs) and tensor cross interpolation (TCI) to the solution of a full set of self-consistent equations for multivariate functions, the so-called parquet equations. We show that the steps needed to evaluate the equations (Bethe-Salpeter equations, parquet equation, and Schwinger-Dyson equation) can be decomposed into basic operations on the QTT-TCI compressed objects. The repeated application of these operations does not lead to a loss of accuracy beyond a specified tolerance and the iterative scheme converges even for numerically demanding parameters. As examples, we take the Hubbard model in the atomic limit and the single impurity Anderson model, where the basic objects in parquet equations, the two-particle vertices, depend on three frequencies, but not on momenta. The results show that this approach is able to overcome major computational bottlenecks of standard numerical methods. The applied methods allow for an exponential increase of the number of grid points included in the calculations, and a corresponding exponential reduction of the computational error, for a linear increase in computational cost.

The Berry curvature, resembling the magnetic field in reciprocal space, offers a captivating avenue for exploring unique electromagnetic phenomena devoid of real-space analogs. Here, we investigate the emergent electromagnetic induction by solenoidal Berry curvature with its field lines forming loops, links, and knots. In stark contrast to the conventional results predicted by Faraday's law, which dictates that alternating magnetic fields yield alternating electric fields with a net zero average, the alternating Berry curvature can engender directional electromagnetic induction. Such an effect is attributed to the presence of singularities in the Berry curvature, accompanied by a $2\pi$ jump in the Berry flux. Notably, this jump does not trigger a diamagnetic impulse, due to the gauge invariance of the Berry phase modulo $2\pi$. Consequently, the induced electric field maintains finite values under time averaging, manifesting itself as a directional pumping current. Our research sheds light on a different type of anomalous electromagnetic induction effect, thereby expanding our comprehension of exotic electromagnetic phenomena.

We study the transition probabilities of a two-point measurement on a quantum system, initially prepared in a thermal state. We find two independent constraints on the difference between transition probabilities when the system is prepared at different temperatures, which both turn out to be particularly restrictive when the measured quantum system is small. These bounds take the form of a thermodynamic and of an energetic constraint because they are associated with the dissipated heat and with the absorbed energy required to increase or to reduce the temperature of the system. The derived constraints apply to arbitrary system Hamiltonians, including interactions or nonlinear energy spectra. We show the relevance of these constraints for the special case where transitions are induced by energy or particle exchange in weakly coupled bipartite systems out of equilibrium. This example is of interest for a wide range of experimentally relevant systems, from molecular junctions to coupled cavities, and can be tested by, for instance, measuring the out-of-equilibrium tunneling current and its noise.

Motivated by a recent experiment reporting the fractional quantum spin Hall effect in twisted ${\mathrm{MoTe}}_2$, we investigate microscopically the prospects of realizing exotic topologically ordered states beyond conventional quantum Hall physics. We show that a non-Abelian spin Hall insulator, a state of two copies of the non-Abelian Moore-Read state, can be stabilized at half filling of time-reversal conjugate Chern bands. We elucidate that the existence of this phase relies on the reduction of opposite-spin interactions at short distances to overcome the Ising ferromagnetism. Moreover, we demonstrate that band mixing provides a generic mechanism for this reduction to be achieved. Quite remarkably, we find that a renormalization of opposite-spin interactions at short distances as small as 15% of the moiré period is sufficient for a direct transition to a completely spin-unpolarized phase which supports the non-Abelian spin Hall insulator. Furthermore, we show that the non-Abelian spin Hall insulator can either break time-reversal symmetry or preserve it depending on the underlying topological order.

Higher-order topological phases (HOTPs) possess localized and symmetry-protected eigenmodes at corners and along hinges in two- and three-dimensional lattices. The numbers of these topological boundary modes will undergo quantized changes at the critical points between different HOTPs. In this work, we reveal unique higher-order topology induced by time-periodic driving at the critical points of topological phase transitions, which has no equilibrium counterparts and also goes beyond the description of gapped topological matter. Using an alternately coupled Creutz ladder and its Floquet-driven descendants as illustrative examples, we analytically characterize and numerically demonstrate the zero and $\pi$ corner modes that could emerge at the critical points between different Floquet HOTPs. Moreover, we propose a unified scheme of bulk-corner correspondence for both gapless and gapped Floquet HOTPs protected by chiral symmetry in two dimensions. Our work reveals the possibility of corner modes surviving topological transitions in Floquet systems and initializes the study of higher-order Floquet topology at quantum criticality.

The investigations of spin angular momentum (SAM) of light have demonstrated many interesting photonic-spin-dependent effects. However, it is still a great challenge to manipulate a photonic SAM state in a designable and dynamic way. Here we propose to electrically control the SAM of light through lithium niobate (LN) domain engineering. In our design, each unit cell consists of a pair of positive and negative domains, which introduces a spin-dependent geometric phase. One can feasibly tune such geometric phase by applying an electric field. After properly arranging LN domains, we have successfully achieved a designed geometric phase distribution for electrically controlled separation of photonic SAM states. Our work paves the way to dynamically manipulate the SAM of light for high-speed beam steering, switchable wave front shaping, and dynamic holography.

The x-ray excited optical luminescence (XEOL) for defect and near band edge (NBE) transitions combined with simultaneous x-ray absorption measurements are experimentally and theoretically studied on single crystalline ZnO and GaN across the Zn and Ga $K$ edges, respectively, in a wide range of sample thicknesses. Increasing the sample thickness leads to the appearance of an inverted line shape and negative edge jump for the XEOL defect response, whereas the line shape of the XEOL NBE edge remains positive. A one-dimensional transport model is developed, which includes experimental geometry, the creation of x-ray generated excitations, diffusion and recombination of the carriers, and reabsorption of x-ray fluorescence and XEOL photons. The model calculations reproduce the experimentally observed changes of the edge shape in the XEOL spectra caused by variation of the sample thickness and reveal surface recombination and optical absorption as the main factors determining the XEOL edge shape for a given sample thickness.

Among noncentrosymmetric structures, chirality has recently been recognized as a novel source of asymmetrical charge/spin transports as exemplified by electrical magnetochiral anisotropy (EMChA) and chirality-induced spin selectivity. Although similar bulk-charge rectification and the Rashba-Edelstein effect in polar systems are quantitively reproducible by theory based on the electronic band structures, the relevance of band parameters in chiral effects remains elusive. Here, by working with a chiral organic superconductor, we experimentally demonstrate a gigantic EMChA and large superconducting diode effect, both of which are difficult to be explained solely by its band parameters. A two-critical-current signature and an enhanced critical field suggested triplet-mixed Cooper pairs with anomalously enhanced spin-orbit coupling above atomic limit. Our results clearly highlight a unique spin-momentum locking with large stiffness beyond the expectation, suggesting an unknown driving force for spin polarization inherent to chirality.

Recent advances in boundary critical phenomena have led to the discovery of a new surface universality class in the three-dimensional $O\left(N\right)$ model. The newly found “extraordinary-log” phase can be realized on a two-dimensional surface for $N<N_c$, with $N_c>3$, and on a plane defect embedded into a three-dimensional system, for any $N$. One of the key features of the extraordinary-log phase is the presence of logarithmic violations of standard finite-size scaling. In this work we study finite-size scaling in the extraordinary-log universality class by means of Monte Carlo simulations of an improved lattice model. We simulate the model with open boundary conditions, realizing the extraordinary-log phase on the surface for $N=2,3$, as well as with fully periodic boundary conditions and in the presence of a plane defect for $N=2,3,4$. In line with theory predictions, renormalization-group invariant observables studied here exhibit a logarithmic dependence on the size of the system. We numerically access not only the leading term in the $\beta$ function governing these logarithmic violations, but also the subleading term, which controls the evolution of the boundary phase diagram as a function of $N$.

Due to the presence of flat Chern bands, moiré transition-metal dichalcogenide (TMD) bilayers are a platform to realize strongly correlated topological phases of fermions such as fractional Chern insulators. TMDs are also known to host long-lived excitons, which inherit the topology of the underlying Chern bands. For the particular example of ${\mathrm{MoTe}}_2/{\mathrm{WSe}}_2$ heterobilayers we perform a time-dependent Hartree-Fock calculation to identify a regime in the phase diagram where the excitons themselves form a topological flat band. This paves a way towards realizing strongly correlated states of bosons in moiré TMDs.

A fundamental longstanding problem in studying spin models is the efficient and accurate numerical simulation of the long-time behavior of larger systems. The exponential growth of the Hilbert space and the entanglement accumulation at long times pose major challenges for current methods. To address these issues, we employ the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) framework to simulate the many-body spin dynamics of the Heisenberg model in various settings, including the Ising and XYZ limits with different interaction ranges and random couplings. Benchmarks with analytical and exact numerical approaches show that ML-MCTDH accurately captures the time evolution of one- and two-body observables in both one- and two-dimensional lattices. A comparison with the discrete truncated Wigner approximation (DTWA) highlights that ML-MCTDH is particularly well-suited for handling anisotropic models and provides more reliable results for two-point observables across all tested cases. The behavior of the corresponding entanglement dynamics is analyzed to reveal the complexity of the quantum states. Our findings indicate that the rate of entanglement growth strongly depends on the interaction range and the presence of disorder. This particular relationship is then used to examine the convergence behavior of ML-MCTDH. Our results indicate that the multilayer structure of ML-MCTDH is a promising numerical framework for handling the dynamics of generic many-body spin systems.

The studies of this paper on the spin-$1/2\mathrm{XXZ}$ chain at finite temperatures $T>0$ have two complementary goals. The first is to identify the spin carriers of all its $S_q>0$ energy eigenstates and to show that their spin elementary currents fully control the spin-transport quantities. Here, $S_q$ is the $q$-spin of the continuous $S{U}_q\left(2\right)$ symmetry of the model for anisotropy $\mathrm{\Delta }>1$. To achieve this goal, our studies rely on a suitable exact physical-spin representation valid in throughout the Hilbert space and associated with normal spin operators, rather than fractionalized particles such as spinons. Both the spin stiffness and the zero-field spin-diffusion constant are expressed in terms of thermal expectation values of the square of the elementary currents carried by the spin carriers. Our second goal is to confirm that the zero-field and finite-temperature spin transport is normal diffusive for $\mathrm{\Delta }>1$. We use two complementary methods that rely on an inequality for the $T>0$ spin stiffness and the above thermal expectation values, respectively, to show that the contributions to ballistic spin transport vanish. Complementarily, for $T>0$ and $\mathrm{\Delta }>1$, the spin-diffusion constant is found to be finite and enhanced upon lowering $T$, reaching its largest yet finite values at low temperatures. Evidence suggests that it diverges in the $\mathrm{\Delta }\to 1$ limit for $T>0$, consistent with $T>0$ anomalous superdiffusive spin transport at $\mathrm{\Delta }=1$ and zero field.

The excited bands in optical lattices manifest an important tool for studying quantum simulation and many-body physics, making it crucial to measure high-band scattering dynamics under strong interactions. This work investigates both experimentally and theoretically the collisional scattering of ${}^6\mathrm{Li}_2$ molecular Bose-Einstein condensate in the $D$ band of a one-dimensional optical lattice, with interaction strength directly tunable via magnetic Feshbach resonance. We find a clear dependence of the $D$-band lifetimes on the interaction strength within the strongly interacting regime, which arises from the fact that the scattering cross section is proportional to the square of the scattering length. The maximum lifetime versus lattice depth is measured to reveal the effects of interactions. We also investigate the scattering channels of $D$-band molecules under different interaction levels and develop a reliable two-body scattering rate equation. This work provides insight into the interplay between interaction and the collisional scattering of high-band bosons in optical lattices, paving the way for research into strong correlation effects in high-band lattice systems.