We present a plausible mechanism for achieving a magnon-magnon level repulsion spectrum originating from the oscillation between the splitting and confluence in a three-magnon scattering process. When a magnetostatic mode on a YIG sphere is pumped by a microwave signal near the magnon resonance frequency with an increasing amplitude, the generated magnon condensate at half of the pumping frequency exerts a backaction to the original magnon mode. Such a strong nonlinear coupling manifests a striking feature of a “bending effect” of the magnetostatic mode spectra, akin to the anticrossing observed in a strongly coupled magnon-photon system.

The recently discovered high-$T_c$ superconductivity in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ with $T_c\approx 80$ K provides another intriguing platform to explore the microscopic mechanism of unconventional superconductivity. In this work, we study a previously proposed bilayer two-orbital model Hamiltonian for ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ [Y. Shen et al., Chin. Phys. Lett. 40, 127401 (2023)] on a plaquette ladder, which is a minimum setup with two-dimensional characteristic. We employ large-scale density matrix renormalization group calculations to accurately determine the ground state of the model. We determine the density, magnetic structure, and the pairing property of the model. We find that with large effective interlayer antiferromagnetic exchange for the $3d_{z^2}$ orbital, the spin, charge, and pairing correlation display quasi-long-range behavior, which could be viewed as a precursor of possible true long-range order in the two-dimensional limit. Interestingly, sign oscillation for the pairing correlation is observed for both the $3d_{x^2-y^2}$ and $3d_{z^2}$ orbitals, indicating the presence of a possible pair density wave in the system. Even though we only study the model on a quasi-one-dimensional plaquette ladder geometry due to the computational difficulty, the results for the spin, charge, and pairing correlation provide valuable insight towards the clarification of the properties of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$.

Krylov complexity measures the spread of an evolved state in a natural basis, induced by the generator of the dynamics and the initial state, and serves as an effective probe for detecting various properties of many-body systems. Here, we study the spread in Hilbert space of the state of an Ising chain subject to a complex-valued transverse magnetic field, initialized in a trivial product state with all spins pointing down. We demonstrate that Krylov spread reveals structural features of many-body systems, which remain hidden in correlation functions that are traditionally employed to determine phase diagrams. When the imaginary part of the spectrum of the non-Hermitian Hamiltonian is gapped, the system's state asymptotically approaches the non-Hermitian Bogoliubov vacuum for this Hamiltonian. We find that the spread of this evolution unravels three different dynamical phases based on how the spread reaches its infinite-time value. We also show that the second derivatives of the spread with respect to the real and imaginary components of the complex magnetic field exhibit algebraic divergence at the transition between gapped and gapless imaginary spectra. Furthermore, we establish a connection between the Krylov spread and the static correlation function for the $z$ components of spins in the underlying non-Hermitian Bogoliubov vacuum, providing a full analytical characterization of correlations across the phase diagram. Specifically, for a gapped imaginary spectrum in a finite magnetic field, we find that the correlation function exhibits an oscillatory behavior that decays exponentially in space. Conversely, for a gapless imaginary spectrum, the correlation function displays an oscillatory behavior with an amplitude that decays algebraically in space; the underlying power law depends on the manifestation of two exceptional points within this phase. Our findings, showing the potential of the Krylov spread in exposing dynamical transitions, motivate further studies of Krylov's complexity in open many-body systems, including monitored ones.

Here, we systematically investigate the microscopic dynamics of collective vibrational excitations (CVEs) in simple liquids, of which the thermodynamic state is unified to the mean atomic free volume. Our results show that longitudinal acoustic CVEs are always observed in simple liquids, even when the liquids are viscous, in which the mean atomic free volume is larger than the cross point of the corresponding mean propagation length and the atomic diffusion limit. This is because some long-wavelength longitudinal acoustic CVEs can still propagate in viscous liquids. However, transverse acoustic CVEs in viscous liquids become localized since both short- and long-wavelength transverse acoustic CVEs have propagation lengths smaller than the atomic diffusion limit. Therefore, transverse acoustic CVEs may not be detected in simple liquids. The propagation length of macroscopic elastic and shear waves which are the mechanical response of long-wavelength longitudinal and transverse CVEs, respectively, is further calculated to quickly determine the propagation-to-localization crossover of CVEs in simple liquids. Our findings here advance the understanding of microscopic dynamics of CVEs in simple liquids.

We study the quantum quench of a finite rate across topological quantum transitions in two-dimensional Chern and $Z_2$ topological insulators. We choose the representative Haldane model and the Kane-Mele model to investigate the behavior of excitation density generated by the quench and the impact of disorder on it. For the Haldane model, as long as the spectral gap is not closed by disorder, we find the excitation density at the end of the quench obeys the power-law decay with decreasing quench rate, and the power is consistent with the prediction of the Kibble-Zurek mechanism. By contrast, the Kibble-Zurek scaling of excitation density is absent in the Kane-Mele model once disorder is switched on, which we attribute to the emergence of a disorder-induced gapless region. In particular, the anti-Kibble-Zurek behavior of excitation density, namely, larger excitation density at slower quench, is observed at suitable model parameters. Moreover, we demonstrate that particle's onsite occupation can be used as a local measurable quantity to probe the breakdown of adiabatic evolution. The difference of onsite occupation between the time-evolved state and the instantaneous ground state at the end of the quench can successfully capture the key features of excitation density for both the Haldane and Kane-Mele models under periodic and more realistic open boundary conditions, thus facilitating the experimental characterization of the quench dynamics in these models.

We present an expansion of a many-body correlation function in a sum of pseudomodes: exponents with complex frequencies that encompass both decay and oscillations. The pseudomode expansion emerges in the framework of the Heisenberg version of the recursion method. This method essentially solves Heisenberg equations in a Lanczos tridiagonal basis constructed in the Krylov space of a given observable. To obtain pseudomodes, we first add artificial dissipation satisfying the dissipative generalization of the universal operator growth hypothesis, and then take the limit of the vanishing dissipation strength. Fast convergence of the pseudomode expansion is facilitated by the localization in the Krylov space, which is generic in the presence of dissipation and can survive the limit of the vanishing dissipation strength. As an illustration, we present pseudomode expansions of infinite-temperature autocorrelation functions in the quantum Ising and $XX$ spin-$1/2$ models on the square lattice. It turns out that it is enough to take a few first pseudomodes to obtain a good approximation to the correlation function.

A key goal in the study of superconductivity is the pursuit of $\mathrm{high}\text{−}{T}_c$ superconductors. Due to the metallization of $\sigma \text{−}\mathrm{bonding}$ electrons, which typically leads to strong electron-phonon coupling, two-dimensional materials based on hexagonal BC monolayers have been suggested as promising candidates for achieving $\mathrm{high}\text{−}{T}_c$ superconductivity. However, compared with graphene, the free-standing BC monolayer faces dynamical instability due to the absence of one $\pi$ electron. In this work, to elucidate the origin of superconductivity in the BC monolayer, we initially stabilized the system by applying feasible biaxial tensile strain, followed by exploring potential electron doping to uncover more superconducting phases, and ultimately provided a complete superconducting phase diagram for the free-standing BC monolayer through systematical ab initio anisotropic Migdal-Eliashberg theory calculations. Our findings indicate that the structural phases between relative tensile strains ${\epsilon }_r^1=(2.2+0.72n_e+1.9n_e^2-3.56n_e^3+1.57n_e^4)\%$ and ${\epsilon }_r^2=(7.1-9.6n_e+17.2n_e^2-17.35n_e^3+6.7n_e^4)\%$, with $n_e$ as electron doping density ranging from zero to one electron per unit cell, are dynamically stable and exhibit a three-gap superconducting nature with the critical temperatures $T_c$ from 76 to $122\mathrm{K}$ and the maximum superconducting gaps ${\mathrm{\Delta }}_{\mathrm{Max}}$ of 19–35 meV. We demonstrated such $\mathrm{high}\text{−}{T}_c$ three-gap superconductivity is closely associated with the Fermi surface which exhibits an anomalously strong electron-phonon coupling and comprises two distinct $\sigma$ Fermi sheets formed by combined $s+p_{x,y}$ states and one $\pi$ Fermi sheet dominated by the $\mathrm{C}\text{−}{p}_z$ orbitals. Moreover, as an account of strong interaction with the $\sigma \text{−}\mathrm{bonding}$ electrons, the in-plane B-C stretching modes govern the strong electron-lattice coupling. Motivated by the route of emergent superconductivity in the strained and doped BC monolayer, we designed 35 two-dimensional materials based on the BC monolayer through atom adsorption, sandwich structuring, and hydrogenation of the adsorption systems, and proved that there are 17 dynamically stable superconductors, e.g., adatoms-BC systems BCLi, BCNa, BCK, BCCu, and BCAg, sandwich structures ${\mathrm{B}}_2{\mathrm{C}}_2\mathrm{Li}$, ${\mathrm{B}}_2{\mathrm{C}}_2\mathrm{Na}$, ${\mathrm{B}}_2{\mathrm{C}}_2\mathrm{K}$, and ${\mathrm{B}}_2{\mathrm{C}}_2\mathrm{Cu}$, and hydrogenated adatoms-BC systems BCLiH and BCCuH. Ab initio anisotropic Migdal-Eliashberg theory calculations demonstrate that all of the 17 newly searched two-dimensional superconductors have strong electron-phonon coupling and $\mathrm{high}\text{−}{T}_c$ multigap superconductivity with the $T_c$ ranging from 33.5 to $118\mathrm{K}$. Further analysis shows that the decorations from adatoms, hydrogenation, or sandwich structuring provide tensile strain and electron doping simultaneously to the BC layer while adjusting interatomic forces, which, thereby drives the system into a superconducting phase. Theses results pave the way for design of two-dimensional $\mathrm{high}\text{−}{T}_c$ multigap superconductors.

Motivated by the desire to investigate the fundamental relationship between impurity-induced states and the sign change of the superconducting order parameter, as well as to explore the impurity effects in Ruddlesden-Popper nickelate superconductors with interlayer pairing, we employ the $T$-matrix approach to study single impurity scattering in unconventional superconductors. Our work focuses on two distinct pairing scenarios: intralayer $d$-wave pairing and interlayer $s$-wave pairing. For systems with intralayer $d$-wave pairing, we establish an intrinsic connection between the $d$-wave pairing symmetry and the emergence of midgap resonant states. Through a combination of analytical derivations and numerical simulations, we demonstrate that the appearance of in-gap states is directly linked to the sign reversal of the order parameter along the Fermi surface. In interlayer pairing systems, our results reveal the presence of pronounced resonant peaks, which can also be attributed to the sign-changing nature of the order parameter. We further extend our analysis to the bilayer nickelate superconductor ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, providing a theoretical investigation of impurity effects in this material. Our findings not only elucidate the complex interplay between pairing symmetries and impurity-induced states in unconventional superconductors but also offer a powerful tool for probing the pairing mechanisms in nickelate-based high-temperature superconductors. This work lays the groundwork for future experimental and theoretical investigations into the unique electronic properties of these emerging materials.

The glass transition represents a long-standing enigma in condensed matter physics and materials science. Traditionally, this transition, often associated with α relaxation, is viewed as a thermally activated process. In this study, by integrating molecular dynamics simulations and experimental verification, we revealed that static loading can effectively reduce the glass transition temperature in the out-of-equilibrium glassy state, exhibiting a distinct stress-temperature equivalence compared to that observed under dynamic loading in the equilibrium liquid state. This indicates that mechanical energy can effectively substitute thermal energy in facilitating the glass transition. At the microscopic level, the application of static load enhances atomic mobility, triggering cooperative atomic movements and fostering the development of “faster-atom” networks, which ultimately facilitate the global motion of numerous atoms necessary for the glass transition. These findings highlight the significance of static load in tailoring the structure and dynamics of metallic glasses.

Fredkin-type kinetic constraints appear in systems ranging from classical interfaces to th e Fredkin and Motzkin quantum spin chains. Here, we identify a pseudolocal conserved charge associated with Fredkin-constrained dynamics that may be leveraged to subdiffusively bound the dynamical exponent $z\ge 5/2$. Our results establish that transport in Fredkin-constrained systems belongs to a distinct dynamical universality class that is separate from ordinary diffusion. This universality class is stable to local perturbations that conserve the pseudolocal charge.

Single-atom magnet (SAM) represents the single bit with ultimate atomic-scale limit in the field of magnetic storage and spintronics. Large magnetic reversal barrier and long magnetic lifetime of SAM are vitally important for its application to single-atom magnetic memory, which is intensely related to the spin dynamics induced by spin-vibration coupling (SVC) between magnetic adatom and substrate. In this work, we investigated the static magnetic energy level, relaxation pathway, SVC interaction, spin dynamics, and magnetization relaxation rate combined with the density functional theory method and crystal field model Hamiltonian analysis as well as ab initio calculations. The static relaxation pathway reveals an effective magnetization reversal barrier ($U_{\mathrm{eff}}$) of 92.1 meV, much higher than the experimental excitation energy of 7.7 meV, which is due to the abundant intermediate SVC-induced spin-vibration states between the ground and first excited magnetic states, especially the state caused by vibrational mode $\hslash \omega =7.56\mathrm{meV}$, opening a fast relaxation channel for magnetization reversal. The quantum tunneling of magnetization (QTM) event is the primary cause of magnetization reversal in the temperature of $1–6\mathrm{K}$, with an estimated QTM relaxation time ($\tau$) of 0.02 s. The spin dynamics demonstrates that the Raman regime is the dominant relaxation mechanism at $6–50\mathrm{K}$, and the relaxation rates in $6–10\mathrm{K}$ almost completely contribute from the two-mode Raman transitions involving vibrational modes of 4.71 and 7.56 meV. The predicted magnetic blocking temperature ($T_{\mathrm{B}}$) of $1.5–17\mathrm{K}$ indicates that the U@MgO system exists a loop hysteresis in this temperature, exhibiting a characteristic SAM behavior. Our SVC calculations suggest that the fast relaxation in U@MgO system can be suppressed by weakening or quenching the SVC interaction for the low-energy vibrational modes. The quantitative predictions of relaxation rate and magnetic blocking temperature provide a guidance on the future magnetic measurements.

We have investigated the quasi-one-dimensional Ni-chain compound ${\mathrm{PbMn}}_2{\mathrm{Ni}}_6{\mathrm{Te}}_2{\mathrm{O}}_{18}$ using theoretical DFT calculations, inelastic neutron scattering, and optical spectroscopy in order to understand the nature of magnetic exchange interactions. Our inelastic neutron scattering study at 5 K on a powder sample reveals two bands of magnetic excitations, the first near 8 meV and the second near 18 meV originating from the antiferromagnetic zone center near $Q=1$ Å. On the other hand, at 100 K (which is above ${\mathrm{T}}_N=86$ K) a broad diffuse scattering signal is observed indicating the presence of short range magnetic correlations. We have analyzed the magnetic excitations based on the Linear Spin Wave Theory (LSWT) and compared the experimentally estimated exchange parameters with the DFT calculations. Our analysis reveals that the value of the exchange parameter at the larger distance ($\mathrm{d}=3.654\AA$) $J_3=4.21\left(8\right)$ meV between Ni-Ni (from interchain) is the strongest amongst the allowed six exchange parameters, which suggests that this system is not really a quasi-one-dimensional and confirmed by the absence of a Haldane gap. We have also presented the electronic structure calculations. The spin-polarized partial density of states (DOS) projected onto the Mn-d and Ni-d orbitals reveals that the $\mathrm{Ni}\text{−}{\mathrm{d}}_{x^2-y^2}$ contribution is dominant below the Fermi level in the spin-up and spin-down channel, while a minimal contribution from spin-up Mn states in the occupied region, suggesting a nearly high-spin state. The estimated Néel temperature, based on experimental exchange parameters is found to be in close agreement with the experimental value.

The origin of the magnetic quadrupole (MQ) interactions in ${\mathrm{Gd}}_3{\mathrm{Ru}}_4{\mathrm{Al}}_{12}$, which is known as a frustrated spin system and as a host material for skyrmion with a centrosymmetric crystal structure, are discussed. The MQ interactions between ferromagnetic (FM) spin trimers with imperfect FM directivity are deduced from a synthesis of dipole Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. The Hamiltonian, which includes both the MQ interactions and dipole interactions is proposed, and magnetic anisotropies, magnetic phase transitions, and the contribution of the MQ interactions to stabilize the skyrmion lattice (SkL) are discussed based on this Hamiltonian. Degrees of MQ freedom carried by the trimers contribute to stabilizing the SkL which appears at finite temperatures.

Hard x-ray angle-resolved photoemission spectroscopy reveals significant changes in the valence band states of ${\mathrm{EuPd}}_2{\mathrm{Si}}_2$ at a temperature $T_V$, where the Eu ions undergo a temperature-induced valence crossover from a magnetic ${\mathrm{Eu}}^{2+}$ state to a low-temperature valence-fluctuating state. The substitution of Pd by Au and Si by Ge results in a decrease in $T_V$ and the emergence of an antiferromagnetic state at low temperatures without valence fluctuations. It has been proposed that the boundary between the antiferromagnetic order and the valence transition represents a first-order phase transition associated with a specific type of second-order critical endpoint. In this scenario, strong coupling effects between fluctuating charge, spin, and lattice degrees of freedom are to be expected. In the case of ${\mathrm{EuPd}}_2{\left({\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x\right)}_2$ with $x=0.13$, which is close to the critical endpoint, a splitting of conduction band states and the emergence of flat bands with a restriction along the $\mathrm{\Gamma }$-X directions have been observed. A comparison with ab initio theory shows a high degree of agreement with the experimental results.

In the intermetallic rare-earth tetragonal ${\mathrm{EuAl}}_4$ system, competing itinerant exchange mechanisms lead to a complex magnetic phase diagram, featuring a centrosymmetric skyrmion lattice. Previous inelastic x-ray scattering (IXS) experiments revealed that the incommensurate charge-density wave (CDW) transition in ${\mathrm{EuAl}}_4$ ($T_{\text{CDW}}=142\mathrm{K}$) is driven by momentum-dependent electron-phonon coupling (EPC). We present the results of IXS under high hydrostatic pressure induced by diamond anvils and show how the EPC in ${\mathrm{EuAl}}_4$ is renormalized and suppressed in the material's temperature-pressure phase diagram. Our findings highlight the crucial role of momentum-dependent EPC in the formation of the CDW in ${\mathrm{EuAl}}_4$ and provide further insights into how external pressure can be used to tune charge ordering in quantum materials.

Supervised and unsupervised machine-learning-based frameworks have been implemented in the past to classify various dynamical phases of disordered quantum systems using rather sophisticated (highly preprocessed or difficult to generate) input data. In this paper, we begin by questioning the existence of a nonergodic extended phase, namely, the many-body critical (MBC) phase in finite systems of an interacting quasiperiodic system. We find that this phase can be separately detected from the other phases, such as the many-body ergodic (ME) and many-body localized (MBL) phases, in the model through supervised neural networks made for both binary and multiclass classification tasks, utilizing, rather unpreprocessed, eigenvalue spacings and eigenvector probability densities as input features. Moreover, the output of our trained neural networks can also indicate the critical points separating ME, MBC, and MBL phases, which are consistent with the same obtained from other conventional methods. We also employ unsupervised learning techniques, particularly principal component analysis (PCA) of eigenvector probability densities, to investigate how this framework, without any training, captures the, rather unknown, many-body phases (ME, MBL, and MBC) and single-particle phases (delocalized, localized, and critical) of the interacting and noninteracting systems, respectively. Our findings reveal that PCA entropy serves as an effective indicator (order parameter) for detecting phase transitions in the single-particle systems. Moreover, this method proves applicable to many-body systems when the data undergoes a suitable preprocessing. Interestingly, when it comes to the extraction of critical (correlation length) exponents through a finite-size scaling, we find that for single-particle systems, scaling collapse of neural network outputs is obtained using components of inverse participation ratio (IPR) as input data. Remarkably, we observe identical critical exponents as obtained from the scaling collapse of the IPR directly for different single-particle phase transitions. However, the current finite-size scaling approach to the network output cannot reliably extract critical exponents for the many-body system that needs further investigation.

Periodically driven systems have a longstanding reputation for establishing rich topological phenomena beyond their static counterpart. In this work, we propose and investigate a periodically driven extended Su-Schrieffer-Heeger model with three sites per unit cell, obtained by replacing the Pauli matrices with their $3\times 3$ counterparts. The system is found to support a number of edge modes over a range of parameter windows, some of which have no static counterparts. Among these edge modes, of particular interest are those which are pinned at a specific quasienergy value. Such quasienergy-fixed edge modes arise due to the interplay between topology and chiral symmetry, which are typically not expected in a three-band static model due to the presence of a bulk band at the only chiral-symmetric energy value, i.e., zero. In our time-periodic setting, another chiral-symmetric quasienergy value exists at half the driving frequency, which is not occupied by a bulk band and could then host chiral-symmetry-protected edge modes ($\pi$ modes). Finally, we verify the robustness of all edge modes against spatial disorder and briefly discuss the prospect of realizing our system in experiments.

In this work, we study an interacting tight-binding model of magic-angle twisted bilayer graphene (MATBG) with a twist angle of $1.{05}^{\circ }$. We derive effective theories based on a mean-field normal state at charge neutrality, thereby including the renormalizations coming from integrating out high-energy modes. In these theories, the flat bands display a sizable increase of the bandwidth, suggesting the renormalization of the magic angle. Additionally, the corresponding wave functions flow towards the limit of perfect particle-hole symmetry and sublattice polarization (the “chiral” limit). We further represent the flat bands in the “vortex Chern” basis and discuss the implications on the dynamics, regarding the “flat” and chiral symmetries of MATBG, as manifested in the symmetry-broken states at neutrality.

Kagome lattices, characterized by unique band structures such as flat bands and van Hove singularities, serve as a compelling platform for exploring the interplay between electronic states such as charge density waves, superconductivity, and topological quantum phenomena. In this study, we employed high-resolution angle-resolved photoemission spectroscopy and first-principles calculations to systematically characterize the distinct surface terminations of cleaved single-crystal ${\mathrm{CsTi}}_3{\mathrm{Bi}}_5$ and elucidate their corresponding band structures, providing critical insights into their intrinsic electronic states. Our findings reveal a pronounced splitting of flat bands on Bi-terminated surfaces, which is absent on Cs-terminated surfaces, indicating distinct surface electronic environments. Notably, the coexistence of original and replicated flat bands points to intricate interfacial interactions, potentially involving phenomena such as charge order, localized orbital hybridization, or surface reconstruction, rather than a straightforward rigid band shift. We find this behavior is attributed to a localized charge-driven hole doping effect at the interface, as supported by theoretical simulations and the observed modulation in band dispersions. These insights deepen our understanding of electronic structure modulation in kagome materials, paving the way for targeted band engineering and the investigation of emergent quantum phenomena such as unconventional superconductivity and topological orders.

We investigate quantum phase transitions in a topological Josephson junction with an embedded ferromagnetic layer, revealing a rich landscape of critical phenomena. The low-energy excitations comprise Majorana fermions propagating along the junction, coupled to the magnons in the ferromagnet. Based on mean-field and renormalization group arguments, we predict Berezinskii-Kosterlitz-Thouless (BKT) transitions in this system, both in the case of a magnetic easy-plane and weak easy-axis anisotropy. In the latter case, this is based on an emergent effective easy plane, spanned by the easy axis and the component of the magnetization, which couples to the Majoranas. We conclude by presenting a conjecture for the full phase diagram of the model. It covers BKT transitions as well as exotic multicritical and supersymmetric points known from related models of interacting real fermions and bosons.