We study the effect that the SU(2) symmetry, and the rich Hilbert space structure that it generates in lattice spin systems, has on the average entanglement entropy of highly excited eigenstates of local Hamiltonians and of random pure states. Focusing on the zero total magnetization sector $(J_z=0)$ for different fixed total spin $J$, we argue that the average entanglement entropy of highly excited eigenstates of quantum-chaotic Hamiltonians and of random pure states has a leading volume-law term whose coefficient $s_A$ depends on the spin density $j=J/\left(\mathfrak{j}L\right)$, with $s_A(j\to 0)=ln(2\mathfrak{j}+1)$ and $s_A(j\to 1)=0$, where $\mathfrak{j}$ is the microscopic spin. We provide numerical evidence that $s_A$ is smaller in highly excited eigenstates of integrable interacting Hamiltonians, which lends support to the expectation that the average eigenstate entanglement entropy can be used as a diagnostic of quantum chaos and integrability for Hamiltonians with non-Abelian symmetries. In the context of Hamiltonian eigenstates we consider spins $\mathfrak{j}=\frac{1}{2}$ and 1, while for our calculations based on random pure states we focus on the spin $\mathfrak{j}=\frac{1}{2}$ case.

We investigate the spin-$\frac{1}{2}$ nearest-neighbor Heisenberg model with the four-site ring-exchange $J_4$ and chiral interaction $J_{\chi }$ on the triangular lattice by using the variational Monte Carlo method. The $J_4$ term induces the quadratic band touching (QBT) quantum spin liquid (QSL) with only a $d+id$ spinon pairing (without hopping term), the nodal $d$-wave QSL and $U\left(1\right)$ QSL with a finite spinon Fermi surface progressively. The effect of the chiral interaction $J_{\chi }$ can enrich the phase diagram with two interesting chiral QSLs (topological orders) with the same quantized Chern number $C=\frac{1}{2}$ and ground-state degeneracy GSD = 2, namely the $U\left(1\right)$ chiral spin liquid (CSL) and ${\mathrm{Z}}_{2}d+id$-wave QSL. The nodal $d$-wave QSL is fragile and will turn to the ${\mathrm{Z}}_{2}d+id$ QSL with any finite $J_{\chi }$ within our numerical calculation. However, in the process from QBT to the ${\mathrm{Z}}_{2}d+id$ QSL with the increase of $J_{\chi }$, an exotic crossover region is found. In this region, the previous QBT state acquires a small hopping term so that it opens a small gap at the band touching points, and leads to an energy minimum which is energetically more favorable compared to another competitive local minimum from the ${\mathrm{Z}}_{2}d+id$ QSL. We dub this state as the proximate QBT QSL and it gives way to the ${\mathrm{Z}}_{2}d+id$ QSL eventually. Therefore, the cooperation of the $J_4$ and $J_{\chi }$ terms favors mostly the ${\mathrm{Z}}_{2}d+id$-wave QSL, so that this phase occupies the largest region in the phase diagram.

Topological materials burgeoned with the discovery of the quantum spin Hall insulators (QSHIs). Since their discovery, QSHIs have been viewed as being ${\mathbb{Z}}_2$ topological insulators. This commonly held viewpoint, however, hides the far richer nature of the QSHI state. Unlike the ${\mathbb{Z}}_2$ topological insulator, which hosts gapless boundary states protected by the time-reversal symmetry, the QSHI does not support gapless edge states because the spin-rotation symmetry breaks down in real systems. Here, we demonstrate that QSHIs hide higher-order topological insulator phases through two exemplar systems. We first consider the Kane-Mele model under an external field and show that it carries an odd spin Chern number ${\mathcal{C}}_s=1$. The model is found to host gapless edge states in the absence of Rashba spin-orbit coupling (SOC). But, a gap opens up in the edge spectrum when SOC is included, and the system turns into a higher-order topological insulator with in-gap corner states emerging in the spectrum of a nanodisk. We also discuss a time-reversal symmetric tight-binding model on a square lattice, and show that it carries an even spin Chern number ${\mathcal{C}}_s=2$. This unique phase has been taken to be topologically trivial because of its gapped edge spectrum. We show it supports in-gap corner states and hosts a higher-order topological phase.

We systematically study the effects of higher-order interactions on the $S=\frac{3}{2},1$ orthogonal dimer chains using exact diagonalization and density matrix renormalization group. Due to frustration and higher spin, there are rich quantum phases, including three Haldane phases, two gapless phases, and several magnetically ordered phases. To characterize these phases and their phase transitions, we study various physical quantities such as energy gap, energy-level crossing, fidelity susceptibility, spin correlation, entanglement spectrum, and central charge. According to our calculations, the biquadratic term can enhance the Haldane phase regions. In particular, we numerically identify that a Haldane phase in $S=\frac{3}{2}$ case is adiabatically connected to the exact AKLT (Affleck, Kennedy, Lieb, and Tasaki) point when adding a bicubic term. Our study on the orthogonal dimer model, which is a 1D version of the Shastry-Sutherland model, provides insights into understanding the possible $S=\frac{3}{2},1$ Haldane phases in quasi-1D and 2D frustrated magnetic materials.

Nonequilibrium energy flows in a driven quantum system coupled to two heat baths are investigated to describe microscopic driven-dissipative processes, based on both a canonical transformation and full counting statistics. The main focus is to understand the interference between the coherent driving and bath induced dissipation. We aim to explore efficient modulation of the quantum energy transport, characterized as transient energy flow, by the Rabi driving and the temperature bias. In particular, steady-state energy flow is divided into three components: temperature bias flow, driving flow, and coherence flow. The driving flow is dominated by the external field driving, and the coherence flow is determined by the interference of two side peaks that are blueshifted and redshifted in Mollow's triplet. The energy flow is mainly contributed by the temperature bias flow at a weak driving limit, and the driving flow is in a strong driving regime. The effects of driving amplitude and temperature bias on the steady-state flow are discussed comprehensively. The results may provide guidance for the efficient control of energy and the information transport in nanodevices driven by an optical field.

We investigated the element-specific electronic structure of a half-metallic Weyl ferromagnet candidate ${\mathrm{Co}}_2\mathrm{FeSi}$ film by utilizing soft-x-ray resonant photoelectron spectroscopy and first-principles calculations with and without considering an on-site Coulomb interaction. An Fe $2p-3d$ resonant photoelectron experiment revealed that the Fe $3d$ states exist around 2 and 4 eV below the Fermi energy. Our calculations, based on the generalized gradient approximation without considering a Coulomb interaction at the Fe site, successfully reproduced the experimentally observed Fe $3d$ partial density of states. Our findings shed light on the highly controversial correlation effect of ${\mathrm{Co}}_2\mathrm{FeSi}$, offering valuable insights into its half metallicity and Weyl semimetallicity.

Assessing the atomic and electronic structure of strongly correlated systems in which the crystal symmetry changes due to emergent lattice distortions, such as charge density waves (CDWs), is nontrivial because the distortions are not necessarily amenable to a traditional crystallographic description. Using advance scattering and modeling techniques, we reveal the evolution of the atomic displacement modes behind the CDW phases of quasi-one-dimensional $\mathrm{Nb}{\mathrm{Te}}_4$ and derive the so far unknown atomic structure of its low-temperature commensurate (C) CDW phase. Electronic structure calculations based on the experimental C-CDW structure data predict the existence of Dirac fermions whose multiplicity turns out to depend on the degree of lattice distortions accounted for in the experimental structure derivation. We argue that the electronic structure of CDW systems in general, and in particular in transition metal tetratellurides, can be strongly impacted by local lattice distortions and, therefore, they should be fully accounted for when their rich physics is considered.

In disordered systems, wave functions in the Schrödinger equation may exhibit a transition from the extended phase to the localized phase, in which the states at the boundaries or mobility edges may exhibit multifractal structures. Meanwhile, the critical phase (CP) in a phase diagram, separating the localized phase and extended phase, in which all states exhibit multifractal structures, has also attracted much attention in the past decades in some particularly designed models with quasiperiodic potentials. However, a generic way to construct the CP on demand still remains elusive. Here, a general approach for this phase is presented using two coupled quasiperiodic chains, where the chains are chosen in such a way that before coupling, one of them has extended states while the other one has localized states. We demonstrate the existence of the CP in the overlapped spectra when interchain coupling is presented, using fractal dimension and minimal scaling index based on multifractal analysis. Then we examine the generality of this physics by changing the forms of interchain coupling and quasiperiodic potential, where the CP also emerges in the overlapped spectra. We account for the emergence of this phase as a result of the effective unbounded potential, which yields singular continuous spectra and excludes the extended states in the overlapped regimes. Finally, the realization of this CP in the continuous model using ultracold atoms with a bichromatic quasiperiodic optical lattice is also discussed. Due to the tunability of the two chains, this work provides a general approach to realizing the CP in a tunable way. This approach may have wide applications in the experimental detection of CP and can be generalized to much more intriguing physics in the presence of interactions for the many-body CP.

Spin torques in magnetic multilayers are produced by spin polarization $P$ of ferromagnetic (F) layers, and increase with growing $P$. The latter, however, cannot exceed the $P=1$ value found in half-metals. We study the $P=1$ case to find what other parameters still influence spin torques in this extreme limit. It is found that the ratio of the exchange gap to Fermi energy strongly affects the properties of the torque. For large values of the gap, the magnitude of exchange spin torque exhibits a sharp peak at very small misalignment angles between magnetizations. This behavior is found to be linked to a transition between Ohmic and tunneling transport regimes through the F/F boundary.

Universal scaling laws govern the density of topological defects generated while crossing an equilibrium continuous phase transition. The Kibble-Zurek mechanism (KZM) predicts the dependence on the quench time for slow quenches. By contrast, for fast quenches, the defect density scales universally with the amplitude of the quench. We show that universal scaling laws apply to dynamic phase transitions driven by an oscillating external field. The difference in the energy response of the system to a periodic potential field leads to energy absorption, spontaneous breaking of symmetry, and its restoration. We verify the associated universal scaling laws, providing evidence that the critical behavior of nonequilibrium phase transitions can be described by time-average critical exponents combined with the KZM. Our results demonstrate that the universality of critical dynamics extends beyond equilibrium criticality, facilitating the understanding of complex nonequilibrium systems.

Accurate and reliable first-principles simulations of lattice thermal conductivity (${\kappa }_{\mathrm{L}}$) of highly anharmonic crystals have long been challenging in condensed matter and materials physics. With recent theoretical advances, the calculation of ${\kappa }_{\mathrm{L}}$ has evolved into a sophisticated process requiring the consideration of higher levels of refinements, such as high-order phonon-phonon scattering, anharmonic phonon renormalization, and heat transport beyond the phonon gas picture. Interatomic force constants (IFCs), however, as a shared pillar of the above concepts, are sometimes ambiguously implemented in this process, resulting in non-negligible uncertainties among different studies. Here, we revisit the ultralow ${\kappa }_{\mathrm{L}}$ of ${\mathrm{Tl}}_3{\mathrm{VSe}}_4$ and make a rigorous comparison of ${\kappa }_{\mathrm{L}}$ obtained from IFCs extracted by different approaches (flavors). We find that the fourth-order IFCs extracted with small-displacement data (0 K) are prone to yield significant phonon frequency shifting (phonon renormalization) and four-phonon scatterings, which lead to distinctively increased or decreased ${\kappa }_{\mathrm{L}}$, respectively. Moreover, the different flavors of second-, third-, and fourth-order IFCs extracted with the same large-displacement data (temperature-dependent) also result in significantly disparate ${\kappa }_{\mathrm{L}}$ owing to the mixing of higher-order IFCs into the lower-order IFCs. Our work discloses the potential uncertainties of ${\kappa }_{\mathrm{L}}$ that arise from the choice of different flavors of IFCs and underscores the pressing need for more rigorous and robust approaches to extracting IFCs.

Competing interactions are the simultaneous presence of conflicting coupling forces in a system, which can lead to the emergence of rich physical properties and phenomena. We have studied artificial spin ices composed of single-domain nanomagnets on triangular arrays using magnetic force microscopy and Monte Carlo simulations. A phase diagram with three distinct phases is obtained analytically through tuning the interaction between local neighboring spins continuously. These phases and phase boundaries are precisely reproduced by experimental data, providing strong evidence for the success of our theoretical model. Further to this, a subsequent study reveals that incorporating long-range interactions results in different phase boundaries. This conclusion is further confirmed by another experiment where a phase transition behavior is observed when the spin correlation within the system exceeds the neighbors within a triangular vertex. These findings indicate that further neighbor interactions in artificial triangular array can significantly affect the magnetic phases of the system, showing significant differences from other geometry-based artificial spin ices.

Higher-order topological phases are gapped phases of matter that host gapless corner or hinge modes. For the case of superconductors, corner or hinge modes are gapless Majorana modes or Majorana zero modes. To construct three-dimensional higher-order topological superconductors, we consider a topological-insulator/superconductor multilayer under in-plane Zeeman coupling. We found three different types of higher-order topological superconductor phases, a second-order topological superconductor phase with Majorana hinge flat bands, a second-order Dirac superconductor phase with surface Majorana cones and Majorana hinge arcs, and nodal-line superconductor phases with drumhead surface states and Majorana hinge arcs.

The Am $5d\text{−}5f$ resonant inelastic x-ray scattering (RIXS) data of americium sesquioxide were measured at incident photon energies throughout the Am $O_{4,5}$ edges. The experiment was supported by calculations using several model approaches. While the experimental Am $O_{4,5}$ x-ray absorption spectrum of ${\mathrm{Am}}_2{\mathrm{O}}_3$ is compared with the spectra calculated in the framework of atomic multiplet and crystal-field multiplet theories and Anderson impurity model (AIM) for the Am(III) system, the recorded Am $5d\text{−}5f$ RIXS data are essentially reproduced by the crystal-field multiplet calculations. A combination of the experimental scattering geometry and theoretical analysis of the character of the electronic states probed during the RIXS process confirms that the ground state of ${\mathrm{Am}}_2{\mathrm{O}}_3$ is singlet ${\mathrm{\Gamma }}_1$. An appearance of the low-intense charge-transfer satellite in the Am $5d\text{−}5f$ RIXS spectra at an energy loss of $\sim 5.5\mathrm{eV}$ suggests weak Am $5f\text{−}\mathrm{O}$ $2p$ hybridization which is in agreement with AIM estimations of the $5f$ occupancy from spectroscopic data in ${\mathrm{Am}}_2{\mathrm{O}}_3$ as being 6.05 electrons.

Motivated by the search for chiral spin liquids (CSL), we consider a simple model defined on the kagome lattice of interacting SU(3) spins (in the fundamental representation) including two-site and three-site permutations between nearest neighbor sites and on triangles, respectively. By combining analytical methods and various numerical techniques, namely, exact Lanczos diagonalizations and tensor network variational approaches, we find a rich phase diagram with short-range entangled (i.e., nontopological) and topological (possibly chiral) gapped spin liquids (SLs). Short-range entangled spin liquids include an Affleck-Kennedy-Lieb-Tasaki (AKLT)-like phase—argued to be a Symmetry-Protected Topological (SPT) phase—and a trimerized phase breaking the inversion center between the up and down triangles of the kagome lattice. A topological SL is stabilized in a restricted part of the phase diagram by the time-reversal symmetry breaking (complex) three-site permutation term. Analyzing the chiral edge modes of this topological SL on long cylinders or on finite disks, we have come up with two competing scenarios, either a CSL or a double Chern-Simons SL characterized by a single or by two counter-propagating Wess-Zumino-Witten $\mathrm{SU}{\left(3\right)}_1$ chiral mode(s), respectively. In the vicinity of the extended ferromagnetic region, we have found a magnetic phase corresponding either to a modulated canted ferromagnet or to a uniform partially magnetized ferromagnet.

The vertex function $\mathrm{\Gamma }(1,2;3)$ within Hedin's equations constitutes a long-standing challenge to electronic-structure theory. We propose an explicit expression for $\mathrm{\Gamma }$ as a function of space and time. This ansatz fulfils the equation of motion within reasonable approximations. The equation of motion is controlled by the screened Coulomb interaction $W$ and the Green's function $G$. Concerning $W$ we find that its dynamics (here approximated by plasmons) is crucial for obtaining a realistic $\mathrm{\Gamma }$. Concerning $G$ the renormalization of the quasiparticle peak and the split-off satellites are important. In combination these effects can be approximated by simple expressions that can easily be incorporated in the determination of the screening and the electronic self-energy. Similar to previous literature we find significant cancellation of such vertex corrections and electronic self-consistency. In the case of silicon as a prototypical semiconductor material we obtain realistic results for the optical spectrum, the electronic spectral function, and the fundamental band gap.

A time-dependent potential barrier has been used to probe the arrival-time distribution of the wave packet of a hot electron by raising the barrier to block the packet upon arrival of the packet at the barrier. To see whether the barrier precisely detects the distribution, it is necessary to study an error caused by a finite rising speed of the barrier. For this purpose, we study transmission of an electron wave packet through the dynamical barrier, and identify two regimes, the semiclassical regime and the quasistatic regime. In each regime, we calculate the arrival-time distribution reconstructed by using the barrier and quantify the error in the detection, the difference of the temporal uncertainty between the wave-packet distribution and the reconstructed distribution. Our finding suggests that for precise detection, the timescale, in which the barrier height rises over the energy distribution of the wave packet and the tunneling energy window of the barrier, has to be much shorter than the temporal uncertainty of the wave packet. The analytical results are confirmed with numerical calculations.

Superconductivity in topological insulators is expected to show very unconventional features such as a $p+ip$ order parameter, Majorana fermions, etc. However, intrinsic superconductivity has been observed in a very limited number of materials in which the pairing symmetry is still a matter of debate. Here, we study the topological crystalline insulator (TCI) ${\left({\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\right)}_{1-y}{\mathrm{In}}_y\mathrm{Te}$, for which a peculiar insulator to superconductor transition was previously reported near the gap inversion transition, where the system is nearly a three-dimensional Dirac semimetal. Both the existence of superconductivity near the three-dimensional Dirac semimetal and the occurrence of an insulator to superconductor transition in an isotropic material are highly unusual. We suggest that the observed phenomena are related to the intrinsic instability of a three-dimensional Dirac semimetal state in ${\left({\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\right)}_{1-y}{\mathrm{In}}_y\mathrm{Te}$ and “flattening” of the bulk valence and conduction bands as they acquire a Mexican-hat-like dispersion on the inverted side of the phase diagram. This favors the pairing instability if the chemical potential is pinned to these flat regions.

The ability to adjust the absorption bandwidth of an optical absorber with high efficiency can facilitate the development of novel photonic and optoelectronic devices. In this work, based on the temporal coupled-mode theory, we establish a connection between the absorption bandwidth of an absorber and radiation engineering with the symmetry-broken quasi-BIC and propose a BIC-inspired strategy to tailor light absorption at critical coupling with a wide range of functionality. Based on this, the manipulation of the broadband or narrow-band quasi-BIC-governed graphene perfect absorber is realized, and the corresponding absorption bandwidth at critical coupling can be drastically adjusted by more than three orders of magnitude. Moreover, we predict and verify the quadratic scalability of the absorption bandwidth on the asymmetry parameter of the quasi-BIC structure, essentially arising from the powerful physics of BIC in radiation engineering. Present work not only provides a profound physical insight into the tailoring functionalities of radiation and in particular absorption by BIC, but also affords new possibilities for research into active optical devices.