The crossing points in band structures play an important role in several physical phenomena. In this paper, we focus on the group information of these crossing points, rather than on the specific $k·p$ models. Specifically, each crossing point can be described by a matrix group and the corresponding set of basis functions. We identify the minimal abstract group that captures all the essential information regarding the crossing point, and then decompose the matrix representation into irreducible representations (irreps) using orthogonality relations. The abstract group and irrep coefficients can be regarded as crossing point indicators. Such indicators are independent of the specific representation matrices and lattice coordinates. As an example, we applied our method to charge-1 Weyl points in 1651 magnetic space groups. We found that although as many as 9988 distinct Hamiltonians may exist before classification, they can ultimately be reduced to only nine abstract groups and 18 distinct symmetry indicators. This significantly reduces the complexity of identifying and characterizing crossing points in band structures. Our findings provide an algebraic classification of crossing points in band structures, which significantly simplifies the analysis and prediction of topological semimetals.

Altermagnets are a class of metallic magnets characterized by spin-split electron bands. As antiferromagnets they lack spontaneous bulk magnetization. The initial description of the momentum-dependent spin splitting of electron bands in altermagnets was based on the spin-group approach, which is valid when relativistic interactions are neglected. Then, spin-orbit coupling has been taken into account in accordance with time-reversal-odd, even-parity irreducible representations of centrosymmetric point groups considered by Fernandes et al. [Phys. Rev. B 109, 024404 (2024)]. Here, we show the inadequacy of this formal approach. The problem of electron band splitting should be discussed based on the crystal symmetry of a concrete altermagnet material. The band spin splitting in the hexagonal altermagnet CrSb is established using the magnetic group formalism that allows the discovery of the additional spin splitting missed in the frame of the exchange approximation. Another type of spin splitting takes place in so-called hidden altermagnets. These types of materials do not possess symmetry with respect to space and time inversion but are symmetric with respect to the product of these operations known as toroidal symmetry. Real-space spin splitting in materials with toroidal symmetry is demonstrated.

Recent experiments engineered special spin-degenerate Andreev bound states in atomic cages of adatoms on superconductors, the Machida-Shibata states, a promising building block for quantum matter. Here, we investigate the formation of time-reversal symmetric bands by hybridizing multiple such states and analyzing their electronic topological properties assuming small on-site electron repulsion. The low-energy theory shows that competing emerging singlet and triplet superconducting pairings drive the formation of topologically nontrivial phases in symmetry class DIII. Therefore, we predict that Kramers pairs of Majorana zero modes will appear at the ends of Machida-Shibata chains, while two-dimensional lattices will host helical Majorana edge modes. Additionally, we discover extended regions in the Brillouin zone with vanishing superconducting pairings, which are lifted by the repulsive electron interactions. Our findings offer new perspectives for manipulating topological superconductivity and pairings in nonmagnetic adatom systems.

The current through a small contact between two 2D regions is theoretically studied. The electron gas viscosity that arises due to electron-electron and electron-impurity scattering is considered. It is found the electron flow corresponds to the ideal Fermi-liquid model rather than the ideal gas one at strong viscosity. It is shown that an electron density inhomogeneity results in the finite contact resistance of the almost ideal flow of the electron gas. The temperature dependence of the resistance is found. The agreement between theory and experiment is discussed.

We report the formation of large-scale steady-state whirlpools in a GaAs-based two-dimensional electron liquid and demonstrate them by straightforward transport measurements. A whirlpool forming inside a circular cavity adjoining a wide conducting channel appears as a negative four-terminal resistance over a broad range of temperatures and cavity sizes. The effect scales with the Gurzhi length, in quantitative accord with the hydrodynamic analogy. Obtained results firmly establish this analogy and probe the limits of its applicability.

Conventional photonic waveguide arrays provide a compact and stable platform for simulating condensed-matter systems, enabling the direct observation of coherent quantum phenomena through optical waves. However, existing photonic lattices often fall short when dealing with complex time-dependent on-site potentials and coupling parameters. At the same time, although the analysis of quantum systems within the framework of band theory has become well established, analytical studies on system dynamics remain relatively scarce. In this work, we develop a tight-binding model for one-dimensional generalized photonic lattices and rigorously derive its validity conditions, offering theoretical support for simulating more diverse driven lattice quantum systems with photonic lattices. Building upon this, we propose an analytical framework to describe the dynamical behavior of a particle in a uniformly driven superlattice under external excitation. The resulting analytical solution equally applies to the optical-field evolution in the corresponding generalized photonic lattice. We further derive an extended form of the conventional dynamic-localization criterion. In addition, exploiting the quantum analogy of waveguide arrays, we directly employ the analytical theory to carry out numerical simulations in three representative types of generalized waveguide structures. These results establish a solid theoretical basis for understanding and controlling the dynamical behavior of photonic lattices and condensed-matter systems, while simultaneously suggesting a feasible route for experimental implementation.

We study composite topological excitations in ferromagnetic superconductors consisting of bound states of magnetic spin textures (skyrmions) and superconducting vortices. Using a Ginzburg-Landau framework with Zeeman coupling between the magnetization and the superconducting magnetic field, we demonstrate that skyrmion-vortex pairs (SVPs) form energetically stable bound states. By analyzing their asymptotic interactions, we identify regimes in which SVPs exhibit both short-range repulsion and long-range attraction, leading to clustering phenomena. Our results provide a field-theoretical basis for understanding suggested pathways for controlling hybrid topological matter through long-range interactions.

Programmable dissipation provides a practical route to steer nonunitary dynamics in periodically driven systems. Here we realize Floquet engineering of state-selective loss modulation in a reconfigurable electroacoustic two-level platform and demonstrate in situ control of the driven dynamics. We show that periodic dissipation links the spectrum of the Floquet operator over a single period to the decay behavior over many periods and enables switching of the dominant Floquet decay mode in real time. We find that the same loss window also admits a formally equivalent generalized measurement description in which the controlled selectivity induced by loss defines a tunable effective measurement strength and thus offers a route to Zeno freezing. We then implement a differential readout of the Aharonov-Anandan geometric phase by using a Zeno-frozen reference arm. Our results establish programmable dissipation as a unified tool for selective control over Floquet decay modes, for connecting loss modulation to measurement-like filtering and stabilization, and for enabling geometric phase readout in reconfigurable non-Hermitian platforms.

We study the effect of magnon interactions on the spin wave spectra of the all-in-all-out phase of the pyrochlore nearest neighbor antiferromagnet with a Dzyaloshinskii-Moriya interaction ($D$). The leading order corrections to spin wave energies indicate a significant renormalization for commonly encountered strengths of the Dzyaloshinskii-Moriya term. For low values of $D$ we find a potential instability of the phase itself, indicated by the renormalization of magnon frequencies to negative values. We have also studied the renormalized spectra in the presence of magnetic fields along three high symmetry directions of the lattice, namely, the [111], [100], and [110] directions. Generically, we find that for a fixed value of the Dzyaloshinskii-Moriya interaction renormalized spectra for the lowest band decrease with an increasing strength of the field. We have also analyzed the limits of the two-magnon continuum and probed the possibility of magnon decay. For a range of $D$ and the field strength we identify possible parameter regimes where the decay of the higher bands of the system are kinematically allowed.

The superfluid-insulator transition in systems of lattice bosons is usually analyzed in the framework of the Bose-Hubbard model, and has been extensively studied by theory and simulations. Less attention has been paid to the remnants of the transition in truncated lattices, with or without periodic boundary conditions. Here we consider the hard-core limit of the extended Bose-Hubbard model on small square and triangular grids—i.e., sections of the square and triangular lattices containing up to 13 sites. By mapping out the zero-temperature phase diagram through exact diagonalization, we find ground-state characteristics that are markedly different from those emerging in the thermodynamic limit, together with similarities. The dichotomy between superfluidlike and insulatinglike behavior is then investigated in two-dimensional systems of a few interacting bosons in the continuum, subject to confining and optical-lattice potentials mimicking the $3\times 3$ square grid. Using path-integral Monte Carlo simulations, we compute kinetic and potential energies, as well as superfluidity and exchange-cycle statistics, finding hints of Bose-Hubbard behavior even in systems of just five particles.

Two prevalent approaches for preparing long-range entangled quantum states are (i) linear-depth sequential unitary (SU) circuits, which apply local unitary gates sequentially, and (ii) constant-depth measurement-feedback (MF) circuits, which employ midcircuit measurements and conditional feedback based on measurement outcomes. Here we establish that a broad class of SU and MF circuits are dual to each other under a spacetime rotation. We investigate this spacetime duality in the preparation of various long-range entangled states, including GHZ states, topologically ordered states, and fractal symmetry-breaking states. As an illustration, applying a spacetime rotation to a linear-depth SU circuit that implements a noninvertible Kramers-Wannier duality—originally used to prepare a one-dimensional (1D) GHZ state—yields a constant-depth MF circuit that implements a ${\mathbb{Z}}_2$ symmetry gauging map, which equivalently prepares the GHZ state. Leveraging this duality, we further propose experimental protocols that require only a constant number of qubits to measure unconventional properties of 1D many-body states. These include (i) measurement of disorder operators, which diagnose the absence of spontaneous symmetry breaking, and (ii) postselection-free detection of measurement-induced long-range order, which emerges in certain symmetry-protected topological phases. We also show that measurement-induced long-range order provides a lower bound for strange correlators, which may be of independent interest.

Topological phases and modes, including the pseudospin Hall effect with robust edge transport and higher-order corner states, provide versatile control of wave propagation and modal confinement in classical wave platforms. Motivated by the need to systematically engineer multigap interface and corner localization with enhanced design freedom in kagome-derived lattices, we theoretically investigate two types of extended kagome lattices within a tight-binding framework. These lattices support a series of localized modes, including pseudospin Hall interface states and corner states in multiple band gaps and at different frequencies. Meanwhile, the extended kagome designs introduce additional tunable structural parameters, offering enhanced flexibility for tailoring topological and localized states. By constructing two types of extended kagome lattices with distinct topological properties, we identify multiple groups of corner states, pseudospin Hall effect achieved by band folding or accidental degeneracy, and type-II corner states without long-range interactions. These results highlight extended kagome lattices as a flexible platform for topological waveguiding and multifrequency corner-state localization.

The utilization of periodic driving to control nonequilibrium topological phases has garnered increasing attention in condensed matter physics. In this work, within the high-frequency limit of Floquet theory, we investigate the effects of circularly polarized light (CPL) on the topological properties of the antiferromagnetic topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. CPL drives topological phase transitions between the axion insulator (AI) and Chern insulator (CI) phases. These transitions exhibit a strong dependence on the layer number. In addition to the topologically nontrivial CI and topologically trivial normal metal phases, we further identify a topologically nontrivial parity-anomaly state, which emerges at the phase-transition point between the AI and CI phases. At these transition points, gapped and gapless Dirac surface states coexist, and the system manifests a half-quantized Hall conductance, which is a defining signature of the parity anomaly. Moreover, the half-quantized Hall conductance under strong dephasing, as well as its robustness against weak disorder, provides direct evidence for the topological nontriviality of this parity-anomaly state.

A two-dimensional (2D) Janus layer has different physical properties than a 2D non-Janus layer. When a van der Waals (vdW) heterostructure contains a Janus layer, some unusual phenomena different from those in a heterostructure made of two non-Janus layers are expected. Here, we study electronic structures and carrier dynamics of a vdW heterostructure WSSe/GaN. Interesting band alignment and anomalous carrier dynamics have been found in the heterostructure. When the Janus layer WSSe is flipped, the band alignment of the heterostructure shifts from type I to type II. Moreover, the type-I heterostructure shows exotic carrier dynamics thoroughly different from those in a traditional type-I heterostructure. Its transfer time of electrons (78 ps) is 200 times that of holes (323 fs), and the recombination time of electrons and holes is 178 ns, which is much longer than that in the type-II heterostructure. By calculating electronic parameters and phonon modes in the heterostructures, we find that the variation of band alignment originates from built-in electric field and surface work functions of the heterostructure. The anomalous carrier dynamics is attributed by the common effects of built-in electric field and electron-hole coupling. Our work not only reveals exotic carrier dynamics in a vdW heterostructure containing a Janus layer but also may extend applications of 2D heterostructures to some fields such as optoelectronics, catalysis, etc.

Kinetic magnetism is an iconic and rare example of collective quantum order that emerges from the interference of paths taken by a hole in a sea of strongly interacting fermions. Here, the lattice topology plays a fundamental role, with odd loops frustrating ferromagnetism, as seen in recent experiments. However, the resulting magnetic order on a general graph has remained elusive. Here, we systematically establish a general principle: that local frustration centers bind singlets while sharing a delocalized hole. This collective effect—absent in exchange magnetism—extends from rectangular grids to random graphs, producing sharp and predictable variation with tunable frustration measures. Our findings demonstrate that one can shape the spin order and tune the net magnetization by embedding kinetic frustration, opening ways of spatially resolved quantum control of many-body systems. We outline a protocol to realize some of the key findings in existing cold-atom setups.

The Hofstadter butterfly (HB) and mobility edges (MEs) are hallmark phenomena of quasiperiodic systems, yet their interplay remains elusive. Here, we demonstrate their coexistence within a tilt-induced quasiperiodic potential on a square lattice, giving rise to a “mobility-edge-embedded Hofstadter butterfly” (MEE-HB). This potential is generated by aligning a periodic potential at an angle relative to the lattice axes—a configuration readily accessible in optical lattice experiments. Using a tight-binding model, we show that for strong potential strength, the MEE-HB manifests as a fractal energy splitting pattern hosting MEs that separate extended and localized states; for weak and intermediate strength, the energy spectrum lacks fractal energy splitting or MEs. Our Harper-like equation shows that the fractal pattern originates from one-dimensional quasiperiodic potentials, while MEs stem from effective long-range hopping. Notably, the MEE-HB exhibits a fractal dimension of $0.8–1.0$, significantly exceeding the $0.4–0.6$ range of the standard butterfly, indicating a denser spectrum. Our findings establish tilt-induced potentials as a versatile platform for exploring the interplay between fractal structures and localization.

We study localization and flat-band formation in lattices generated by repeated bond inflation of square, honeycomb, and triangular parent lattices. Replacing each bond by a finite tight-binding chain produces several distinct classes of flat bands: chain-induced flat bands at the eigenenergies of the inserted chains, symmetry-protected zero-energy flat bands in bipartite bond-inflated lattices, and nearly flat junction bands near the spectral edges for sufficiently long chains. We analyze these mechanisms for ordered Lieb-$L, {\mathrm{super}}^L\mathrm{honeycomb}$, and ${\mathrm{super}}^L\mathrm{triangular}$ lattices and examine their response to bond disorder, site disorder, random magnetic flux, and randomness in the inflation process itself. While bond and site disorder broaden most flat bands, the zero-energy chiral band and the junction-induced flat bands remain robust under certain perturbations. Remarkably, substantial flat-band features also persist in randomly bond-inflated graphs, even in the absence of translational symmetry. In particular, the number of zero-energy states is found to be well estimated by the matching deficiency $N-2\nu \left(G\right)$, indicating that local tree-like structure continues to control the low-energy nullity. These results identify bond-inflated lattices as a broad class of systems in which geometry alone generates robust localization in both ordered and random settings.

We study the quantum dynamics generated by the repeated action of a nonunitary evolution operator on a system of qubits. Breaking unitarity can lead to the purification of mixed initial states, which corresponds to the loss of sensitivity to initial conditions, and hence the absence of a key signature of dynamical chaos. However, the scrambling of quantum information can delay purification to times that are exponential in system size. Here we study purification in systems whose evolution operators are fixed in time, where all aspects of the dynamics are, in principle, encoded in spectral properties of the evolution operator for a single time step. The operators that we study consist of global Haar random unitary operators and nonunitary single-qubit operations. We show that exponentially slow purification arises from a distribution of eigenvalues in the complex plane that forms a ring with sharp edges at large radii, with the eigenvalue density exponentially large near these edges. We argue that the sharp edges of the eigenvalue distribution arise from level attraction along the radial direction in the complex plane. By calculating the spectral form factor, we also show that there is level repulsion around the azimuthal direction, even close to the outer edge of the ring of eigenvalues. Our results connect this spectral signature of quantum chaos to the sensitivity of the system to its initial conditions.

Recent work has proposed fading ergodicity as a mechanism for many-body ergodicity breaking. Here, we show that two paradigmatic random matrix ensembles, the Rosenzweig-Porter model and the ultrametric model, fall within the same universality class of ergodicity breaking when embedded in a many-body Hilbert space of spins $1/2$. By calibrating the parameters of both models via their Thouless times, we demonstrate that the matrix elements of local observables display similar statistical properties, allowing us to identify the fractal phase of the Rosenzweig-Porter model with the fading-ergodicity regime. This correspondence is further supported through the analyses of quantum-quench dynamics of local observables, their temporal fluctuations and power spectra, and survival probabilities. Our findings reveal that local observables thermalize within the fading-ergodicity regime on timescales shorter than the Heisenberg time, thus providing a unified framework for understanding ergodicity breaking across these distinct models.