AI for Science

The Kitaev honeycomb model has attracted significant interest due to its quantum spin liquid ground state, fractionalized Majorana excitations, and topological properties. Motivated by these features, we introduce a quasi-one-dimensional Kitaev-like spin chain derived from a truncated honeycomb geometry. The resulting Majorana band structure contains both dispersive and flat bands, with a gap closing at a critical anisotropy that separates trivial and chiral topological phases. Under open boundary conditions, the topological regime hosts zero-energy edge modes protected by chiral symmetry, placing the system in the BDI symmetry class with a quantized winding number. In the excited spectrum, localized plaquette modes emerge near zero energy and can be tuned by introducing domains of negative plaquettes. The dynamical spin correlation function reveals broad continua associated with fractionalized excitations, together with characteristic low-energy spectral weight from edge Majorana modes. These features distinguish the present system from conventional Heisenberg spin chains and provide experimentally relevant fingerprints of chiral topological order. Our model thus establishes a conceptual bridge between the two-dimensional Kitaev spin liquid and Kitaev's one-dimensional quantum wire.

Altermagnets are collinear magnetically ordered states that exhibit momentum-dependent spin splitting in the absence of net magnetization and spin-orbit coupling (SOC). Related spin-splitting patterns, however, can also emerge in noncollinear magnetic systems with large SOC. Here we show, via a microscopic model, that the all-in-all-out (AIAO) state in pyrochlore iridates constitutes a noncollinear counterpart of a $d$-wave altermagnet stabilized by strong SOC. Starting from a microscopic $j_{\mathrm{eff}} = 1/2$ tight-binding model on the pyrochlore lattice, we demonstrate that electronic interactions favor the AIAO phase and analyze its symmetry properties. We show that the AIAO order parameter transforms as an $A_{2g}^{-}$ octupolar magnetic moment, breaking time-reversal symmetry while preserving inversion and zero net magnetization. Using group-theory analysis and mean-field calculations, we demonstrate that this symmetry enforces both a spin-polarized momentum-dependent lifting of band degeneracies that is similar to that of a collinear $d$-wave cubic altermagnet, but also a band splitting at zero-momentum. We show that the latter feature is captured by a low-energy model similar to the Luttinger-Kohn model for cubic semiconductors. Our results identify pyrochlore iridates as a platform for noncollinear counterparts of altermagnetism and provide a general symmetry framework for spin-split phenomena in spin-orbit coupled materials.

Spin triplet superconductors are considered a promising platform for dissipationless spin transport, where spin currents are carried by spin triplet Cooper pairs. In this paper, we propose that the spin triplet superconductivity and spin supercurrent can be engineered in an altermagnetic superconducting nanowire, where a one-dimensional nanowire is placed on the surface of an s-wave superconductor and in proximity to the altermagnet. Using the nonequilibrium Green's function method, we demonstrate a nonzero equal spin Andreev reflection coefficient at the normal metal-altermagnetic superconducting nanowire interface, thereby verifying the injection of spin triplet Cooper pairs. Furthermore, we systematically investigate the spin transport properties in this hybrid system under a spin bias. Our results demonstrate that these properties can be effectively tuned by the chemical potential and spin bias orientation. Our proposal provides a pathway toward realizing dissipationless spin transport.

We investigate shells of active oriented solid, materials in which orientationally ordered active particles are embedded in a deformable elastic surface. Focusing on cylindrical geometries, we show that active stresses drive a new class of buckling instabilities and nonlinear patterns absent in passive shells. Linear stability analysis reveals that the unstable buckling mode is selected by the nematic orientation and activity sign, leading to axial, circumferential, and helical deformations. Remarkably, circumferential modes become unstable at arbitrarily small activity due to the absence of stretching costs. The results of the linear stability analysis are corroborated by full nonlinear simulations, which further uncover steady diamond shaped patterns and persistent dynamical states including oscillations, traveling domain walls, and propagating waves. Our results establish fundamental buckling modes and emergent patterns in shells of active oriented solid materials, with potential relevance to active biological tissues and engineered responsive materials.

We investigate the influence of nonlocal interactions on superconducting correlations within the extended Hubbard model. In addition to the on-site Coulomb interaction and nearest-neighbor hopping, we include next-nearest-neighbor hopping together with several physically relevant nonlocal terms, namely nearest-neighbor Coulomb interaction, correlated hopping, exchange interaction, and pair hopping. Using Lanczos exact diagonalization on a $4\times4$ cluster, supported by projector quantum Monte Carlo simulations for selected parameter regimes, we analyze pairing correlations in both the s- and d-wave channels. We demonstrate that nonlocal interactions exert a highly nontrivial and symmetry-dependent influence on superconducting correlations. While the on-site repulsion in cooperation with next-nearest-neighbor hopping enhances d-wave pairing tendencies, correlated hopping and nearest-neighbor Coulomb interaction strongly promote s-wave correlations, whereas exchange and pair-hopping interactions can efficiently suppress superconductivity beyond relatively small critical strengths. When all nonlocal interactions are considered simultaneously, the resulting phase diagrams reveal a complex interplay and competition between different pairing symmetries. Our results highlight the crucial role of extended interactions in shaping the pairing landscape of strongly correlated systems and demonstrate that a comprehensive treatment beyond the minimal Hubbard model is essential for a realistic description of unconventional superconductivity.

We propose a scheme to realize topological superconductor and Majorana bound states (MBSs) in a one-dimensional metal nanowire on the surface of a helical altermagnet and in proximity to an s-wave superconductor, removing the requirement of conventional spin-orbit coupling and net magnetism. Through gauge transformation, we demonstrate that the helical frame naturally induces spin-momentum locking while the altermagnetism breaks time-reversal symmetry. The topological superconducting phase is well tuned by chemical potential, altermagnet strength, and helical frequency. Besides, our transport calculation results reveal quantized conductance signatures: a 2e2/h zero-bias peak at nanowire ends and a 4e2/h tunneling conductance at the domain wall of nanowires with opposite chirality, detected via metal lead and scanning tunneling microscopy, respectively. Our research offers new perspectives on finding MBSs.

Quantum spin glasses are often considered testbeds for studying quantum optimization algorithms and as such have been the subject of various quantum advantage claims. Here we investigate the near adiabatic dynamics of biclique quantum spin glasses within the (discrete) truncated Wigner approximation (TWA). Benchmarks on small systems show that TWA recovers sample-to-sample fluctuations of the Edwards-Anderson order parameter, over a wide range of annealing times, with increasing fidelity when the system size increases. We extract critical exponents from the Binder cumulant in line with theoretical expectations, reproducing recent quantum experiments. The computational cost of the method is minimal and it can easily be applied to tens of thousands of qubits.

The interplay of topological surface states and magnetism gives rise to unconventional transport behaviors such as the anomalous Hall effect (AHE) and anomalous Nernst effect (ANE). Antiperovskites such as Mn$3$SnC, which are nodal-line semimetals and exhibit concurrent antiferromagnetic (AFM) and ferromagnetic (FM) ordering, provide a fertile ground for anomalous transport phenomena. Here, we report that the anomalous transport (AHE and ANE) in this compound is predominantly governed by the intrinsic Berry-curvature effect. We establish a unified relationship between the AHE and ANE using Mott's relation. Electron scattering by both AFM and FM magnons is manifested in the anomalous Nernst signal. The ratio of the anomalous Nernst conductivity to the anomalous Hall conductivity, $|α^A{xy}|/σ^A_{xy}$, constitutes a sizable fraction of $k_B/e$, indicating a strong Berry-curvature contribution to the ANE.

We use new homotopy-theoretic tools to prove the existence of smooth $U(1)$- and $Sp(1)$-actions on infinite families of exotic spheres. Such families of spheres are propagated by the complex and quaternionic analogues of the Mahowald invariant (also known as the root invariant). In particular, we prove that the complex (respectively, quaternionic) Mahowald invariant takes an element of the $k$-th stable stem $π_k^s$ represented by a homotopy sphere $Σ^k$ to an element of a higher stable stem $π_{k+\ell}^s$ represented by another homotopy sphere $Σ^{k+\ell}$ equipped with a smooth $U(1)$- (respectively, $Sp(1)$-) action with fixed points the original homotopy sphere $Σ^k\subset Σ^{k+\ell}$.

We prove Demailly's Conjecture concerning the lower bound for the Waldschmidt constant in terms of the initial degree of the second symbolic powers for any set of generic points or very general points in $\mathbb{P}^N$. We also discuss the Harbourne-Huneke Containment and the aforementioned Demailly's Conjecture for general points and show the results for sufficiently many general points and general points in projective spaces with low dimensions.