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In magnetically ordered insulators, elementary quasiparticles manifest as spin waves - collective motions of localized magnetic moments propagating through the lattice - observed via inelastic neutron scattering. In effective spin-1/2 systems where geometric frustrations suppress static magnetic order, spin excitation continua can emerge, either from degenerate classical spin ground states or from entangled quantum spins characterized by emergent gauge fields and deconfined fractionalized excitations. Comparing the spin Hamiltonian with theoretical models can unveil the microscopic origins of these zero-field spin excitation continua. Here, we use neutron scattering to study spin excitations of the two-dimensional (2D) triangular-lattice effective spin-1/2 antiferromagnet CeMgAl11O19. Analyzing the spin waves in the field-polarized ferromagnetic state, we find that the spin Hamiltonian is close to an exactly solvable 2D triangular-lattice XXZ model, where degenerate 120$^\circ$ ordered ground states - umbrella states - develop in the zero temperature limit. We then find that the observed zero-field spin excitation continuum matches the calculated ensemble of spin waves from the umbrella state manifold, and thus conclude that CeMgAl11O19 is the first example of an exactly solvable spin liquid on a triangular lattice where the spin excitation continuum arises from the ground state degeneracy., Comment: 11 pages, 5 figures

In the search of quantum spin liquid (QSLs), spin-1/2 triangular-lattice Heisenberg antiferromagnets (TLHAFs) have always been viewed as fertile soils. Despite the true magnetically-ordered ground state, anisotropy has been considered to play a significant role in stabilizing a QSL state. However, the nature and ground state of the most anisotropic case, the triangular-lattice Ising antiferromagnet (TLIAF), remains elusive and controversial. Here, we report specific heat and thermal conductivity measurements on a newly-discovered Ising-type QSL candidate PrMgAl11O19. At zero field, the magnetic specific heat shows a quadratic temperature dependence. On the contrary, no direct positive magnetic contribution to thermal conductivity was detected, ruling out the presence of mobile gapless fermionic excitations. Further analysis of phonon thermal conductivity reveals that the phonons are strongly scattered by thermally-activated magnetic excitations out of a gap, which exhibits a linear dependence with magnetic field. These results demonstrate that the spin-1/2 TLIAF PrMgAl11O19 has a gapped Z2 QSL ground state., Comment: 24 pages, 4 figures

Recently, the Hofstadter spectrum of a twisted $\mathrm{WSe_2/MoSe_2}$ heterobilayer has been observed in experiment [C. R. Kometter, et al. Nat.Phys.19, 1861 (2023)], but the origin of Hofstadter states remains unclear. Here, we present a comprehensive theoretical interpretation of the observed Hofstadter states by calculating its accurate Hofstadter spectrum. We point out that the valley Zeeman effect, a unique feature of the transition metal dichalcogenide (TMD) materials, plays a crucial role in determining the shape of the Hofstadter spectrum, due to the narrow bandwidth of the moir\'e bands. This is distinct from the graphene-based moir\'e systems. We further predict that the Hofstadter spectrum of the moir\'e flat band, which was not observed in experiment, can be observed in the same system with a larger twist angle $2^\circ\lesssim\theta \lesssim 3^\circ$. Our theory paves the way for further studies of the interplay between the Hofstadter states and correlated insulting states in such moir\'e lattice systems., Comment: 7 pages, 4 figures

Digital watermarking methods are commonly used to safeguard digital media copyrights by confirming ownership and deterring unauthorized use. However, without reliable third-party oversight, these methods risk security vulnerabilities during watermark extraction. Furthermore, digital media lacks tangible ownership attributes, posing challenges for secure copyright transfer and tracing. This study introduces DataSafe, a copyright protection scheme that combines physical unclonable functions (PUFs) and blockchain technology. PUF devices use their unique fingerprints for blockchain registration. Subsequently, these devices incorporate invisible watermarking techniques to embed digital watermarks into media for copyright protection. The watermark verification process is confined within the devices, preserving confidentiality during extraction, validating identities during copyright exchanges, and facilitating blockchain-based traceability of copyright transfers. The implementation of a prototype system on the LPC55S69-EVK development board is detailed, illustrating the practicality and effectiveness of the proposed solution.

Quantum spin liquids (QSLs) represent a novel state where spins are highly entangled but do not order even at zero temperature due to strong quantum fluctuations. Such a state is mostly studied in Heisenberg models defined on geometrically frustrated lattices. Here, we turn to a new triangular-lattice antiferromagnet PrMgAl$_{11}$O$_{19}$, in which the interactions are believed to be of Ising type. Magnetic susceptibility measured with an external field along the $c$ axis is two orders of magnitude larger than that with a field in the $ab$ plane, displaying an ideal easy-axis behavior. Meanwhile, there is no magnetic phase transition or spin freezing observed down to 1.8 K. Ultralow-temperature specific heat measured down to 50 mK does not capture any phase transition either, but a hump at 4.5 K, below which the magnetic specific heat exhibits a quasi-quadratic temperature dependence that is consistent with a Dirac QSL state. Inelastic neutron scattering technique is also employed to elucidate the nature of its ground state. In the magnetic excitation spectra, there is a gapless broad continuum at the base temperature 55~mK, in favor of the realization of a gapless QSL. Our results provide a scarce example for the QSL behaviors observed in an Ising-type magnet, which can serve as a promising platform for future research on QSL physics based on an Ising model., Comment: 11 pages, 5 figures