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We introduce a new method for analysing the Bose-Hubbard model for an array of bosons with nearest neighbor interactions. It is based on a number-theoretic implementation of the creation and annihilation operators that constitute the model. One of the advantages of this approach is that it facilitates computation with arbitrary accuracy, enabling nearly perfect numerical experimentation. In particular, we provide a rigorous computer assisted proof of quantum phase transitions in finite systems of this type. Furthermore, we investigate properties of the infinite array via harmonic analysis on the multiplicative group of positive rationals. This furnishes an isomorphism that recasts the underlying Fock space as an infinite tensor product of Hecke spaces, i.e., spaces of square-integrable periodic functions that are a superposition of non-negative frequency harmonics. Under this isomorphism, the number-theoretic creation and annihilation operators are mapped into the Kastrup model of the harmonic oscillator on the circle. It also enables us to highlight a kinship of the model at hand with an array of spin moments with a local anisotropy field. This identifies an interesting physical system that can be mapped into the model at hand., Comment: 12 pages, 3 figures; submitted; accepted in Quantum

The monolayer halides CrX$_3$ (X=Cl, Br, I) attract significant attention for realizing 2D magnets with genuine long-range order (LRO), challenging the Mermin-Wagner theorem. Here, we show that monolayer CrCl$_3$ has the unique benefit of exhibiting tunable magnetic anisotropy upon applying a compressive strain. This opens the possibility to use CrCl$_3$ for producing and studying both ferromagnetic and antiferromagnetic 2D Ising-type LRO as well as the Berezinskii-Kosterlitz-Thouless (BKT) regime of 2D magnetism with quasi-LRO. Using state-of-the-art density functional theory, we explain how realistic compressive strain could be used to tune the monolayer's magnetic properties so that it could exhibit any of these phases. Building on large-scale quantum Monte Carlo simulations, we compute the phase diagram of strained CrCl$_3$, as well as the magnon spectrum with spin-wave theory. Our results highlight the eminent suitability of monolayer CrCl$_3$ to achieve very high BKT transition temperatures, around 50 K, due to their singular dependence on the weak easy-plane anisotropy of the material., 6 pages (4 figures) + 4 pages (6 figures)

The experimental realization of a coupled spin pair has been reported by Heiko Webber et.al and its theoretical description has been previously discussed including the condition that local magnetization of the junction is required for the individual moments to affect the electrons in the molecular ligand through the Kondo interaction. Here in this work, we show that when the couple spin pair is placed in an interferometry set up of the Aharonov-Bohm type additional features related to the switching behavior of the coupled spin pair emerge. This features lead to a phase dependent exchange magnetic field coming from the ferromagnets in proximity with the molecule, a phase dependent commutation of the singlet/triplet ground state around zero bias and it leads to variations in the voltage dependent effective exchange profile between the spin pair. These predictions contribute to the acceptance of the hypothesis that spin polarization can be harvested from quantum coherence in molecular quantum mechanics