Anuradha Jagannathan — Page 3

arXiv2002

Quantum Antiferromagnetism in Quasicrystals

The antiferromagnetic Heisenberg model is studied on a two-dimensional bipartite quasiperiodic lattice. The distribution of local staggered magnetic moments is determined on finite square approximants with up to 1393 sites, using the Stochastic Series Expansion Quantum Monte Carlo method. A non-trivial inhomogeneous ground state is found. For a given local coordination number, the values of the magnetic moments are spread out, reflecting the fact that no two sites in a quasicrystal are identical. A hierarchical structure in the values of the moments is observed which arises from the self-similarity of the quasiperiodic lattice. Furthermore, the computed spin structure factor shows antiferromagnetic modulations that can be measured in neutron scattering and nuclear magnetic resonance experiments. This generic model is a first step towards understanding magnetic quasicrystals such as the recently discovered Zn-Mg-Ho icosahedral structure.

cond-mat.str-el↗

arXiv1994

Energy level statistics of electrons in a 2D quasicrystal

A numerical study is made of the spectra of a tight-binding hamiltonian on square approximants of the quasiperiodic octagonal tiling. Tilings may be pure or random, with different degrees of phason disorder considered. The level statistics for the randomized tilings follow the predictions of random matrix theory, while for the perfect tilings a new type of level statistics is found. In this case, the first-, second- level spacing distributions are well described by lognormal laws with power law tails for large spacing. In addition, level spacing properties being related to properties of the density of states, the latter quantity is studied and the multifractal character of the spectral measure is exhibited.

cond-mat↗