Quasicrystals are ordered but never repeat, so the shortcuts used to simulate crystals do not apply and large calculations are costly. Milla Kolehmainen, Jose Lado and Anouar Moustaj of QMAT's Correlated Quantum Materials group at Aalto University show that the substitution rules that generate one-dimensional quasicrystals define a finite automaton whose transition matrices are exactly the tensors of a matrix product state.

This yields an exact, compact tensor-network representation of the quasicrystal Hamiltonian at any size. The team constructed Fibonacci, silver-mean and Tribonacci quasicrystals and, combining the approach with the kernel polynomial method, computed spectral densities for chains of more than a billion sites, directly resolving the hierarchical structure of their spectra.

The preprint has not yet been peer reviewed.

Image: QMAT