2D MPS-DMRG: Quantum dimer model on a two-dimensional quasicrystal

Complex many-body quantum systems constitute many of the most interesting topics in physics, from quantum spin chains to frustrated magnets to quantum dimers and loops originally introduced to model high-temperature superconductors. But such phases are notoriously difficult, owing to the exponential scaling of Hilbert space, with the problem increasingly difficult in higher dimensions. Variational methods such as MPS-DMRG (matrix product state density matrix renormalisation group) offer access to low-lying energy states of such interacting systems, for example finding the ground states of large 1D many body systems to high accuracy. However, DMRG has found limited application in 2D or higher.

We successfully apply MPS-DMRG to quantum dimer model on large 2D systems, approximating the thermodynamic limit. The method is made tractable by placing the models on a modification of the Ammann Beenker tiling. Bearing the symmetries of a physical quasicrystal, the tiling features long-range order without periodicity. The dimer models combine with these symmetries so as to admit degrees of freedom similar to those in 1D ladders. We present an overview of ordered phases, phase transitions, entanglement entropy, and onsite and long-range correlations.

This work is with Felix Flicker and Natalia Chepiga.