Felix Flicker

Exact Solution to the Quantum and Classical Dimer Models on the 'Spectre' Aperiodic Monotiling

Rigorously proving quark confinement constitutes one of the Millennium prize problems. A simpler case is the quantum dimer model on the square lattice. This microscopic model allows a systematic construction of a field theory in its long-wavelength limit. Here, deconfined phases cannot exist owing to the proliferation of instantons. It was believed that the same result must hold for quantum dimer models on all planar bipartite graphs, where confinement relates to periodicity of dimers. We provide a counterexample on the recently discovered 'Spectre' aperiodic monotiling [1]. By exactly solving the quantum (and classical) dimer model in this setting, we show that excitations can be separated to infinite distance at zero energy cost at all points in the phase diagram [2]. I will also show ongoing work in which we construct a field theory from fully packed loops on another aperiodic planar bipartite tiling [3], to see how confinement returns.

[1] D. Smith, J. S. Myers, C. S. Kaplan, and C. Goodman-Strauss, arXiv:2305.17743
[2] S. Singh and F. Flicker, arXiv:2309.14447
[3] S. Singh, J. Lloyd, and F. Flicker, arXiv:2302.01940