Aperiodicity and Confinement in Dimer Models
Speaker: Felix Flicker (Bristol University) is the author of
Abstract: Certain particles, such as quarks, cannot appear in isolation. This phenomenon, called confinement, has proven difficult to capture mathematically: a Millennium Prize Problem asks for a proof of confinement in QCD. In condensed matter physics, quantum dimer models provide a setting to study confinement. Here, periodic dimer order implies confined excitations. This survives to an effective field theory. This begs the question: what if quantum dimers are placed in aperiodic settings? If periodic arrangements are impossible, can confinement occur in the emergent field theory?
After recapping our work on classical models in aperiodic tilings [1,2] I will present an exact solution to the quantum dimer model on the ‘Spectre’ aperiodic monotiling. We find deconfinement across the phase diagram [3]. However, the model does not admit an effective field theory. Hence, in ongoing work, we identify the most general structures that do admit such descriptions. In the classical model we find an infinite temperature deconfinement transition tunable by graph geometry. Turning to quantum dimers we argue that all the features present in periodic settings in fact survive to general graphs.
[1] Shobhna Singh, Jerome Lloyd, and Felix Flicker
Hamiltonian cycles on Ammann-Beenker Tilings
Physical Review X 14, 031005 (2024)
[2] Doruk Efe Gökmen, Sounak Biswas, Sebastian D. Huber, Zohar Ringel, Felix Flicker, and Maciej Koch-Janusz
Compression theory for inhomogeneous systems
Nature Communications 15, 10214 (2024)
[3] Shobhna Singh and Felix Flicker
Exact solution to the quantum and classical dimer models on the spectre aperiodic monotiling
Physical Review B 109, L220303 (2024)