ICMCS seminar - Constraints and Aperiodicity

Title: Constraints and Aperiodicity

Abstract: Some of the most important phenomena in physics arise when correlations emerge from local constraints. I will outline results for a range of constrained models in the new setting of aperiodic tilings. On the Ammann Beenker tiling we prove the existence of Hamiltonian cycles (visiting each vertex precisely once), and thereby solve a range of problems including the three-colouring problem and the travelling salesperson problem [1]. On the recently discovered ‘Spectre’ aperiodic monotiling we exactly solve the interacting quantum dimer model [2]. I will highlight recent and ongoing work in which we generalise these results to random graphs. This ongoing work includes the development of a new machine learning approach (RSMI-NE) for studying constrained models in large networks without periodicity [3].

[1] Shobhna Singh, Jerome Lloyd, and Felix Flicker
Hamiltonian cycles on Ammann-Beenker Tilings
Physical Review X 14, 031005 (2024)

[2] 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)

[3] 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)

Join Zoom Meeting
https://ed-ac-uk.zoom.us/j/81211470751

Meeting ID: 812 1147 0751
Passcode: ICMCS123