ICMCS seminar - Aperiodicity and Particle Confinement

Title: Aperiodicity and Particle Confinement

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. One of the few rigorous results in this area is
Polyakov's demonstration that particles are always confined in compact
2+1D U(1) gauge theories. This result is invoked in condensed matter
physics in the context of quantum dimer models. Dimers are
non-overlapping pairs of neighbouring edges (like dominoes on a chess
board). On bipartite lattices quantum dimer models coarse grain to
compact QED. Polyakov's result suggests that 'monomer' particle
excitations must then be confined. Microscopically, confinement results
from periodic dimer arrangements. 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?

In this talk I will answer these questions. After recapping our work on
classical models in aperiodic tilings [1,2] I will present recent work
in which we exactly solve 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
description. Hence, in ongoing work, we identify the most general
structures that do admit such descriptions. In the classical dimer model
we find a confinement-deconfinement phase transition tunable by graph
geometry, which we argue is an example of UV-IR mixing. Remarkably, this
survives to infinite temperature. We demonstrate that long-range ordered
dimer configurations always exist, regardless of periodicity, giving a
microscopic origin of confinement. 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)

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

Meeting ID: 812 1147 0751
Passcode: ICMCS123