Hyperbolic lattices and two-dimensional Yang-Mills theory

Abstract

Hyperbolic lattices are a new type of synthetic quantum matter emulated in circuit quantum electrodynamics and electric-circuit networks, where particles coherently hop on a discrete tessellation of two-dimensional negatively curved space. While real-space methods and a reciprocal-space hyperbolic band theory have been recently proposed to analyze the energy spectra of those systems, discrepancies between the two sets of approaches remain. In this work, we reconcile those approaches by first establishing an equivalence between hyperbolic band theory and $U(N)$ topological Yang-Mills theory on higher-genus Riemann surfaces. We then show that moments of the density of states of hyperbolic tight-binding models correspond to expectation values of Wilson loops in the quantum gauge theory and become exact in the large-$N$ limit.

published version. main text: 5.5 pages; supplemental material: 11 pages

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Cited by in corpus (7)

• Topological linear response of hyperbolic Chern insulators
• Hyperbolic Spin Liquids
• Wormhole-induced effective coupling in SYK chains
• Holographic Foliations: Self-Similar Quasicrystals from Hyperbolic Honeycombs
• Walking on Archimedean Lattices: Insights from Bloch Band Theory
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices