Dynamic mass generation on two-dimensional electronic hyperbolic lattices

Abstract

Free electrons hopping on hyperbolic lattices embedded on a negatively curved space can foster (a) Dirac liquids, (b) Fermi liquids, and (c) flat bands, respectively characterized by a vanishing, constant, and divergent density of states near the half filling. From numerical self-consistent mean-field Hartree analyses, we show that nearest-neighbor Coulomb and on-site Hubbard repulsions respectively give rise to charge-density-wave and antiferromagnetic orders featuring staggered patterns of average electronic density and magnetization in all these systems, when the hyperbolic tessellation is accomplished by periodic arrangements of even $p$-gons. Both quantum orders dynamically open mass gaps near the charge neutrality point via spontaneous symmetry breaking. Only on hyperbolic Dirac materials these orderings take place via quantum phase transitions (QPTs) beyond critical interactions, which however decrease with increasing curvature, showcasing curvature-induced weak-coupling QPTs. We present scaling of these masses with the corresponding interaction strengths.

Published version in PRB as a Letter (Editor's Suggestion): 6 Pages, 3 Figures & 1 Table (Supplementary Material as Ancillary file)

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Cited by in corpus (8)

• Hyperbolic Spin Liquids
• Emergence of a Boundary-Sensitive Phase in Hyperbolic Ising Models
• Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
• Quantum geometric tensors from sub-bundle geometry
• Walking on Archimedean Lattices: Insights from Bloch Band Theory
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