Global phase diagram of two-dimensional dirty hyperbolic Dirac liquids

Fuente: arXiv
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Autores principales: Leong, Christopher A., Salib, Daniel J., Roy, Bitan
Formato: Preprint
Publicado: 2025
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author Leong, Christopher A.
Salib, Daniel J.
Roy, Bitan
author_facet Leong, Christopher A.
Salib, Daniel J.
Roy, Bitan
contents Within the framework of the canonical nearest-neighbor tight-binding model for spinless fermions, a family of two-dimensional bipartite hyperbolic lattices hosts massless Diraclike excitations near half-filling with the iconic vanishing density of states (DOS) near zero energy. We show that a collection of such ballistic quasiparticles remains stable against sufficiently weak pointlike charge impurities, a feature captured by the vanishing average [$ρ_{a}(0)$] and typical [$ρ_{t}(0)$] DOS at zero energy, computed by employing the kernel polynomial method in sufficiently large $\{ 10, 3\}$ hyperbolic lattices (Schläfli symbol) with more than $10^8$ and $10^5$ sites, respectively, with open boundary conditions. However, at moderate disorder the system enters a metallic state via a continuous quantum phase transition where both $ρ_{a}(0)$ and $ρ_{t}(0)$ become finite. With increasing strength of disorder, ultimately an Anderson insulator sets in, where only $ρ_{t}(0) \to 0$. The resulting phase diagram for dirty Dirac fermions living on a hyperbolic space solely stems from the background negative spatial curvature, as confirmed from the vanishing $ρ_{t}(0)$ for arbitrarily weak disorder on honeycomb lattices, fostering relativistic fermions on a flatland, as the thermodynamic limit is approached.
format Preprint
id arxiv_https___arxiv_org_abs_2512_05109
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Global phase diagram of two-dimensional dirty hyperbolic Dirac liquids
Leong, Christopher A.
Salib, Daniel J.
Roy, Bitan
Mesoscale and Nanoscale Physics
Disordered Systems and Neural Networks
Statistical Mechanics
High Energy Physics - Theory
Within the framework of the canonical nearest-neighbor tight-binding model for spinless fermions, a family of two-dimensional bipartite hyperbolic lattices hosts massless Diraclike excitations near half-filling with the iconic vanishing density of states (DOS) near zero energy. We show that a collection of such ballistic quasiparticles remains stable against sufficiently weak pointlike charge impurities, a feature captured by the vanishing average [$ρ_{a}(0)$] and typical [$ρ_{t}(0)$] DOS at zero energy, computed by employing the kernel polynomial method in sufficiently large $\{ 10, 3\}$ hyperbolic lattices (Schläfli symbol) with more than $10^8$ and $10^5$ sites, respectively, with open boundary conditions. However, at moderate disorder the system enters a metallic state via a continuous quantum phase transition where both $ρ_{a}(0)$ and $ρ_{t}(0)$ become finite. With increasing strength of disorder, ultimately an Anderson insulator sets in, where only $ρ_{t}(0) \to 0$. The resulting phase diagram for dirty Dirac fermions living on a hyperbolic space solely stems from the background negative spatial curvature, as confirmed from the vanishing $ρ_{t}(0)$ for arbitrarily weak disorder on honeycomb lattices, fostering relativistic fermions on a flatland, as the thermodynamic limit is approached.
title Global phase diagram of two-dimensional dirty hyperbolic Dirac liquids
topic Mesoscale and Nanoscale Physics
Disordered Systems and Neural Networks
Statistical Mechanics
High Energy Physics - Theory
url https://arxiv.org/abs/2512.05109