Global phase diagram of two-dimensional dirty hyperbolic Dirac liquids
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909943873929216 |
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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 |