Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $\beta$
| Autor: | Akemann, Gernot, Mielke, Adam, Päßler, Patricia |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Phys. Rev. E 106 (2022) 014146 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.106.014146 |
| Popis: | A random matrix representation is proposed for the two-dimensional (2D) Coulomb gas at inverse temperature $\beta$. For $2\times 2$ matrices with Gaussian distribution we analytically compute the nearest neighbour spacing distribution of complex eigenvalues in radial distance. Because it does not provide such a good approximation as the Wigner surmise in 1D, we introduce an effective $\beta_{\rm eff}(\beta)$ in our analytic formula, that describes the spacing obtained numerically from the 2D Coulomb gas well for small values of $\beta$. It reproduces the 2D Poisson distribution at $\beta=0$ exactly, that is valid for a large particle number. The surmise is used to fit data in two examples, from open quantum spin chains and ecology. The spacing distributions of complex symmetric and complex quaternion self-dual ensembles of non-Hermitian random matrices, that are only known numerically, are very well fitted by non-integer values $\beta=1.4$ and $\beta=2.6$ from a 2D Coulomb gas, respectively. These two ensembles have been suggested as the only two symmetry classes, where the 2D bulk statistics is different from the Ginibre ensemble. Comment: 6+9 pages, 4+5 figures; v2: 3 references added, typos corrected; v3: version to appear in Phys. Rev. E, 12 pages |
| Databáze: | arXiv |
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