### GUE-chGUE transition preserving chirality at finite matrix size

Kanazawa T, Kieburg M (2018)
Journal of Physics. A: Mathematical and Theoretical 51(34): 345202.

Zeitschriftenaufsatz | Veröffentlicht| Englisch

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Autor/in
Kanazawa, Takuya; Kieburg, MarioUniBi
Abstract / Bemerkung
We study a random matrix model which interpolates between the singular values of the Gaussian unitary ensemble (GUE) and of the chiral Gaussian unitary ensemble (chGUE). This symmetry crossover is analogous to the one realized by the Hermitian Wilson Dirac operator in lattice QCD, but our model preserves chiral symmetry of chGUE, exactly unlike the Hermitian Wilson Dirac operator. This difference has a crucial impact on the statistics of near-zero eigenvalues, though both singular value statistics build a Pfaffian point process. The model in the present work is motivated by the Dirac operator of 3D staggered fermions, 3D QCD at finite isospin chemical potential, and 4D QCD at high temperature. We calculate the spectral statistics at finite matrix dimension. For this purpose, we derive the joint probability density of the singular values, the skew-orthogonal polynomials and the kernels for the k-point correlation functions. The skew-orthogonal polynomials are constructed by the method of mixing bi-orthogonal and skew-orthogonal polynomials, which is an alternative approach to Mehta's one. We compare our results with Monte Carlo simulations and study the limits to chGUE and GUE. As a side product, we also calculate a new type of a unitary group integral.
Stichworte
random matrix theory; Pfaffian point process; skew-orthogonal; polynomials; RMT application in QCD; symmetry transition; chiral random; matrices
Erscheinungsjahr
2018
Zeitschriftentitel
Journal of Physics. A: Mathematical and Theoretical
Band
51
Ausgabe
34
Art.-Nr.
345202
ISSN
1751-8113
eISSN
1751-8121
Page URI
https://pub.uni-bielefeld.de/record/2930504

### Zitieren

Kanazawa T, Kieburg M. GUE-chGUE transition preserving chirality at finite matrix size. Journal of Physics. A: Mathematical and Theoretical. 2018;51(34): 345202.
Kanazawa, T., & Kieburg, M. (2018). GUE-chGUE transition preserving chirality at finite matrix size. Journal of Physics. A: Mathematical and Theoretical, 51(34), 345202. doi:10.1088/1751-8121/aace3b
Kanazawa, T., and Kieburg, M. (2018). GUE-chGUE transition preserving chirality at finite matrix size. Journal of Physics. A: Mathematical and Theoretical 51:345202.
Kanazawa, T., & Kieburg, M., 2018. GUE-chGUE transition preserving chirality at finite matrix size. Journal of Physics. A: Mathematical and Theoretical, 51(34): 345202.
T. Kanazawa and M. Kieburg, “GUE-chGUE transition preserving chirality at finite matrix size”, Journal of Physics. A: Mathematical and Theoretical, vol. 51, 2018, : 345202.
Kanazawa, T., Kieburg, M.: GUE-chGUE transition preserving chirality at finite matrix size. Journal of Physics. A: Mathematical and Theoretical. 51, : 345202 (2018).
Kanazawa, Takuya, and Kieburg, Mario. “GUE-chGUE transition preserving chirality at finite matrix size”. Journal of Physics. A: Mathematical and Theoretical 51.34 (2018): 345202.

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### Quellen

arXiv: 1804.03985

Inspire: 1667182