article
GUE-chGUE transition preserving chirality at finite matrix size
published
yes
Takuya
Kanazawa
author
Mario
Kieburg
author 39774202
29104678
department
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.
Iop Publishing2018
eng
random matrix theoryPfaffian point processskew-orthogonalpolynomialsRMT application in QCDsymmetry transitionchiral randommatrices
Journal of Physics. A: Mathematical and Theoretical
1751-8113
1751-8121
1804.03985
1667182
00043913950000110.1088/1751-8121/aace3b
5134
Kanazawa T, Kieburg M (2018) <br /><em> Journal of Physics. A: Mathematical and Theoretical</em> 51(34): 345202.
T. Kanazawa and M. Kieburg, “GUE-chGUE transition preserving chirality at finite matrix size”, <em> Journal of Physics. A: Mathematical and Theoretical</em>, vol. 51, 2018, : 345202.
T. Kanazawa, and M. Kieburg, “GUE-chGUE transition preserving chirality at finite matrix size”, <em> Journal of Physics. A: Mathematical and Theoretical</em>, <strong>2018</strong>, <em>51</em>, : 345202.
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Kanazawa, T., & Kieburg, M. (2018). GUE-chGUE transition preserving chirality at finite matrix size. <em> Journal of Physics. A: Mathematical and Theoretical</em>, <em>51</em>(34), 345202. doi:10.1088/1751-8121/aace3b</div>
Kanazawa, T., and Kieburg, M. (2018). GUE-chGUE transition preserving chirality at finite matrix size. <em> Journal of Physics. A: Mathematical and Theoretical</em> 51:345202.
Kanazawa, T., & Kieburg, M. (2018). GUE-chGUE transition preserving chirality at finite matrix size. <em> Journal of Physics. A: Mathematical and Theoretical</em>, <em>51</em>(34), 345202. doi:10.1088/1751-8121/aace3b
Kanazawa T, Kieburg M. GUE-chGUE transition preserving chirality at finite matrix size. <em> Journal of Physics. A: Mathematical and Theoretical</em>. 2018;51(34): 345202.
Kanazawa, T.; Kieburg, M. (2018): GUE-chGUE transition preserving chirality at finite matrix size <em> Journal of Physics. A: Mathematical and Theoretical</em>,51:(34):345202
Kanazawa T, Kieburg M (2018) <br />GUE-chGUE transition preserving chirality at finite matrix size.<br /> Journal of Physics. A: Mathematical and Theoretical 51(34): 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, T., & Kieburg, M., 2018. GUE-chGUE transition preserving chirality at finite matrix size. <em> Journal of Physics. A: Mathematical and Theoretical</em>, 51(34): 345202.
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Kanazawa, T. & Kieburg, M. (2018). GUE-chGUE transition preserving chirality at finite matrix size. <em> Journal of Physics. A: Mathematical and Theoretical</em>, <em>51</em>(34): 345202. Iop Publishing. doi:10.1088/1751-8121/aace3b.</div>
Kanazawa, Takuya, and Kieburg, Mario. “GUE-chGUE transition preserving chirality at finite matrix size”. <em> Journal of Physics. A: Mathematical and Theoretical</em> 51.34 (2018): 345202.
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Kanazawa, Takuya, and Kieburg, Mario. 2018. “GUE-chGUE transition preserving chirality at finite matrix size”. <em> Journal of Physics. A: Mathematical and Theoretical</em> 51 (34): 345202.</div>
29305042018-08-21T09:22:54Z2018-08-21T12:06:53Z