---
_id: '2930504'
abstract:
- lang: eng
text: 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.
article_number: '345202'
article_type: original
author:
- first_name: Takuya
full_name: Kanazawa, Takuya
last_name: Kanazawa
- first_name: Mario
full_name: Kieburg, Mario
id: '39774202'
last_name: Kieburg
citation:
ama: 'Kanazawa T, Kieburg M. GUE-chGUE transition preserving chirality at finite
matrix size. * Journal of Physics. A: Mathematical and Theoretical*. 2018;51(34):
345202.'
angewandte-chemie: 'T. Kanazawa, and M. Kieburg, “GUE-chGUE transition preserving
chirality at finite matrix size”, * Journal of Physics. A: Mathematical and
Theoretical*, **2018**, *51*, : 345202.'
apa: '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'
apa_indent: '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

'
bio1: 'Kanazawa T, Kieburg M (2018)

GUE-chGUE transition preserving chirality
at finite matrix size.

Journal of Physics. A: Mathematical and Theoretical
51(34): 345202.'
chicago: 'Kanazawa,
Takuya, and Kieburg, Mario. 2018. “GUE-chGUE transition preserving chirality at
finite matrix size”. * Journal of Physics. A: Mathematical and Theoretical*
51 (34): 345202.

'
default: 'Kanazawa T, Kieburg M (2018)

* Journal of Physics. A: Mathematical
and Theoretical* 51(34): 345202.'
dgps: 'Kanazawa,
T. & Kieburg, M. (2018). GUE-chGUE transition preserving chirality at finite
matrix size. * Journal of Physics. A: Mathematical and Theoretical*, *51*(34):
345202. Iop Publishing. doi:10.1088/1751-8121/aace3b.

'
frontiers: 'Kanazawa, T., and Kieburg, M. (2018). GUE-chGUE transition preserving
chirality at finite matrix size. * Journal of Physics. A: Mathematical and
Theoretical* 51:345202.'
harvard1: 'Kanazawa, T., & Kieburg, M., 2018. GUE-chGUE transition preserving
chirality at finite matrix size. * Journal of Physics. A: Mathematical and
Theoretical*, 51(34): 345202.'
ieee: ' 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.'
lncs: ' Kanazawa, T., Kieburg, M.: GUE-chGUE transition preserving chirality at
finite matrix size. Journal of Physics. A: Mathematical and Theoretical. 51,
: 345202 (2018).'
mla: '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.'
wels: 'Kanazawa, T.; Kieburg, M. (2018): GUE-chGUE transition preserving chirality
at finite matrix size * Journal of Physics. A: Mathematical and Theoretical*,51:(34):345202'
date_created: 2018-08-21T09:22:54Z
date_updated: 2018-08-21T12:06:53Z
department:
- _id: '29104678'
doi: 10.1088/1751-8121/aace3b
external_id:
arxiv:
- '1804.03985'
inspire:
- '1667182'
isi:
- '000439139500001'
intvolume: ' 51'
isi: 1
issue: '34'
keyword:
- random matrix theory
- Pfaffian point process
- skew-orthogonal
- polynomials
- RMT application in QCD
- symmetry transition
- chiral random
- matrices
language:
- iso: eng
publication: ' Journal of Physics. A: Mathematical and Theoretical'
publication_identifier:
eissn:
- 1751-8121
issn:
- 1751-8113
publication_status: published
publisher: Iop Publishing
quality_controlled: '1'
status: public
title: GUE-chGUE transition preserving chirality at finite matrix size
type: journal_article
user_id: '67994'
volume: 51
year: '2018'
...