---
res:
bibo_abstract:
- 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.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Takuya
foaf_name: Kanazawa, Takuya
foaf_surname: Kanazawa
- foaf_Person:
foaf_givenName: Mario
foaf_name: Kieburg, Mario
foaf_surname: Kieburg
foaf_workInfoHomepage: http://www.librecat.org/personId=39774202
bibo_doi: 10.1088/1751-8121/aace3b
bibo_issue: '34'
bibo_volume: 51
dct_date: 2018^xs_gYear
dct_identifier:
- UT:000439139500001
dct_isPartOf:
- http://id.crossref.org/issn/1751-8113
- http://id.crossref.org/issn/1751-8121
dct_language: eng
dct_publisher: Iop Publishing@
dct_subject:
- random matrix theory
- Pfaffian point process
- skew-orthogonal
- polynomials
- RMT application in QCD
- symmetry transition
- chiral random
- matrices
dct_title: GUE-chGUE transition preserving chirality at finite matrix size@
...