We study the realization of conformal symmetry in the QHE as part of the W∞ algebra. Conformal symmetry can be realized already at the classical level and implies the complexification of coordinate space. Its quantum version is not unitary. Nevertheless, it can be rendered unitary by a suitable modification of its definition which amounts to taking proper care of the quantum measure. The conseq...

The class of norm–dependent Random Matrix Ensembles is studied in the presence of an external field. The probability density in those ensembles depends on the trace of the squared random matrices, but is otherwise arbitrary. An exact mapping to superspace is performed. A transformation formula is derived which gives the probability density in superspace as a single integral over the probability...

In a recent study we have obtained correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random N × N matrices, both in the bulk and at the soft edge of the spectrum. In the present study these results are used to similarly analyze the eigenvalue density for Gaussian and Laguerre random matrix ensembles with or...

A non-singular sesquilinear form is constructed that is preserved by the Lawrence-Krammer representation. It is shown that if the polynomial variables q and t of the Lawrence-Krammer representation are chosen to be appropriate algebraically independant unit complex numbers, then the form is negativedefinite Hermitian. Since unitary matrices diagonalize, the conjugacy class of a matrix in the un...

The field-induced phase transitions in FeBr2-type crystal under hydrostatic pressure have been determined in terms of Landau's theory, with the paramagnetic phase described by a unitary or a non-unitary group. The sets of low-temperature symmetry groups implied by these two descriptions partly overlap.

Recently, Kalkreuter obtained complete Dirac spectra for SU (2) lattice gauge theory both for staggered fermions and for Wilson fermions. The lattice size was as large as 12 4. We performed a statistical analysis of these data and found that the eigenvalue correlations can be described by the Gaussian Symplectic Ensemble for staggered fermions and by the Gaussian Orthogonal Ensemble for Wilson ...

Symmetry-protected topological superconductors (TSCs) can host multiple Majorana zero modes (MZMs) at their edges or vortex cores, while whether the braiding in such systems is non-Abelian general remains an open question. Here we uncover theory unitary symmetry-protected statisitcs of MZMs and propose experimental realization. We show that two vortices with each hosting $N$ generically reduces...