Multiple non-hermitian phase transitions on quantum torus surface

TL;DR

This paper explores non-Hermitian phase transitions in a quantum fermion system confined to a torus surface, revealing how geometry and imaginary mass components influence these transitions.

Contribution

It introduces a numerical analysis of non-Hermitian phase transitions on quantum torus surfaces considering geometric effects via tetrad formalism.

Findings

Identification of non-Hermitian phase transitions influenced by torus geometry

Numerical eigenvalue and eigenfunction calculations for Dirac fermions

Demonstration of the impact of imaginary mass components on phase behavior

Abstract

In this paper we investigate the arising of non-hermitian phase transitions on quantum torus surfaces. We consider a single fermion whose dynamics is governed by the Dirac equation confined to move on a quantum torus surface. The effects of the geometry are take into account by using the tetrad formalism and the spin connection. The Dirac equation gives rise to two coupled first-order differential equations for each spinor component. The eigenvalues and eigenfunctions for each spinor component are computed numerically and the non-hermitian phase transitions are investigated in terms of the geometric features of the torus and the magnitude of the imaginary component of the mass.