Exactly solvable $\mathcal{PT}$-symmetric models in two dimensions

TL;DR

This paper introduces a family of exactly solvable two-dimensional $ ext{PT}$-symmetric models in circular geometries, revealing complex phase diagrams with multiple re-entrant symmetric phases and tunable symmetry-breaking thresholds.

Contribution

It provides the first explicit construction of exactly solvable 2D $ ext{PT}$-symmetric potentials, expanding understanding of $ ext{PT}$ symmetry breaking in higher dimensions.

Findings

Multiple re-entrant $ ext{PT}$ symmetric phases identified.

$ ext{PT}$ symmetry threshold can be tuned via gain-loss potentials.

Explicit solutions demonstrate complex phase diagram in 2D $ ext{PT}$ models.

Abstract

Non-hermitian, $\mathcal{PT}$-symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly solvable, two-dimensional, $\mathcal{PT}$ potentials for a non-relativistic particle confined in a circular geometry. We show that the $\mathcal{PT}$ symmetry threshold can be tuned by introducing a second gain-loss potential or its hermitian counterpart. Our results explicitly demonstrate that $\mathcal{PT}$ breaking in two dimensions has a rich phase diagram, with multiple re-entrant $\mathcal{PT}$ symmetric phases.