PT phase transition in multidimensional quantum systems

Abstract

Non-Hermitian PT-symmetric quantum-mechanical Hamiltonians generally exhibit a phase transition that separates two parametric regions, (i) a region of unbroken PT symmetry in which the eigenvalues are all real, and (ii) a region of broken PT symmetry in which some of the eigenvalues are complex. This transition has recently been observed experimentally in a variety of physical systems. Until now, theoretical studies of the PT phase transition have generally been limited to one-dimensional models. Here, four nontrivial coupled PT-symmetric Hamiltonians, $H=p^2/2+x^2/2+q^2/2+y^2/2+ig{x}^{2}y$, $H=p^2/2+x^2/2+q^2/2+y^2+ig{x}^{2}y$, $H=p^2/2+x^2/2+q^2/2+y^2/2+r^2/2+z^2/2+igxyz$, and $H=p^2/2+x^2/2+q^2/2+y^2+r^2/2+3z^2/2+igxyz$ are examined. Based on extensive numerical studies, this paper conjectures that all four models exhibit a phase transition. The transitions are found to occur at $g\approx 0.1$, $g\approx 0.04$, $g\approx 0.1$, and $g\approx 0.05$. These results suggest that the PT phase transition is a robust phenomenon not limited to systems having one degree of freedom.

15 pages, 14 figures

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Cited by in corpus (8)

• Non-hermitean hamiltonians with unitary and antiunitary symmetry
• PT-symmetry broken by point-group symmetry
• Is space-time symmetry a suitable generalization of parity-time symmetry?
• Detecting exceptional points through dynamics in non-Hermitian systems
• Non-Hermitian oscillators with $T_d$ symmetry
• Detection of unbroken phase of non-Hermitian system via Hermitian factorization surface
• PT symmetric lattices with a local degree of freedom
• Functional renormalization group for non-Hermitian and $\mathcal{P}\mathcal{T}$-symmetric systems