The PT -symmetric non-Hermitian systems have been widely studied and explored both in theory and in experiment due to their various interesting features.In this work we focus on the dynamical features of a triplequbit system, one of which evolves under a local PT -symmetric Hamiltonian.An abnormal dynamic pattern in the entropy evolution process is identified that presents a parameter-dependent stable state, determined by the non-Hermiticity of Hamiltonian in the broken phase of PT symmetry.The entanglement and mutual information of a two-body subsystem can increase beyond the initial values, which do not exist in the Hermitian and two-qubit PT -symmetric systems.Moreover, an experimental demonstration of the stable states in non-Hermitian systems with nonzero entropy and entanglement is realized on a four-qubit quantum simulator with nuclear spins.Our work reveals the distinctive dynamic features in the triple-qubit PT -symmetric system and paves the way for practical quantum simulation of multiparty non-Hermitian system on quantum computers.
Abstract Parity Time Reversal (PT) phase transition is a typical characteristic of most of the PT symmetric non-Hermitian (NH) systems. Depending on the theory, a particular system and spacetime dimensionality PT phase transition has various interesting features. In this article we review some of our works on PT phase transitions in quantum mechanics (QM) as well as in Quantum Field theory (QFT). We demonstrate typical characteristics of PT phase transition with the help of several analytically solved examples. In one dimensional QM, we consider examples with exactly as well as quasi exactly solvable (QES) models to capture essential features of PT phase transition. The discrete symmetries have rich structures in higher dimensions which are used to explore the PT phase transition in higher dimensional systems. We consider anisotropic SHOs in two and three dimensions to realize some connection between the symmetry of original hermitian Hamiltonian and the unbroken phase of the NH system. We consider the 2+1 dimensional massless Dirac particle in the external magnetic field with PT symmetric non-Hermitian spin-orbit interaction in the background of the Dirac oscillator potential to show the PT phase transition in a relativistic system. A small mass gap, consistent with the other approaches and experimental observations is generated only in the unbroken phase of the system. Finally we develop the NH formulation in an SU(N) gauge field theoretic model by using the natural but unconventional Hermiticity properties of the ghost fields. Deconfinement to confinement phase transition has been realized as PT phase transition in such a non-hermitian model.
The occurrence of parity-time reversal
(PT) symmetry breaking is discussed in a non-Hermitian spin chain. The Hermiticity of the model is broken by the presence of an alternating, imaginary, transverse magnetic field. A full real spectrum, which occurs if and only if all the eigenvectors are
PT symmetric, can appear only in presence of dimerization, i.e., only if the hopping amplitudes between nearest-neighbor spins assume alternate values along the chain. In order to make a connection between such system and the Hermitian world, we study the critical magnetic properties of the model and look for the conditions that would allow to observe the same phase diagram in the absence of the imaginary field. Such procedure amounts to renormalizing the spin-spin coupling amplitudes.
We find a different effect for the behavior of von Neumann entropy. For this we derive the framework for describing von Neumann entropy in non-Hermitian quantum systems and then apply it to a simple interacting
PT-symmetric bosonic system. We show that our model is well defined even in the
PT-broken regime with the introduction of a time-dependent metric and that it displays three distinct behaviors relating to the
PT symmetry of the original time-independent Hamiltonian. When the symmetry is unbroken, the entropy undergoes rapid decay to zero (so-called ``sudden death'') with a subsequent revival. At the exceptional point it decays asymptotically to zero and when the symmetry is spontaneously broken it decays asymptotically to a finite constant value (``eternal life'').
By investigating information flow between a general parity-time (PT-)symmetric non-Hermitian system and an environment, we find that the complete information retrieval from the environment can be achieved in the PT-unbroken phase, whereas no information can be retrieved in the PT-broken phase. The PT-transition point thus marks the reversible-irreversible criticality of information flow, around which many physical quantities such as the recurrence time and the distinguishability between quantum states exhibit power-law behavior. Moreover, by embedding a PT-symmetric system into a larger Hilbert space so that the entire system obeys unitary dynamics, we reveal that behind the information retrieval lies a hidden entangled partner protected by PT symmetry. Possible experimental situations are also discussed.
Non-Hermitian systems having parity-time (
PT) symmetry can undergo a transition, spontaneously breaking the symmetry. Ultracold atomic gases provide an ideal platform to study interaction effects on the transition. We consider a model system of
N bosons of two components confined in a tight trap. Radio-frequency and laser fields are coupled to the bosons such that the single-particle Non-Hermitian Hamiltonian ${h}_{\mathcal{P}T}=\ensuremath{-}i\mathrm{\ensuremath{\Gamma}}{\ensuremath{\sigma}}_{z}+J{\ensuremath{\sigma}}_{x}$, which has
PT symmetry, can be simulated in a passive way, namely, in the physical system there is only incurred atom loss but no gain. We show that when interatomic interactions are tuned to maintain the symmetry, the
PT-symmetry-breaking transition is affected only by the SU(2) variant part of the interatomic interactions. We find that the transition point ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{tr}}$ decreases as the strength of this interaction part or
N increases; in the strong strength limit for this interaction part, ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{tr}}$ scales as the strength to the power of $\ensuremath{-}(N\ensuremath{-}1)$. We also give signatures of the
PT-symmetric and the symmetry-breaking phases for the interacting bosons in experiment.