In the global framework of quantum theory, the individual quantum systems seem clearly separated into two families with the respective manifestly Hermitian and hiddenly Hermitian operators of their Hamiltonian. In the light of certain preliminary studies, these two families seem to have an empty overlap. In this paper, we will show that whenever the interaction potentials are chosen to be weakly nonlocal, the separation of the two families may disappear. The overlapsaliasinterfaces between the Hermitian and non-Hermitian descriptions of a unitarily evolving quantum system in question may become nonempty. This assertion will be illustrated via a few analytically solvable elementary models.In the global framework of quantum theory, the individual quantum systems seem clearly separated into two families with the respective manifestly Hermitian and hiddenly Hermitian operators of their Hamiltonian. In the light of certain preliminary studies, these two families seem to have an empty overlap. In this paper, we will show that whenever the interaction potentials are chosen to be weakly nonlocal, the separation of the two families may disappear. The overlapsaliasinterfaces between the Hermitian and non-Hermitian descriptions of a unitarily evolving quantum system in question may become nonempty. This assertion will be illustrated via a few analytically solvable elementary models.

arXiv:1710.03470Advances in High Energy PhysicsJan 1, 20185 citations

Steady-state properties of quantum non-Hermitian lattice models

A. H. McDonald, Ryo Hanai, Aashish A. Clerk

Bulletin of the American Physical SocietyMar 17, 20210 citations

Exploring tunable non-Hermitian spin models based on dissipative bosonic atoms

Yu‐Yan Fang, Zuo-Yuan Zhang, Changyue Sun +2 more

We investigate the dynamical lattice behavior of ultracold bosonic atoms loaded into an optical lattice with two-body dissipation. In the Mott insulating limit, the resulting system can emulate a variety of spin-1/2 non-Hermitian Heisenberg models such as the non-Hermitian Ising, XX, and XXZ models. These different spin models are implemented by tuning the parameter spaces of the hopping amplitude, the loss rates of atoms, and on-site interaction of strength. Moreover, utilizing the improved non-Hermitian density-matrix renormalization group (NH-DMRG) algorithm, we present the correlation functions, Bell nonlocality $(\mathcal{B})$ , and quantum Fisher information (QFI) of the non-Hermitian spin systems, where the QFI inversion and order-of-magnitude reduction demonstrate a high sensitivity to the non-Hermitian system parameters. In addition, there exists a parameter space where non-Hermitian and Hermitian systems exhibit the same phase transition behavior as indicated by QFI and $\mathcal{B}$ . Our results open a new avenue toward the quantum simulation and observation of non-Hermitian many-body systems.We investigate the dynamical lattice behavior of ultracold bosonic atoms loaded into an optical lattice with two-body dissipation. In the Mott insulating limit, the resulting system can emulate a variety of spin-1/2 non-Hermitian Heisenberg models such as the non-Hermitian Ising, XX, and XXZ models. These different spin models are implemented by tuning the parameter spaces of the hopping amplitude, the loss rates of atoms, and on-site interaction of strength. Moreover, utilizing the improved non-Hermitian density-matrix renormalization group (NH-DMRG) algorithm, we present the correlation functions, Bell nonlocality $(\mathcal{B})$, and quantum Fisher information (QFI) of the non-Hermitian spin systems, where the QFI inversion and order-of-magnitude reduction demonstrate a high sensitivity to the non-Hermitian system parameters. In addition, there exists a parameter space where non-Hermitian and Hermitian systems exhibit the same phase transition behavior as indicated by QFI and $\mathcal{B}$. Our results open a new avenue toward the quantum simulation and observation of non-Hermitian many-body systems.

Physical review. B./Physical review. BFeb 28, 20251 citation

Hermitian/non-Hermitian interfaces in Schroedinger picture

Miloslav Znojil

In any unitary quantum theory with Hilbert space metric $\Theta$ the Schr\{o}dinger equation may be either Hermitian ( $\Theta=I$ ) or non-Hermitian ( $\Theta \neq I$ ). For local potentials the corresponding classes of quantum systems are clearly separated and the two families of the respective Hamiltonians have an empty overlap. Via elementary solvable examples we demonstrate that whenever the potentials are chosen weakly nonlocal, the separation may disappear and the overlaps {\it alias} interfaces may become non-empty.In any unitary quantum theory with Hilbert space metric $\Theta$ the Schr\{o}dinger equation may be either Hermitian ($\Theta=I$) or non-Hermitian ($\Theta \neq I$). For local potentials the corresponding classes of quantum systems are clearly separated and the two families of the respective Hamiltonians have an empty overlap. Via elementary solvable examples we demonstrate that whenever the potentials are chosen weakly nonlocal, the separation may disappear and the overlaps {\it alias} interfaces may become non-empty.

Oct 10, 20170 citations

(\mathcal{B})

, and quantum Fisher information (QFI) of the non-Hermitian spin systems, where the QFI inversion and order-of-magnitude reduction demonstrate a high sensitivity to the non-Hermitian system parameters. In addition, there exists a parameter space where non-Hermitian and Hermitian systems exhibit the same phase transition behavior as indicated by QFI and

\mathcal{B}

. Our results open a new avenue toward the quantum simulation and observation of non-Hermitian many-body systems.

In any unitary quantum theory with Hilbert space metric

\Theta

the Schr\{o}dinger equation may be either Hermitian (

\Theta=I

) or non-Hermitian (

\Theta \neq I

). For local potentials the corresponding classes of quantum systems are clearly separated and the two families of the respective Hamiltonians have an empty overlap. Via elementary solvable examples we demonstrate that whenever the potentials are chosen weakly nonlocal, the separation may disappear and the overlaps {\it alias} interfaces may become non-empty.