On an Exactly-Solvable One-Dimensional Non-Hermitian Lattice

Miloslav Znojil

Andreas Fring, Rebecca Tenney

L. Jin, Z. Song

We explore a way of finding the link between a non-Hermitian Hamiltonian and a Hermitian one. Based on the analysis of Bethe ansatz solutions for a class of non-Hermitian Hamiltonians and the scattering problems for the corresponding Hermitian Hamiltonians, it is shown that a scattering state of an arbitrary Hermitian lattice embedded in a chain as the scattering center shares the same wavefunction with the corresponding non-Hermitian tight binding lattice, which consists of the Hermitian lattice with two additional on-site complex potentials, no matter whether the non-Hermitian is broken symmetry or even non- symmetry. Exactly solvable models are presented to demonstrate the main points of this paper.

F. Cannata, M. V. Ioffe, D. N. Nishnianidze

Liang Mao, Xuanpu Yang, Ming‐Jie Tao +2 more

The non-Hermitian skin effect, in which eigenstates of non-Hermitian Hamiltonians are localized at one boundary in the open boundary condition, has attracted great interest recently. In this paper, we investigate the skin effect in one-dimensional dissipative quantum many-body systems, which we call the Liouvillian skin effect (LSE). We rigorously identify the existence of the LSE for generalized boundary conditions by solving the Liouvillian superoperator of an exactly solvable model with the advantage of the Bethe ansatz. The LSE is sensitive to boundary conditions where the signature is reflected in eigenfunctions of the system. We confirm that the LSE is fragile to a tiny coflow boundary hopping with non-Hermitian current but can survive a counterflow boundary hopping in the thermodynamic limit. Our work provides a prototypical example of exactly solvable dissipative quantum many-body lattice systems exhibiting the LSE for generalized boundary conditions. It can be further extended to other integrable open quantum many-body models.

Sharareh Sayyad, José Luis Lado

The interacting phase diagram of a non-Hermitian one-dimensional model featuring topologically different phases is demonstrated. Furthermore, the exact solution in the integrable regime, which has been extended to the nonintegrable regime by employing exact diagonalization and matrix product state methods, is presented. The present results are expected to pave a new pathway toward characterizing non-Hermitian topology in realistic interacting quantum many-body systems.