Non-Hermitian Parent Hamiltonian and Composite Quantum Phases
Date:
In this talk, I plan to introduce our two recent works (arXiv: 2301.12448, arXiv: 2304.04588) on non-Hermitian interacting spin systems. I will begin with introducing the basic concept of tensor networks, and the conventional parent Hamiltonian method for Hermitian systems. Next, I will discuss our proposed non-Hermitian parent Hamiltonian (nH-PH), where one can start from two different matrix product states (MPS) and construct a local Hamiltonian such that these states are zero-energy modes. I will then introduce a class of new topological phases in non-Hermitian interacting systems without Hermitian counterparts, denoted as composite quantum phases. With the nH-PH approach, we construct a spin-1 model to realize this type of exotic phases. I will finally show the phase diagram of our model and demonstrate that such novel phases can exist extensively in non-Hermitian systems.