Non-Hermitian Parent Hamiltonian from Generalized Quantum Covariance Matrix

• URL: http://arxiv.org/abs/2307.03107v1
• Date: Thu, 6 Jul 2023 16:27:22 GMT
• Title: Non-Hermitian Parent Hamiltonian from Generalized Quantum Covariance Matrix
• Authors: Yin Tang, W. Zhu
• Abstract summary: We provide a systematical and efficient way to construct non-Hermitian Hamiltonian from a single pair of biorthogonal eigenstates. Our work sheds light on future exploration on non-Hermitian physics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum inverse problem is defined as how to determine a local Hamiltonian from a single eigenstate? This question is valid not only in Hermitian system but also in non-Hermitian system. So far, most attempts are limited to Hermitian systems, while the possible non-Hermitian solution remains outstanding. In this work, we generalize the quantum covariance matrix method to the cases that are applicable to non-Hermitian systems, through which we are able to explicitly reconstruct the non-Hermitian parent Hamiltonian from an arbitrary pair of biorthogonal eigenstates. As concrete examples, we successfully apply our approach in spin chain with Lee-Yang singularity and a non-Hermitian interacting fermion model. Some generalization and further application of our approach are also discussed. Our work provides a systematical and efficient way to construct non-Hermitian Hamiltonian from a single pair of biorthogonal eigenstates and shed light on future exploration on non-Hermitian physics.

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