Bootstrapping non-Hermitian Quantum System

TL;DR

This paper extends the bootstrap method to non-Hermitian quantum systems, enabling the calculation of complex eigenspectra and capturing phase transitions, thus broadening the technique's applicability beyond Hermitian cases.

Contribution

It establishes bootstrap conditions for non-Hermitian systems and demonstrates their effectiveness in generating eigenspectra for complex potentials, including PT-symmetric Hamiltonians.

Findings

Successfully generated eigenspectra for complex polynomial potentials.

Captured PT-symmetric phase transitions using the bootstrap method.

Extended bootstrap applicability to non-Hermitian quantum systems.

Abstract

Recently, the ``Bootstrap" technique was applied in Quantum Mechanics to solve the eigenspectra of Hermitian Hamiltonians and extended to non-Hermitian PT-symmetric systems. However, its application has been limited to real spectra. In this work, we establish bootstrap conditions for the non-Hermitian system and generate eigenspectra for a generic complex polynomial potential, which includes PT-symmetric Hamiltonians as a special case. Additionally, we demonstrate the method's ability to obtain eigenspectra under various boundary conditions imposed on the eigenfunction, including the notable application of capturing the PT-symmetric phase transition.