Null bootstrap for non-Hermitian Hamiltonians

TL;DR

This paper introduces the principle of nullness to ensure physical stability in quantum systems, applying it to bootstrap methods for both Hermitian and non-Hermitian anharmonic oscillators.

Contribution

It proposes the nullness principle to handle unbounded states and extends bootstrap techniques to non-Hermitian Hamiltonians, a novel approach in quantum stability analysis.

Findings

Nullness principle effectively decouples dangerous low-energy states.

Bootstrap methods applied to non-Hermitian systems show promising stability insights.

The approach enhances understanding of spectral properties in complex quantum systems.

Abstract

A stable physical system has an energy spectrum that is bounded from below. For quantum systems, the dangerous states of unboundedly low energies should decouple and become null. We propose the principle of nullness and apply it to the bootstrap study of Hermitian and non-Hermitian anharmonic oscillators.