Null bootstrap for non-Hermitian Hamiltonians

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.

v4: 8 pages, 3 figures, title changed in accord to the published version (but also applies to Hermitian Hamiltonians!), Fig.3 added about the relation between the positive and the null bootstrap, footnote 19 added about the double well potential, discussion improved; v3: a new section added about ladder operators and matrix elements, minor improvements, typos corrected, references added

References in corpus (16)

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• Bootstrapping Mixed Correlators in the 3D Ising Model
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• Bootstrapping More QM Systems
• Inverse Bootstrapping Conformal Field Theories
• Bootstrapping Bloch bands
• Bootstrapping Calabi-Yau Quantum Mechanics
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• Bootstrapping microcanonical ensemble in classical system
• Ising model close to $d=2$

Cited by in corpus (13)

• Taming Dyson-Schwinger equations with null states
• Solving anharmonic oscillator with null states: Hamiltonian bootstrap and Dyson-Schwinger equations
• Principle of minimal singularity for Green's functions
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• ${\varphi }^n$ trajectory bootstrap
• Non-Hermitian Generalization of Rayleigh-Schrödinger Perturbation Theory
• Analytic trajectory bootstrap for matrix models
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Bootstrapping Shape Invariance: Numerical Bootstrap as a Detector of Solvable Systems
• Bootstrap Method in Theoretical Physics
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations
• Bootstrapping periodic quantum systems