Bootstrap methods for digitized scalar field theory
- URL: http://arxiv.org/abs/2312.10559v1
- Date: Sat, 16 Dec 2023 23:17:58 GMT
- Title: Bootstrap methods for digitized scalar field theory
- Authors: Zane Ozzello, Yannick Meurice
- Abstract summary: General positivity constraints linking various powers of observables in energy eigenstates can be used to locate acceptable regions for the energy eigenvalues.
Recursive methods are derived by looking at the commutation relations of the observables with the Hamiltonian.
We discuss how this self-consistent (bootstrap) approach can be applied to the study of digitized scalar field theory in the harmonic basis.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: General positivity constraints linking various powers of observables in
energy eigenstates can be used to sharply locate acceptable regions for the
energy eigenvalues, provided that efficient recursive methods are available to
calculate the matrix elements. These recursive methods are derived by looking
at the commutation relations of the observables with the Hamiltonian. We
discuss how this self-consistent (bootstrap) approach can be applied to the
study of digitized scalar field theory in the harmonic basis. Using known
results, we develop the method by testing on quantum systems, including the
harmonic and anharmonic oscillators. We report recent numerical results for up
to four coupled anharmonic oscillators. From here, we consider the possibility
of using the groundwork of this method as a means of studying phase transitions
in 1+1 dimensions.
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