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Bootstrapping more QM systems

Journal Article · · Journal of Physics. A, Mathematical and Theoretical
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Abstract

We test the bootstrap approach for determining the spectrum of one dimensional Hamiltonians. In this paper we focus on problems that have a two parameter search space in the bootstrap approach: the double well and a periodic potential associated with the Mathieu equation. For the double well, we compare the bootstrapped energies with contributions from perturbative and non-perturbative results, finding good agreement. For the periodic potentials, we notice that the bootstrap approach gives the band structure of the periodic potential, but it has trouble finding the quasi-momentum of the system. To make further progress on determining the dispersion relation of the bands, new techniques are needed.

Research Organization:
Univ. of Iowa, Iowa City, IA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
SC0019139
OSTI ID:
1979451
Journal Information:
Journal of Physics. A, Mathematical and Theoretical, Vol. 55, Issue 27; ISSN 1751-8113
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English

References (8)

Numerical bootstrap in quantum mechanics December 2021
Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents June 2014
Loop space Hamiltonians and numerical methods for large-N gauge theories March 1983
Loop-space hamiltonians and numerical methods for large-N gauge theories (II) March 1984
Numerical solution of lattice Schwinger-Dyson equations in the large-N limit October 1985
Loop equations and bootstrap methods in the lattice August 2017
Bootstraps to strings: solving random matrix models with positivity June 2020
Exact solutions of Mathieu’s equation April 2020

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Related Subjects

Physics