Application of Bootstrap to $\theta$-term

Abstract

Recently, novel numerical computation on quantum mechanics by using a bootstrap method was proposed by Han, Hartnoll, and Kruthoff. We consider whether this method works in systems with a $\theta$-term, where the standard Monte-Carlo computation may fail due to the sign problem. As a starting point, we study quantum mechanics of a charged particle on a circle in which a constant gauge potential is a counterpart of a $\theta$-term. We find that it is hard to determine physical quantities as functions of $\theta$ such as $E(\theta )$, except at $\theta =0$ and $\pi$. On the other hand, the correlations among observables for energy eigenstates are correctly reproduced for any $\theta$. Our results suggest that the bootstrap method may work not perfectly but sufficiently well, even if a $\theta$-term exists in the system.

arXiv comment16 pages, 5 figures.v3: matches published version in PRD, appendix on the details of the numerical bootstrap was added

References in corpus (18)

• M Theory As A Matrix Model: A Conjecture
• A Large-N Reduced Model as Superstring
• Tensor renormalization group approach to 2D classical lattice models
• High density QCD on a Lefschetz thimble?
• Theta Dependence In The Large N Limit Of Four-Dimensional Gauge Theories
• The Complex Langevin method: When can it be trusted?
• Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature
• Complex Langevin: Etiology and Diagnostics of its Main Problem
• Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions
• The argument for justification of the complex Langevin method and the condition for correct convergence
• Bootstrapping Matrix Quantum Mechanics
• Loop Equations and bootstrap methods in the lattice
• Bootstraps to Strings: Solving Random Matrix Models with Positivity
• Numerical Bootstrap in Quantum Mechanics
• Bootstrapping More QM Systems
• Gauge cooling for the singular-drift problem in the complex Langevin method --a test in Random Matrix Theory for finite density QCD
• Bootstrapping Bloch bands
• Bootstrapping Simple QM Systems

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