Application of Bootstrap to $\theta$-term

• URL: http://arxiv.org/abs/2109.02701v3
• Date: Sun, 22 May 2022 14:16:11 GMT
• Title: Application of Bootstrap to $\theta$-term
• Authors: Yu Aikawa, Takeshi Morita, Kota Yoshimura
• Abstract summary: We study quantum mechanics of a charged particle on a circle in which a constant gauge potential is a counterpart of a $theta$-term. It is hard to determine physical quantities as functions of $theta$ such as $E(theta)$, except at $theta=0$ and $pi$. Our results suggest that the bootstrap method may work not perfectly but sufficiently well, even if a $theta$-term exists in the system.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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