Application of bootstrap to a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>θ</mml:mi></mml:math> term

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