Strong <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math> problem in the quantum rotor

Recent studies have claimed that the strong <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi><a:mi>P</a:mi></a:math> problem does not occur in QCD, proposing a new order of limits in volume and topological sectors when studying observables on the lattice. In order to shed light on this issue, we study the effect of the topological <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>θ</c:mi></c:math>-term on a simple quantum mechanical rotor that allows a lattice description. The topological susceptibility and the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>θ</e:mi></e:math>-dependence of the energy spectrum are both computed using local lattice correlation functions. The sign problem is overcome by considering Taylor expansions in <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>θ</g:mi></g:math>, exploiting automatic differentiation methods for Monte Carlo processes. Our findings confirm the conventional wisdom on the strong <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>C</i:mi><i:mi>P</i:mi></i:math> problem. Published by the American Physical Society 2024