In this work we focus on computing the conformal dimensions $D(j_L,j_R)$ of local fields that transform in an irreducible representation of $SU(2)\times SU(2)$ labeled with $(j_L,j_R)$ at the $O(4)$ Wilson-Fisher fixed point using the Monte Carlo method. In the large charge expansion, among the sectors with a fixed large value of $j=\max (j_L,j_R)$, the leading sector has $|j_L-j_R|=0$ and the subleading one has $|j_L-j_R|=1$. Since Monte Carlo calculations at large $j$ become challenging in the traditional lattice formulation of the $O(4)$ model, a qubit regularized $O(4)$ lattice model was used recently to compute $D(j,j)$. Here we extend those calculations to the subleading sector. Our Monte Carlo results in the range $2\le j\le 20$ fit well to the expected large $j$ expansion $D(j,j-1)-D(j,j)\sim {\lambda }_0+{\lambda }_{1/2}/\sqrt{j}+{\lambda }_1/j+{\lambda }_{3/2}/j^{3/2}$, but we have to assume that at least one of the purely quantum mechanical contributions ${\lambda }_0$ or ${\lambda }_1$ is nonzero. Assuming ${\lambda }_0=0$ as conjectured recently, we find ${\lambda }_{1/2}\approx 2.1(1)$, ${\lambda }_1\approx 2.3(2)$, and ${\lambda }_{3/2}\approx 1.2(2)$.

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• Effective field theory
• Lattice field theory
• Lower-dimensional field theories
• Nonperturbative effects in field theory
• Sigma models
• Quantum Monte Carlo