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In this work we focus on computing the conformal dimensions $D(j_L,j_R)$ oflocal fields that transform in an irreducible representation of $SU(2) \timesSU(2)$ labeled with $(j_L,j_R)$ at the $O(4)$ Wilson-Fisher fixed point usingthe Monte Carlo method. In the large charge expansion, among the sectors with afixed large value of $j = {\rm max}(j_L,j_R)$, the leading sector has$|j_L-j_R| = 0$ and the sub-leading one has $|j_L-j_R| = 1$. Since Monte Carlocalculations at large $j$ become challenging in the traditional latticeformulation of the $O(4)$ model, a qubit regularized $O(4)$ lattice model wasused recently to compute $D(j,j)$. Here we extend those calculations to thesub-leading sector. Our Monte Carlo results up to $j=20$ fit well to the form$D(j,j-1)-D(j) \sim \lambda_{1/2}/\sqrt{j} + \lambda_1/j +\lambda_{3/2}/j^{3/2}$, consistent with recent predictions of the large chargeexpansion. Taking into account systematic effects in our fitting procedures weestimate the two leading coefficients to be $\lambda_{1/2}=2.08(5)$,$\lambda_1=2.2(3)$.

Sub-leading conformal dimensions at the O(4) Wilson-Fisher fixed point