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

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) x 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 vertical bar j(L) - j(R)vertical bar = 0 and the subleading one has vertical bar jL - j(R)vertical bar = 1. Since Monte Carlo calculations at large j become challenging in the traditional lattice formulation of the 0(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 <= j <= 20 fit well to the expected large j expansion D(j, j - 1) - D(j, j) similar to lambda(0) +lambda(1/2)/root j+ lambda(1)/j + 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) approximate to 2.1(1), lambda(1) approximate to 2.3(2), and lambda(3/2) approximate to 1.2(2).

Automated summary

This work focuses on computing the conformal dimensions of local fields in an SU(2) x SU(2) irreducible representation at the O(4) Wilson-Fisher fixed point using the Monte Carlo method. The results show the relationship between the dimensions of the leading and subleading sectors in the large charge expansion, providing numerical values for certain contributions.