The matrix elements in Eq. (B12) are given in Refs. [51–53]: with the coefficients and the anomalous dimensions In this appendix we provide a derivation of Eqs. (63) and (72) which give the relation- ship between the Euclidean space correlation functions which are the direct results of our simulations and the matrix elements between normalized Hilbert space states which we wish to determine. In this appendix, all quantities are written in lattice units. The derivation of Eq. (63) follows the standard steps of inserting a complete set of energy eigenstates into the Green’s functions C $^{LW}$( t, t$_{0}$ ) and C $^{WW}$( t, t$_{0}$ ) which are defined in Eqs. (59) and (60) and appear in the numerator and denominator of Eq. (63): C $^{WW}$( t, t$_{0}$ ) = n |〈 n | A W 0 (0) $^{†}$| 0 〉| $^{2}$e − E$_{n}$ ( t − t$_{0}$ $^{)}$, (C2) C $^{LW}$( t, t$_{0}$ ) = ∑ n ∑ ⃗x ∈ $_{V}$〈 0 | A L $_{0}$( ⃗ x, 0) | n 〉〈 n | A W 0 (0) $^{†}$| 0 〉 e − E$_{n}$ ( t − t$_{0}$ ) (C1) γ (0) =   − 6 C$_{F}$ 0 1 + 1 /N$_{c}$ − 6 C$_{F}$ + 4(1 + 1 /N$_{c}$ )   , (B18) γ (1) 11 = − N$_{c}$ − 1 12 N$_{c}$ ( 127 N 2 c + 143 N$_{c}$ + 63 − 57 /N$_{c}$ +8 π $^{2}$( N 2 c − 2 N$_{c}$ + 4 /N$_{c}$ ) − N$_{f}$ (28 N$_{c}$ + 44) ) . (B19) d ( N$_{f}$ ) i = γ (0) ii / 2 β$_{0}$, (B16) J ( N$_{f}$ ) 11 = γ (1) 11 / 2 β$_{0}$ − γ (0) 11 β$_{1}$/ 2 β 2 $_{0}$, (B17) U ( N$_{f}$ ) 22 ( µ $^{′}$, µ ) = ( α ( N$_{f}$ ) s ( µ $^{′}$) α ( N$_{f}$ ) s ( µ ) ) d ( N f ) 2 + O ( α$_{s}$ ) , (B15) U ( N$_{f}$ ) 21 ( µ $^{′}$, µ ) = − 1 4    ( α ( N$_{f}$ ) s ( µ $^{′}$) α ( N$_{f}$ ) s ( µ ) ) d ( N f ) 1 − ( α ( N$_{f}$ ) s ( µ $^{′}$) α ( N$_{f}$ ) s ( µ ) ) d ( N f ) 2    + O ( α$_{s}$ ) , (B14) ( N f ) U ( N$_{f}$ ) 11 ( µ $^{′}$, µ ) = ( α ( N$_{f}$ ) s ( µ $^{′}$) α ( N$_{f}$ ) s ( µ ) ) d ( N f ) 1 ( 1 + J ( N$_{f}$ ) 11 α ( N$_{f}$ ) s ( µ $^{′}$) − α ( N$_{f}$ ) s ( µ ) 4 π ) + O ( α 2 $_{s}$) , (B13) Appendix C: Finding matrix elements from Green’s functions 49