Numerical Evidence of Emergent Symmetry in Spin-1/2 Heisenberg Chain

The antiferromagnetic Heisenberg chain is expected to have an extended symmetry, SU(2)xSU(2), in the infrared limit, whose physical interpretation is that the spin and dimer order parameters form the components of a common 4-dimensional vector. Here we numerically investigate this emergent symmetry using quantum Monte Carlo simulations of a modified Heisenberg chain (the J-Q model) in which the logarithmic scaling corrections of the conventional Heisenberg chain can be avoided. We show how the two- and three-point spin and dimer correlation functions approach their forms constrained by conformal field theory as the system size increases and characterize the scaling corrections due to violations of the extended symmetry caused by the finite system size. Because of these corrections, it is harder to observe the asymptotic behavior than in simpler conformal field-theory realizations such as the transverse-field Ising chain.