Quantum Monte Carlo detection of SU(2) symmetry breaking in the participation entropies of line subsystems

Using quantum Monte Carlo simulations, we compute the participation (Shannon-Rényi) entropies for groundstate wave functions of Heisenberg antiferromagnets for one-dimensional (line) subsystems of length LL embedded in two-dimensional (L\times LL×L) square lattices. We also study the line entropy at finite temperature, i.e. of the diagonal elements of the density matrix, for three-dimensional (L\times L\times LL×L×L) cubic lattices. The breaking of SU(2) symmetry is clearly captured by a universal logarithmic scaling term l_q\ln LlqlnL in the Rényi entropies, in good agreement with the recent field-theory results of Misguish, Pasquier and Oshikawa . We also study the dependence of the log prefactor l_qlq on the Rényi index qq for which a transition is detected at q_c\simeq 1qc≃1.