Abstract
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.
Highlights
For SU(2) symmetry breaking, we show that the logarithmic correction in the entanglement entropy, which reflects the number of Nambu-Goldstone modes nNG = 2, appears in the participation entropy, and that this fundamental feature is captured by the minimal line subsystem considered
Our QMC results for participation entropies of various Rényi indices q are displayed in Fig. 4 which clearly show that the subsystem participation entropy grows with system size with a logarithmic correction that leads to a visible curvature
We focus on the ground state of the two-dimensional (L × L) antiferromagnetic Heisenberg model Eq (2) at J2 = −J1 for which we built the histogram of the line subsystem during series expansion (SSE) simulations performed at inverse temperature β J1 = 4L
Summary
The entanglement of ground states in quantum many body systems has been found to reflect fundamental features and universal aspects [1,2,3], such as spontaneous symmetry breaking, topological properties, as well as geometrical aspects of the entanglement bipartition (e.g. corner contributions). In the case of a system that spontaneously breaks a continuous symmetry, recent analytical [4,5,6,7,8,9] and numerical [7, 10,11,12,13] results indicate that subleading corrections to the scaling of the entanglement entropy are logarithmic with system size, with a prefactor proportional to the number of Nambu-Goldstone modes nNG associated to the broken symmetry. For SU(2) symmetry breaking, we show that the logarithmic correction in the entanglement entropy, which reflects the number of Nambu-Goldstone modes nNG = 2, appears in the participation entropy, and that this fundamental feature is captured by the minimal line subsystem considered.
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