Entanglement entropy of two disjoint intervals in \(c = 1\) theories. (English) Zbl 1456.81346
Summary: We study the scaling of the Rényi entanglement entropy of two disjoint blocks of critical lattice models described by conformal field theories with central charge c = 1. We provide the analytic conformal field theory result for the second order Rényi entropy for a free boson compactified on an orbifold describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual line. We have checked this prediction in cluster Monte Carlo simulations of the classical two-dimensional AT model. We have also performed extensive numerical simulations of the anisotropic Heisenberg quantum spin chain with tree tensor network techniques that allowed us to obtain the reduced density matrices of disjoint blocks of the spin chain and to check the correctness of the predictions for Rényi and entanglement entropies from conformal field theory. In order to match these predictions, we have extrapolated the numerical results by properly taking into account the corrections induced by the finite length of the blocks on the leading scaling behavior.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
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