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Article Dans Une Revue Physical Review B: Condensed Matter and Materials Physics (1998-2015) Année : 2015

Universal logarithmic corrections to entanglement entropies in two dimensions with spontaneously broken continuous symmetries

Résumé

We explore the R\'enyi entanglement entropies of a one-dimensional (line) subsystem of length $L$ embedded in two-dimensional $L\times L$ square lattice for quantum spin models whose ground-state breaks a continuous symmetry in the thermodynamic limit. Using quantum Monte Carlo simulations, we first study the $J_1 - J_2$ Heisenberg model with antiferromagnetic nearest-neighbor $J_1>0$ and ferromagnetic second-neighbor couplings $J_2\le 0$. The signature of SU(2) symmetry breaking on finite size systems, ranging from $L=4$ up to $L=40$ clearly appears as a universal additive logarithmic correction to the R\'enyi entanglement entropies: $l_q \ln L$ with $l_q\simeq 1$, independent of the R\'enyi index and values of $J_2$. We confirm this result using a high precision spin-wave analysis (with restored spin rotational symmetry) on finite lattices up to $10^5\times 10^5$ sites, allowing to explore further non-universal finite size corrections and study in addition the case of U(1) symmetry breaking. Our results fully agree with the prediction $l_q=n_G/2$ where $n_G$ is the number of Goldstone modes, by Metlitski and Grover [arXiv:1112.5166].

Dates et versions

hal-01153291 , version 1 (19-05-2015)

Identifiants

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David J. Luitz, Xavier Plat, Fabien Alet, Nicolas Laflorencie. Universal logarithmic corrections to entanglement entropies in two dimensions with spontaneously broken continuous symmetries. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2015, 91 (15), pp.155145. ⟨10.1103/PhysRevB.91.155145⟩. ⟨hal-01153291⟩
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