Entanglement Entropy in the O(N) Model

By M. Metlitski, C. Fuertes, S. Sachdev. 2009

136 citations recorded by the source corpus.

It is generally believed that in spatial dimension d > 1 the leading contribution to the entanglement entropy S = - tr rho_A log rho_A scales as the area of the boundary of subsystem A. The coefficient of this "area law" is non-universal. However, in the neighbourhood of a quantum critical point S is believed to possess subleading universal corrections. In the present work, we study the entanglement entropy in the quantum O(N) model in 1 0 limit of the Wilson-Fisher fixed point is distinct from the Gaussian fixed point. In addition, we compute the correlation length correction to the Renyi entropy S_n = (log tr rho^n_A)/(1-n) in epsilon and large-N expansions. For N -> infinity, this correction generally scales as N^2 rather than the naively expected N. Moreover, the Renyi entropy has a phase transition as a function of n for d close to 3.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2447597044bc990aa6c18b9ade1556ab4cb10196

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Nuclear and High Energy Physics

Citations in the corpus

Entanglement entropy from a holographic viewpoint (2012, methodology): “See also [72, 73] for the analysis of the entanglement entropy in three-dimensional O(N) vector models and Chern–Simons theories.”
Diagnostics of Mixed-State Topological Order and Breakdown of Quantum Memory (2023, background): “Here, it is an interesting question to verify whether the prefactor c is universal or not [53], and we leave it for future study [54].”
Entanglement Entropy of Black Holes (2011, background): “In d dimensions one obtains [205] (see also [175] for a related discussion)”
Holographic mutual information is monogamous (2011, background): “5 (5)Entanglement entropies in the O(N) model at large N were studied in the paper [26].”
Holographic entanglement entropy: an overview (2009, background): “Thus, our holographic approach which can be applied to strongly coupled theories will provide a powerful complementary method.”
Holographic Fermi surfaces and entanglement entropy (2011, background): “stems. Here we would like to study the case where the subsystem A is given by a circular disk with radius l. In conformal ﬁeld theories, we obtain SA = γ · l ǫ − δ, (3.42) where γ and δ are constants [17,21,28]. In the presence of the Fermi surfaces, we again expect SA = γ · l ǫ + ˜η ·lkF loglkF +··”
Rényi entropies for free field theories (2011, methodology): “More generally, we can deviate away from the CFT with a relevant operator which generates a mass scale m; then the Rényi entropies obey [27]”
Holographic c-theorems in arbitrary dimensions (2010, background): “We can infer that the entanglement entropy decreases along RG flows for certain known examples in d = 3 (and 2) [69, 70, 71].”
Hidden Fermi surfaces in compressible states of gauge-gravity duality (2011, background): “[57] M.”
Topological entanglement entropy of a Bose-Hubbard spin liquid (2011, background): “term from a cylindrical geometry without corners as in [21] we might find a different result [23] One interesting possibility is studying a system on the Klein bottle, which also has Euler characteristic zero and hence does not require defects in the lattice.”