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      Entanglement Entropy of Systems with Spontaneously Broken Continuous Symmetry

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          Abstract

          We study entanglement properties of systems with spontaneously broken continuous symmetry. We find that in addition to the expected area law behavior, the entanglement entropy contains a subleading contribution which diverges logarithmically with the subsystem size in agreement with the Monte Carlo simulations of A. Kallin et. al. (Phys. Rev. B 84, 165134 (2011)). The coefficient of the logarithm is a universal number given simply by \(N_G (d-1)/2\), where \(N_G\) is the number of Goldstone modes and \(d\) is the spatial dimension. This term is present even when the subsystem boundary is straight and contains no corners, and its origin lies in the interplay of Goldstone modes and restoration of symmetry in a finite volume. We also compute the "low-energy" part of the entanglement spectrum and show that it has the same characteristic "tower of states" form as the physical low-energy spectrum obtained when a system with spontaneously broken continuous symmetry is placed in a finite volume.

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          Author and article information

          Journal
          2011-12-21
          2015-01-08
          Article
          1112.5166
          35053d30-ac27-4b9a-a435-8ea5cff153e5

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          39 pages, 1 figure. v2: added section III with a new derivation of the main result and an exact calculation of the full entanglement spectrum
          cond-mat.str-el hep-th quant-ph

          Condensed matter,Quantum physics & Field theory,High energy & Particle physics

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