Entanglement entropy in the O(N) model
Source: Phys. Rev. B 80, 115122 (2009); doi:10.1103/PhysRevB.80.115122
Published 23 September 2009
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It is generally believed that in spatial dimension d>1, the leading contribution to the entanglement entropy S=−tr 
A log A scales as the area of the boundary of subsystem A. The coefficient of this “area law” is nonuniversal. However, in the neighborhood 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<d<3. We use an expansion in 
=3−d to evaluate (i) the universal geometric correction to S for an infinite cylinder divided along a circular boundary; (ii) the universal correction to S due to a finite correlation length. Both corrections are different at the Wilson-Fisher and Gaussian fixed points, and the 
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 Sn=
log tr 
in and large-N expansions. For N![[infinity]](http://scitation.aip.org/stockgif3/infin.gif)
, this correction generally scales as N2 rather than the naively expected N. Moreover, the Renyi entropy has a phase transition as a function of n for d close to 3.
©2009 The American Physical Society
A log A scales as the area of the boundary of subsystem A. The coefficient of this “area law” is nonuniversal. However, in the neighborhood 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<d<3. We use an expansion in =3−d to evaluate (i) the universal geometric correction to S for an infinite cylinder divided along a circular boundary; (ii) the universal correction to S due to a finite correlation length. Both corrections are different at the Wilson-Fisher and Gaussian fixed points, and the 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 Sn= and large-N expansions. For N, this correction generally scales as N2 rather than the naively expected N. Moreover, the Renyi entropy has a phase transition as a function of n for d close to 3.
©2009 The American Physical Society
| History: | Received 28 May 2009; revised 12 August 2009; published 23 September 2009 |
| Permalink: |
http://link.aps.org/abstract/PRB/v80/e115122 |
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- L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. 80, 517 (2008).
- L. Bombelli, R. K. Koul, J. H. Lee, and R. D. Sorkin, Phys. Rev. D 34, 373 (1986).
- M. Srednicki, Phys. Rev. Lett. 71, 666 (1993).
- S. Ryu and T. Takayanagi, Phys. Rev. Lett. 96, 181602 (2006).
- D. V. Fursaev, Phys. Rev. D 73, 124025 (2006).
- E. Fradkin and J. E. Moore, Phys. Rev. Lett. 97, 050404 (2006).
- B. Hsu, M. Mulligan, E. Fradkin, and E.-A. Kim, Phys. Rev. B 79, 115421 (2009).
- A. Vishwanath, L. Balents, and T. Senthil, Phys. Rev. B 69, 224416 (2004).
- E. Fradkin, D. A. Huse, R. Moessner, V. Oganesyan, and S. L. Sondhi, Phys. Rev. B 69, 224415 (2004).
- M. Vojta, C. Buragohain, and S. Sachdev, Phys. Rev. B 61, 15152 (2000).
- M. A. Metlitski and S. Sachdev, Phys. Rev. B 77, 054411 (2008).
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