Abstract
We study the entanglement entropy of random partitions in one- and two-dimensional critical fermionic systems. In an infinite system we consider a finite, connected (hypercubic) domain of linear extent L, the points of which with probability p belong to the subsystem. The leading contribution to the average entanglement entropy is found to scale with the volume as a(p)LD, where a(p) is a non-universal function, to which there is a logarithmic correction term, b(p)LD−1 ln L. In 1D the prefactor is given by b(p)=c/3f(p), where c is the central charge of the model and f(p) is a universal function. In 2D the prefactor has a different functional form of p below and above the percolation threshold.
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References
L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)
P. Calabrese, J. Cardy, B. Doyon, J. Phys. A 42, 500301 (2009)
J. Eisert, M. Cramer, M.B. Plenio, Rev. Mod. Phys. 82, 277 (2010)
N. Laflorencie, Phys. Rep. 643, 1 (2016)
C.H. Bennett, H.J. Bernstein, S. Popescu, B. Schumacher, Phys. Rev. A 53, 2046 (1996)
C. Holzhey, F. Larsen, F. Wilczek, Nucl. Phys. B 424, 443 (1994)
P. Calabrese, J. Cardy, J. Stat. Mech. 2004, P06002 (2004)
G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003)
J.I. Latorre, E. Rico, G. Vidal, Quantum Inf. Comput. 4, 048 (2004)
I. Peschel, J. Phys. A: Math. Gen. 36, L205 (2003)
B.-Q. Jin, V.E. Korepin, J. Stat. Phys. 116, 79 (2004)
A.R. Its, B.-Q. Jin, V.E. Korepin, J. Phys. A 38, 2975 (2005)
R. Its, B.-Q. Jin, V.E. Korepin, inFields Institute Communications, Universality and Renormalization, edited by I. Bender and D. Kreimer (2007), Vol. 50, p. 151
F. Iglói, R. Juhász, Europhys. Lett. 81, 57003 (2008)
M.M. Wolf, Phys. Rev. Lett. 96, 010404 (2006)
W. Li, L. Ding, R. Yu, S. Haas, Phys. Rev. B 74, 073103 (2006)
S. Farkas, Z. Zimborás, J. Math. Phys. 48, 102110 (2007)
B. Swingle, Phys. Rev. Lett. 105, 050502 (2010)
T. Barthel, M.-C. Chung, U. Schollwöck, Phys. Rev. A 74, 022329 (2006)
D. Gioev, I. Klich, Phys. Rev. Lett. 96, 100503 (2006)
G. Refael, J.E. Moore, Phys. Rev. Lett. 93, 260602 (2004)
R. Santachiara, J. Stat. Mech. Theor. Exp. 2006, L06002 (2006)
N.E. Bonesteel, K. Yang, Phys. Rev. Lett. 99, 140405 (2007)
G. Refael, J.E. Moore, Phys. Rev. B 76, 024419 (2007)
N. Laflorencie, Phys. Rev. B 72 140408 (R) (2005)
F. Iglói, Y.-Ch. Lin, J. Stat. Mech. 2008, P06004 (2008)
G. De Chiara, S. Montangero, P. Calabrese, R. Fazio, J. Stat.Mech. 2006, L03001 (2006)
For a review, see: F. Iglói, C. Monthus, Phys. Rep. 412, 277 (2005)
F. Iglói, C. Monthus, Eur. Phys. J. B 91, 290 (2018)
I.A. Kovács, F. Iglói, Europhys. Lett. 97, 67009 (2012)
F. Iglói, I. Peschel, Europhys. Lett. 89, 40001 (2010)
A. Hamma, D.A. Lidar, S. Severini, Phys. Rev. A 81, 010102(R) (2010)
S. Vijay, L. Fu, Phys. Rev. B 91, 22 (2015)
A.Y. Kitaev, Phys. Usp. 44, 131 (2001)
P. Pfeuty, Phys. Lett. A 72, 245 (1979)
I. Peschel, Braz. J. Phys. 42, 267 (2012)
V. Eisler, I. Peschel, J. Stat. Mech. 2018, 104001 (2018)
W. Li, L. Ding, R. Yu, T. Roscilde, S. Haas Phys. Rev. B 74, 073103 (2006)
P.S. Grinchuk, O.S. Rabinovich, J. Exp. Theor. Phys. 96, 301 (2003)
D. Stauffer, A. Aharony,Introduction To Percolation Theory (Taylor and Francis, London, 1992)
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Contribution to the Topical Issue “Recent Advances in the Theory of Disordered Systems”, edited by Ferenc Iglói and Heiko Rieger.
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Roósz, G., Kovács, I.A. & Iglói, F. Entanglement entropy of random partitioning. Eur. Phys. J. B 93, 8 (2020). https://doi.org/10.1140/epjb/e2019-100496-y
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DOI: https://doi.org/10.1140/epjb/e2019-100496-y