Built on

C. Holzhey, F. Larsen, and F.Wilczek, Nucl. Phys. B 424, 443 (1994); C. G. Callan and F. Wilczek, Phys. Lett. B 333, 55 (1994); G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003); P. Calabrese and J. Cardy, J. Stat. Mech. P06002 (2004)
2004
Earlier work this paper cites.
A. Hamma, R.Ionicioiu, P.Zanardi, Phys. Lett. A 337, 22 (2005); A. Hamma, R. Ionicioiu, and P. Zanardi, Phys. Rev. A 71, 022315 (2005); A. Kitaev, J. Preskill, Phys. Rev. Lett. 96 110404 (2006); M. Levin, X.-G. Wen, Phys. Rev. Lett., 96, 110405 (2006)
2006
Earlier work this paper cites.
P. Hayden, R. Jozsa, D. Petz, A. Winter, Commun. Math. Phys., 246(2):359-374 (2004). F. Verstraete, J.I. Cirac, Phys. Rev. B 73, 094423 (2006)
2006
Earlier work this paper cites.
A. Kitaev, Phys.-Usp. 44 131 (2001), arXiv:cond-mat/0010440; or sections 2 - 3 of A. Kitaev, Annals of Physics 321 (2006) 2–111, arXiv:cond-mat/0506438
2006
Earlier work this paper cites.
M. Srednicki, Phys. Rev. Lett. 71 (1993) 666-669 J. I. Latorre, E. Rico, G. Vidal, Quant. Inf. Comput. 4 (2004) 48-92. M.B. Plenio, J. Eisert, J. Dreissig, and M. Cramer Rev. Lett. 94, 060503 (2005). S. Bravyi, M. B. Hastings, and F. Verstraete, Phys. Rev. Lett. 97, 050401 (2006). J. Eisert, T. J. Osborne, Phys. Rev. Lett. 97, 150404 (2006). M. B. Hastings, JSTAT, P08024 (2007). Ll. Masanes, Phys. Rev. A 80, 052104 (2009). J. Eisert, M. Cramer, and M.B. Plenio, Rev. Mod. Phys. 82, 277 (2010). B. Swingle, Phys. Rev. D 86, 065007 (2012). T. Nishioka, S. Ryu, T. Takayanagi, J. Phys. A 42, 504008 (2009)
2009
Earlier work this paper cites.

Similar

Then

F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Phys. Rev. B 81, 064439 (2010). X. Chen, Z.-C. Gu, and X.-G. Wen, Phys. Rev. B 83, 035107 (2011). N. Schuch, D. Perez-Garcia, I. Cirac, Phys. Rev. B 84, 165139 (2011). X. Chen, Z.-C. Gu, Z.-X. Liu, X.-G. Wen, Phys. Rev. B 87, 155114 (2013)
2013
Later among the works it cites.
P. Calabrese, J. Cardy, E. Tonni, J. Stat. Mech. P11001 (2009). B. Swingle, arXiv:1010.4038. J. Cardy, J. Phys. A: Math. Theor. 46 (2013) 285402. J. Schachenmayer, B. P. Lanyon, C. F. Roos, and A. J. Daley, Phys. Rev. X 3, 031015 (2013)
Original
2013
Later among the works it cites.
G. Vidal and R.F. Werner, Phys. Rev. A 65, 32314 (2002). P. Calabrese, J. Cardy, and E. Tonni, Phys. Rev. Lett. 109, 130502 (2012). P. Calabrese, J. Cardy, and E. Tonni, J. Stat. Mech. P02008 (2013). P. Calabrese, L. Tagliacozzo, E. Tonni, J. Stat. Mech. P05002 (2013). V. Alba, J. Stat. Mech. P05013 (2013) Y.A. Lee and G. Vidal, Phys. Rev. A 88, 042318 (2013). C. Castelnovo, Phys. Rev. A 88, 042319 (2013)
2013
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2014

Entanglement contour

Chen, Yangang, Vidal, Guifre

Understand

In the context of characterizing the structure of quantum entanglement in many-body systems, we introduce the entanglement contour, a tool to identify which real-space degrees of freedom contribute, and how much, to the entanglement of a region A with the rest of the system B.

The entanglement contour provides a complementary, more refined approach to characterizing entanglement than just considering the entanglement entropy between A and B, with several concrete advantages.
We illustrate this in the context of ground states and quantum quenches in fermionic quadratic systems.
For instance, in a quantum critical system in $D = 1$ spatial dimensions, the entanglement contour allows us to determine the central charge of the underlying conformal field theory from just a single partition of the system into regions A and B, (using the entanglement entropy for the same task requires considering several partitions).

Built on

C. Holzhey, F. Larsen, and F.Wilczek, Nucl. Phys. B 424, 443 (1994); C. G. Callan and F. Wilczek, Phys. Lett. B 333, 55 (1994); G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003); P. Calabrese and J. Cardy, J. Stat. Mech. P06002 (2004)
2004
Earlier work this paper cites.
A. Hamma, R.Ionicioiu, P.Zanardi, Phys. Lett. A 337, 22 (2005); A. Hamma, R. Ionicioiu, and P. Zanardi, Phys. Rev. A 71, 022315 (2005); A. Kitaev, J. Preskill, Phys. Rev. Lett. 96 110404 (2006); M. Levin, X.-G. Wen, Phys. Rev. Lett., 96, 110405 (2006)
2006
Earlier work this paper cites.
P. Hayden, R. Jozsa, D. Petz, A. Winter, Commun. Math. Phys., 246(2):359-374 (2004). F. Verstraete, J.I. Cirac, Phys. Rev. B 73, 094423 (2006)
2006
Earlier work this paper cites.
A. Kitaev, Phys.-Usp. 44 131 (2001), arXiv:cond-mat/0010440; or sections 2 - 3 of A. Kitaev, Annals of Physics 321 (2006) 2–111, arXiv:cond-mat/0506438
2006
Earlier work this paper cites.
M. Srednicki, Phys. Rev. Lett. 71 (1993) 666-669 J. I. Latorre, E. Rico, G. Vidal, Quant. Inf. Comput. 4 (2004) 48-92. M.B. Plenio, J. Eisert, J. Dreissig, and M. Cramer Rev. Lett. 94, 060503 (2005). S. Bravyi, M. B. Hastings, and F. Verstraete, Phys. Rev. Lett. 97, 050401 (2006). J. Eisert, T. J. Osborne, Phys. Rev. Lett. 97, 150404 (2006). M. B. Hastings, JSTAT, P08024 (2007). Ll. Masanes, Phys. Rev. A 80, 052104 (2009). J. Eisert, M. Cramer, and M.B. Plenio, Rev. Mod. Phys. 82, 277 (2010). B. Swingle, Phys. Rev. D 86, 065007 (2012). T. Nishioka, S. Ryu, T. Takayanagi, J. Phys. A 42, 504008 (2009)
2009
Earlier work this paper cites.

Similar

Then

F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Phys. Rev. B 81, 064439 (2010). X. Chen, Z.-C. Gu, and X.-G. Wen, Phys. Rev. B 83, 035107 (2011). N. Schuch, D. Perez-Garcia, I. Cirac, Phys. Rev. B 84, 165139 (2011). X. Chen, Z.-C. Gu, Z.-X. Liu, X.-G. Wen, Phys. Rev. B 87, 155114 (2013)
2013
Later among the works it cites.
P. Calabrese, J. Cardy, E. Tonni, J. Stat. Mech. P11001 (2009). B. Swingle, arXiv:1010.4038. J. Cardy, J. Phys. A: Math. Theor. 46 (2013) 285402. J. Schachenmayer, B. P. Lanyon, C. F. Roos, and A. J. Daley, Phys. Rev. X 3, 031015 (2013)
Original
2013
Later among the works it cites.
G. Vidal and R.F. Werner, Phys. Rev. A 65, 32314 (2002). P. Calabrese, J. Cardy, and E. Tonni, Phys. Rev. Lett. 109, 130502 (2012). P. Calabrese, J. Cardy, and E. Tonni, J. Stat. Mech. P02008 (2013). P. Calabrese, L. Tagliacozzo, E. Tonni, J. Stat. Mech. P05002 (2013). V. Alba, J. Stat. Mech. P05013 (2013) Y.A. Lee and G. Vidal, Phys. Rev. A 88, 042318 (2013). C. Castelnovo, Phys. Rev. A 88, 042319 (2013)
2013
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

P. Calabrese and J. Cardy, J. Stat. Mech. P04010 (2005). M. Fagotti, P. Calabrese, Phys. Rev. A 78, 010306(R) (2008). P. Calabrese, F. H. L. Essler, and M. Fagotti, J. Stat. Mech. P07016 (2012). B. M. McCoy, E. Barouch, and D. B. Abraham, Phys. Rev. A 4, 2331 (1971). K. Sengupta, S. Powell, and S. Sachdev, Phys. Rev. A 69, 053616 (2004). F. Igloi, H. Rieger, Phys. Rev. Lett. 85, 3233 (2000). H. Liu, S. Josephine Suh, Phys. Rev. Lett. 112, 011601 (2014). J. Cardy and P. Calabrese, Phys. Rev. Lett. 96, 136801 (2006). H. Rieger and F. Igloi, Phys. Rev. B, 84, 165117 (2011)

2011

Cited alongside, same era.

V. Alba, M. Haque, A. M. Laeuchli, Phys. Rev. Lett. 108, 227201 (2012)

2012

Cited alongside, same era.

M. Nozaki, T. Numasawa, T. Takayanagi, arXiv: 1302.5703. M. Nozaki, T. Numasawa, A. Prudenziati, T. Takayanagi, arXiv: 1304.7100

Cited in the paper.

This form for the entanglement contour is suggested by an exact calculation of the entanglement entropy S ⁡ ( A ) S(A) involving a conformal map that produces a new region A ′ A^{\prime} in a thermal state [Rob Myers, private communication

Original

Cited in the paper.

M.-C. Chung and I. Peschel, Phys. Rev. B, 62, 4191 (2000). S.-A. Cheong and C. L. Henley, Phys. Rev. B, 69, 075112 (2004). I. Peschel, J. Stat. Mech. (2004) P06004. V. Eisler and I. Peschel, J. Stat. Mech. (2007) P06005. V. Eisler, D. Karevski, T. Platini, I. Peschel, J. Stat. Mech. (2008) P01023. B. Nienhuis, M. Campostrini, and P. Calabrese, J. Stat. Mech. P02063 (2009). I. Peschel and V. Eisler, J. Phys. A: Math. Theor. 42 (2009) 504003. V. Eisler and I. Peschel, J. Stat. Mech. (2013) P04028

2013

Later among the works it cites.