Fetching the paper…

Reading the bibliography…

2017

Flow Equation Holography

Kehrein, Stefan

Original
PDF
Post on X

Understand

The Ryu-Takayanagi conjecture establishes a remarkable connection between quantum systems and geometry.

Specifically, it relates the entanglement entropy to minimal surfaces within the setting of AdS/CFT correspondence.
This Letter shows how this idea can be generalised to generic quantum many-body systems within a perturbative expansion where the region whose entanglement properties one is interested in is weakly coupled to the rest of the system.
A simple expression is derived that relates a unitary disentangling flow in an emergent RG-like direction to the min-entropy of the region under consideration.

Flow Equation Holography · Around

Built on

G. ’t Hooft, in: Salamfestschrift
1993
Earlier work this paper cites.
F. Wegner, Ann. Phys. (Leipzig) 506
1994
Earlier work this paper cites.
C. Holzhey, F. Larsen, and F. Wilczek, Nucl. Phys. B 424
1994
Earlier work this paper cites.
L. Susskind, J. Math. Phys. 36
1995
Earlier work this paper cites.
S. Kehrein and A. Mielke, Ann. Physik (Leipzig) 6
1997
Earlier work this paper cites.
J. M. Maldacena, Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Phys. Lett. B 428
1998
Earlier work this paper cites.
S. Kehrein, Phys. Rev. Lett. 83
1999
Earlier work this paper cites.

Similar

P. Calabrese and J. Cardy, J. Stat. Mech. P06002 (2004)
2004
Cited alongside, same era.
S. Ryu and T. Takayanagi, Phys. Rev. Lett. 96
2006
Cited alongside, same era.
S. Ryu and T. Takayanagi, JHEP 0608
2006
Cited alongside, same era.
A. Riera and J. I. Latorre, Phys. Rev. A 74
2006
Cited alongside, same era.
A. Kitaev and K. Preskill, Phys. Rev. Lett. 96
2006
Cited alongside, same era.
S. Kehrein, The flow equation approach to many-particle systems
2006
Cited alongside, same era.
G. Vidal, Phys. Rev. Lett. 99
2007
Cited alongside, same era.

Then

J. Eisert, M. Cramer, and M. B. Plenio, Rev. Mod. Phys. 82
2010
Later among the works it cites.
V. Eisler and I. Peschel, Ann. Phys. (Berlin) 522
2010
Later among the works it cites.
H. Casini, M. Huerta, and R. C. Myers, JHEP 05
2011
Later among the works it cites.
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information
2011
Later among the works it cites.
B. Swingle, Phys. Rev. D 86
2012
Later among the works it cites.
M. Nozaki, S. Ryu, and T. Takayanagi, JHEP 10
2012
Later among the works it cites.
P. Calabrese, M. Mintchev, and E. Vicari, Europhys. Lett. 97
2012

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. Phys. A 42

2009

Cited alongside, same era.

In the flow equation method the flow is usually expressed with respect to a parameter B B with dimension (Energy) -2

Cited in the paper.

At half filling there is an exact analytical result for arbitrary g g [ 15 ] , which is plotted as the dashed line in Fig. 3

Cited in the paper.

For the translation-invariant case g = 1 g=1 there is an analytic result [ 27 ] which has been used to validate my exact diagonalization numerics for d = 2 d=2 . The agreement is excellent for all μ \mu in Fig. 4

Cited in the paper.

These considerations can be extended to the situation when the region B B consists of multiple disjoint intervals. This will be worked out in a latter publication

Cited in the paper.

Later among the works it cites.

J. Haegeman, T. J. Osborne, H. Verschelde, and F. Verstraete, Phys. Rev. Lett. 110

2013

Later among the works it cites.