Built on

H. Shapourian, P. Ruggiero, S. Ryu, and P. Calabrese, Twisted and untwisted negativity spectrum of free fermions
Original
1906
Earlier work this paper cites.
Y. Kusuki, J. Kudler-Flam, and S. Ryu, Derivation of Holographic Negativity in AdS 3
Original
1907
Earlier work this paper cites.
A. Almheiri, R. Mahajan, J. Maldacena, and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry
Original
1908
Earlier work this paper cites.
K. Inamura, R. Kobayashi, and S. Ryu, Non-local order parameters and quantum entanglement for fermionic topological field theories
Original
1911
Earlier work this paper cites.
G. Penington, S. H. Shenker, D. Stanford, and Z. Yang, Replica wormholes and the black hole interior
Original
1911
Earlier work this paper cites.
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation
Original
1911
Earlier work this paper cites.
L. R. Ford and D. R. Fulkerson, Maximal flow through a network
1956
Earlier work this paper cites.
P. Elias, A. Feinstein, and C. Shannon, A note on the maximum flow through a network
1956
Earlier work this paper cites.
G. Kreweras, Sur les partitions non croisées d’un cycle
1972
Earlier work this paper cites.
D. N. Page, Average entropy of a subsystem
1993
Earlier work this paper cites.
A. Peres, Separability criterion for density matrices
1996
Earlier work this paper cites.
M. Horodecki, P. Horodecki, and R. Horodecki, Separability of mixed states: necessary and sufficient conditions
1996
Earlier work this paper cites.
K. Zyczkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, On the volume of the set of mixed entangled states
1998
Earlier work this paper cites.
J. Eisert and M. B. Plenio, A comparison of entanglement measures
1999
Earlier work this paper cites.
R. Simon, Peres-Horodecki Separability Criterion for Continuous Variable Systems
2000
Earlier work this paper cites.
G. Vidal and R. F. Werner, Computable measure of entanglement
2002
Earlier work this paper cites.
L. Gurvits, Classical deterministic complexity of Edmonds’ problem and quantum entanglement
2003
Earlier work this paper cites.
M. B. Plenio, Logarithmic Negativity: A Full Entanglement Monotone That is not Convex
2005
Earlier work this paper cites.
S. Ryu and Y. Hatsugai, Entanglement entropy and the berry phase in the solid state
2006
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT
2006
Earlier work this paper cites.

Similar

S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy
2006
Cited alongside, same era.
H. Li and F. D. M. Haldane, Entanglement spectrum as a generalization of entanglement entropy: Identification of topological order in non-abelian fractional quantum hall effect states
Original
2008
Cited alongside, same era.
W.-z. Guo, Entanglement spectrum of geometric states
Original
2008
Cited alongside, same era.
MIT press, 2009
T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to algorithms · 2009
Cited alongside, same era.
S. Gharibian, Strong NP-Hardness of the Quantum Separability Problem
Original
2010
Cited alongside, same era.

Then

R. Nandkishore and D. A. Huse, Many-Body Localization and Thermalization in Quantum Statistical Mechanics
Original
2015
Later among the works it cites.
P. Calabrese and J. Cardy, Quantum quenches in 1 + 1 dimensional conformal field theories
2016
Later among the works it cites.
P. Ruggiero, V. Alba, and P. Calabrese, Negativity spectrum of one-dimensional conformal field theories
Original
2016
Later among the works it cites.
P. Hayden, S. Nezami, X.-L. Qi, N. Thomas, M. Walter, and Z. Yang, Holographic duality from random tensor networks
Original
2016
Later among the works it cites.
G. B. Mbeng, V. Alba, and P. Calabrese, Negativity spectrum in 1d gapped phases of matter
Original
2017

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2021

Negativity Spectra in Random Tensor Networks and Holography

Kudler-Flam, Jonah, Narovlansky, Vladimir, Ryu, Shinsei

Understand

Negativity is a measure of entanglement that can be used both in pure and mixed states.

The negativity spectrum is the spectrum of eigenvalues of the partially transposed density matrix, and characterizes the degree and "phase" of entanglement.
For pure states, it is simply determined by the entanglement spectrum.
We use a diagrammatic method complemented by a modification of the Ford-Fulkerson algorithm to find the negativity spectrum in general random tensor networks with large bond dimensions.

Built on

H. Shapourian, P. Ruggiero, S. Ryu, and P. Calabrese, Twisted and untwisted negativity spectrum of free fermions
Original
1906
Earlier work this paper cites.
Y. Kusuki, J. Kudler-Flam, and S. Ryu, Derivation of Holographic Negativity in AdS 3
Original
1907
Earlier work this paper cites.
A. Almheiri, R. Mahajan, J. Maldacena, and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry
Original
1908
Earlier work this paper cites.
K. Inamura, R. Kobayashi, and S. Ryu, Non-local order parameters and quantum entanglement for fermionic topological field theories
Original
1911
Earlier work this paper cites.
G. Penington, S. H. Shenker, D. Stanford, and Z. Yang, Replica wormholes and the black hole interior
Original
1911
Earlier work this paper cites.
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation
Original
1911
Earlier work this paper cites.
L. R. Ford and D. R. Fulkerson, Maximal flow through a network
1956
Earlier work this paper cites.
P. Elias, A. Feinstein, and C. Shannon, A note on the maximum flow through a network
1956
Earlier work this paper cites.
G. Kreweras, Sur les partitions non croisées d’un cycle
1972
Earlier work this paper cites.
D. N. Page, Average entropy of a subsystem
1993
Earlier work this paper cites.
A. Peres, Separability criterion for density matrices
1996
Earlier work this paper cites.
M. Horodecki, P. Horodecki, and R. Horodecki, Separability of mixed states: necessary and sufficient conditions
1996
Earlier work this paper cites.
K. Zyczkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, On the volume of the set of mixed entangled states
1998
Earlier work this paper cites.
J. Eisert and M. B. Plenio, A comparison of entanglement measures
1999
Earlier work this paper cites.
R. Simon, Peres-Horodecki Separability Criterion for Continuous Variable Systems
2000
Earlier work this paper cites.
G. Vidal and R. F. Werner, Computable measure of entanglement
2002
Earlier work this paper cites.
L. Gurvits, Classical deterministic complexity of Edmonds’ problem and quantum entanglement
2003
Earlier work this paper cites.
M. B. Plenio, Logarithmic Negativity: A Full Entanglement Monotone That is not Convex
2005
Earlier work this paper cites.
S. Ryu and Y. Hatsugai, Entanglement entropy and the berry phase in the solid state
2006
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT
2006
Earlier work this paper cites.

Similar

S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy
2006
Cited alongside, same era.
H. Li and F. D. M. Haldane, Entanglement spectrum as a generalization of entanglement entropy: Identification of topological order in non-abelian fractional quantum hall effect states
Original
2008
Cited alongside, same era.
W.-z. Guo, Entanglement spectrum of geometric states
Original
2008
Cited alongside, same era.
MIT press, 2009
T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to algorithms · 2009
Cited alongside, same era.
S. Gharibian, Strong NP-Hardness of the Quantum Separability Problem
Original
2010
Cited alongside, same era.

Then

R. Nandkishore and D. A. Huse, Many-Body Localization and Thermalization in Quantum Statistical Mechanics
Original
2015
Later among the works it cites.
P. Calabrese and J. Cardy, Quantum quenches in 1 + 1 dimensional conformal field theories
2016
Later among the works it cites.
P. Ruggiero, V. Alba, and P. Calabrese, Negativity spectrum of one-dimensional conformal field theories
Original
2016
Later among the works it cites.
P. Hayden, S. Nezami, X.-L. Qi, N. Thomas, M. Walter, and Z. Yang, Holographic duality from random tensor networks
Original
2016
Later among the works it cites.
G. B. Mbeng, V. Alba, and P. Calabrese, Negativity spectrum in 1d gapped phases of matter
Original
2017

Beyond the bibliography

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

Open on alphaXiv

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F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Entanglement spectrum of a topological phase in one dimension

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G. Aubrun, Partial transposition of random states and non-centered semicircular distributions

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2010

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H. Shapourian, S. Liu, J. Kudler-Flam, and A. Vishwanath, Entanglement negativity spectrum of random mixed states: A diagrammatic approach

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J. K. Basak, D. Basu, V. Malvimat, H. Parihar, and G. Sengupta, Islands for Entanglement Negativity

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