Fetching the paper…

Reading the bibliography…

2021

Target space entanglement in quantum mechanics of fermions and matrices

Sugishita, Sotaro

Original
PDF
Post on X

Understand

We consider entanglement of first-quantized identical particles by adopting an algebraic approach.

In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models.
We show that the upper bounds of the general R\'enyi entropies are $N \log 2$ for $N$ particles or an $N\times N$ matrix.
We compute the target space entanglement entropy and the mutual information in a free one-matrix model.

Target space entanglement in quantum mechanics of fermions and matrices · Around

Built on

S. R. Das, S. Hampton, and S. Liu, “Quantum Quench in Non-relativistic Fermionic Field Theory: Harmonic traps and 2d String Theory,” JHEP
Original
1903
Earlier work this paper cites.
H. Barghathi, E. Casiano-Diaz, and A. Del Maestro, “Operationally accessible entanglement of one-dimensional spinless fermions,” Phys. Rev. A
Original
1905
Earlier work this paper cites.
R. Bonsignori, P. Ruggiero, and P. Calabrese, “Symmetry resolved entanglement in free fermionic systems,” J. Phys. A
Original
1907
Earlier work this paper cites.
E. A. Mazenc and D. Ranard, “Target Space Entanglement Entropy,” arXiv:1910.07449 [hep-th]
Original
1910
Earlier work this paper cites.
T. Anous, J. L. Karczmarek, E. Mintun, M. Van Raamsdonk, and B. Way, “Areas and entropies in BFSS/gravity duality,” SciPost Phys
Original
1911
Earlier work this paper cites.
T. T. Wu, “Theory of toeplitz determinants and the spin correlations of the two-dimensional ising model. i,” Physical Review
1966
Earlier work this paper cites.
M. E. Fisher and R. E. Hartwig, “Toeplitz determinants: some applications, theorems, and conjectures,” Advances in Chemical Physics: Stochastic processes in chemical physics
1969
Earlier work this paper cites.
E. Brezin, C. Itzykson, G. Parisi, and J. B. Zuber, “Planar Diagrams,” Commun. Math. Phys
1978
Earlier work this paper cites.
Academic Press, 1981
L. Shepp and I. Olkin, “Entropy of the sum of independent bernoulli random variables and of the multinomial distribution,” in Contributions to Probability · 1981
Earlier work this paper cites.
L. Bombelli, R. K. Koul, J. Lee, and R. D. Sorkin, “A Quantum Source of Entropy for Black Holes,” Phys. Rev. D
1986
Earlier work this paper cites.
V. A. Kazakov and A. A. Migdal, “Recent Progress in the Theory of Noncritical Strings,” Nucl. Phys. B
1988
Earlier work this paper cites.
M. Srednicki, “Entropy and area,” Phys. Rev. Lett
1993
Earlier work this paper cites.
11, 1994
J. Polchinski, “What is string theory?,” in NATO Advanced Study Institute: Les Houches Summer School, Session 62: Fluctuating Geometries in Statistical Mechanics and Field Theory · 1994
Earlier work this paper cites.
S. R. Das, “Geometric entropy of nonrelativistic fermions and two-dimensional strings,” Phys. Rev. D
1995
Earlier work this paper cites.
T. Banks, W. Fischler, S. H. Shenker, and L. Susskind, “M theory as a matrix model: A Conjecture,” Phys. Rev. D
1997
Earlier work this paper cites.
D. E. Berenstein, J. M. Maldacena, and H. S. Nastase, “Strings in flat space and pp waves from N=4 superYang-Mills,” JHEP
2002
Earlier work this paper cites.
H. M. Wiseman and J. A. Vaccaro, “Entanglement of indistinguishable particles shared between two parties,” Physical Review Letters
2003
Earlier work this paper cites.
I. Peschel, “Calculation of reduced density matrices from correlation functions,” Journal of Physics A: Mathematical and General
2003
Earlier work this paper cites.

Similar

S. R. Das, A. Kaushal, G. Mandal, and S. P. Trivedi, “Bulk Entanglement Entropy and Matrices,” J. Phys. A
Original
2004
Cited alongside, same era.
Springer Science & Business Media, 2004
M. Ohya and D. Petz, Quantum entropy and its use · 2004
Cited alongside, same era.
P. Zanardi, D. A. Lidar, and S. Lloyd, “Quantum tensor product structures are observable induced,” Phys. Rev. Lett
2004
Cited alongside, same era.
H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, “A Subsystem-Independent Generalization of Entanglement,” Phys. Rev. Lett
2004
Cited alongside, same era.
B.-Q. Jin and V. E. Korepin, “Quantum spin chain, toeplitz determinants and the fisher–hartwig conjecture,” Journal of Statistical Physics
2004
Cited alongside, same era.

Then

T. Faulkner, A. Lewkowycz, and J. Maldacena, “Quantum corrections to holographic entanglement entropy,” JHEP
Original
2013
Later among the works it cites.
A. P. Balachandran, T. R. Govindarajan, A. R. de Queiroz, and A. F. Reyes-Lega, “Entanglement and Particle Identity: A Unifying Approach,” Phys. Rev. Lett
Original
2013
Later among the works it cites.
A. P. Balachandran, T. R. Govindarajan, A. R. de Queiroz, and A. F. Reyes-Lega, “Algebraic Approach to Entanglement and Entropy,” Phys. Rev. A
Original
2013
Later among the works it cites.
E. Bianchi and R. C. Myers, “On the Architecture of Spacetime Geometry,” Class. Quant. Grav
Original
2014
Later among the works it cites.
V. Balasubramanian, B. D. Chowdhury, B. Czech, J. de Boer, and M. P. Heller, “Bulk curves from boundary data in holography,” Phys. Rev. D

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

J. I. Latorre, E. Rico, and G. Vidal, “Ground state entanglement in quantum spin chains,” Quant. Inf. Comput

2004

Cited alongside, same era.

P. Calabrese and J. L. Cardy, “Entanglement entropy and quantum field theory,” J. Stat. Mech

2004

Cited alongside, same era.

S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett

2006

Cited alongside, same era.

S. Ryu and T. Takayanagi, “Aspects of Holographic Entanglement Entropy,” JHEP

2006

Cited alongside, same era.

I. Klich, “Lower entropy bounds and particle number fluctuations in a Fermi sea,” J. Phys. A

2006

Cited alongside, same era.

V. E. Hubeny, M. Rangamani, and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP

2007

Cited alongside, same era.

H. Casini and M. Huerta, “Entanglement entropy in free quantum field theory,” J. Phys. A

2009

Cited alongside, same era.

2014

Later among the works it cites.

R. C. Myers, J. Rao, and S. Sugishita, “Holographic Holes in Higher Dimensions,” JHEP

2014

Later among the works it cites.

H. Casini, M. Huerta, and J. A. Rosabal, “Remarks on entanglement entropy for gauge fields,” Phys. Rev. D

2014

Later among the works it cites.

N. Engelhardt and A. C. Wall, “Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime,” JHEP

2015

Later among the works it cites.

S. A. Hartnoll and E. Mazenc, “Entanglement entropy in two dimensional string theory,” Phys. Rev. Lett

2015

Later among the works it cites.

T. Miyagawa, N. Shiba, and T. Takayanagi, “Double-Trace Deformations and Entanglement Entropy in AdS,” Fortsch. Phys

2016

Later among the works it cites.

S. Sugishita, “Entanglement entropy for free scalar fields in AdS,” JHEP

2016

Later among the works it cites.

D. Harlow, “The Ryu–Takayanagi Formula from Quantum Error Correction,” Commun. Math. Phys

2017

Later among the works it cites.

E. Hillion and O. Johnson, “A proof of the Shepp–Olkin entropy concavity conjecture,” Bernoulli

2017

Later among the works it cites.

A. Belin, N. Iqbal, and S. F. Lokhande, “Bulk entanglement entropy in perturbative excited states,” SciPost Phys

2018

Later among the works it cites.

M. Goldstein and E. Sela, “Symmetry-resolved entanglement in many-body systems,” Phys. Rev. Lett

Original

2018

Later among the works it cites.

A. Lukin, M. Rispoli, R. Schittko, M. E. Tai, A. M. Kaufman, S. Choi, V. Khemani, J. Léonard, and M. Greiner, “Probing entanglement in a many-body–localized system,” Science

2019

Later among the works it cites.

P. Harremoes, “Binomial and poisson distributions as maximum entropy distributions,” IEEE Transactions on Information Theory

2041

Closest in time.

P. Calabrese, J. Cardy, and E. Tonni, “Entanglement entropy of two disjoint intervals in conformal field theory,” J. Stat. Mech

2069

Closest in time.