Analytical results for the entanglement Hamiltonian of a free-fermion chain

Eisler, Viktor; Peschel, Ingo

doi:10.1088/1751-8121/aa76b5

Analytical results for the entanglement Hamiltonian of a free-fermion chain

Mar 23, 2017

19 pages

Published in:

J.Phys.A 50 (2017) 28, 284003

Published: Jun 21, 2017

e-Print:

1703.08126 [cond-mat.stat-mech]

DOI:

10.1088/1751-8121/aa76b5

View in:

pdf

reference search65 citations

Citations per year

Abstract: (IOP)

We study the ground-state entanglement Hamiltonian for an interval of N sites in a free-fermion chain with arbitrary filling. By relating it to a commuting operator, we find explicit expressions for its matrix elements in the large-N limit. The results agree with numerical calculations and show that deviations from the conformal prediction persist even for large systems.

Note:

21 pages, 8 figures. Dedicated to John Cardy on the occasion of his 70th birthday. v2: minor corrections, published version

References(25)

Figures(0)

[1]

Entanglement entropy in extended quantum systems

- J.Phys.A A 42 (2009) 50, 500301
•
DOI:
- 10.1088/1751-8121/42/50/500301

[2]

Axion Cosmology

David J. E. Marsh
(
- King's Coll. London
)

- Phys.Rept. 643 (2016) 1-79
•
e-Print:
- 1510.07633
•
DOI:
- 10.1016/j.physrep.2016.06.005

[2]

Quantum entanglement in condensed matter systems

Nicolas Laflorencie
(
- Toulouse III U.
)

- Phys.Rept. 646 (2016) 1-59
•
e-Print:
- 1512.03388
•
DOI:
- 10.1016/j.physrep.2016.06.008

[3]

Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States

Hui Li
(
- Princeton U.
)
,
F. Haldane
(
- Princeton U.
)

- Phys.Rev.Lett. 101 (2008) 1, 010504
•
e-Print:
- 0805.0332
•
DOI:
- 10.1103/PhysRevLett.101.010504

[4]

Special Review: Entanglement in Solvable Many-Particle Models

Ingo Peschel

- Braz.J.Phys. 42 (2012) 3, 267-291
•
DOI:
- 10.1007/s13538-012-0074-1

[5]

Density-matrix spectra for integrable models Crossref:

Peschel I
,
Kaulke M
,
Legeza Ö

- Annals Phys. 8 (1999) 153
•
DOI:
- 10.1002/(SICI)1521-3889(199902)8:2<153::AID-ANDP153>3.0.CO;2-N

[6]

Density matrices for a chain of oscillators

- J.Phys.A 32 (1999) 48, 8419,
- Journal of Physics A: Mathematical and General 32 (1999) 48, 8419-8428
•
e-Print:
- cond-mat/9906224
•
DOI:
- 10.1088/0305-4470/32/48/305

[7]

Angular quantization and the density matrix renormalization group

Jose C. Gaite
(
- INTA, Madrid and
- Madrid, IMAFF
)

- Mod.Phys.Lett.A 16 (2001) 1109-1116
•
e-Print:
- cond-mat/0106049
•
DOI:
- 10.1142/S0217732301004364

[8]

Entanglement hamiltonians in two-dimensional conformal field theory

John Cardy
(
- UC, Berkeley and
- Oxford U.
)
,
Erik Tonni
(
- SISSA, Trieste and
- INFN, Trieste
)

- J.Stat.Mech. 1612 (2016) 12, 123103
•
e-Print:
- 1608.01283
•
DOI:
- 10.1088/1742-5468/2016/12/123103

[9]

Towards a derivation of holographic entanglement entropy

- JHEP 05 (2011) 036
•
e-Print:
- 1102.0440
•
DOI:
- 10.1007/JHEP05(2011)036

[10]

Entanglement Temperature and Entanglement Entropy of Excited States

Gabriel Wong
(
- Virginia U.
)
,
Israel Klich
(
- Virginia U.
)
,
Leopoldo A. Pando Zayas
(
- Michigan U., MCTP
)
,
Diana Vaman
(
- Virginia U.
)

- JHEP 12 (2013) 020
•
e-Print:
- 1305.3291
•
DOI:
- 10.1007/JHEP12(2013)020

[11]

Evolution operators in conformal field theories and conformal mappings: Entanglement Hamiltonian, the sine-square deformation, and others

Xueda Wen
(
- Illinois U., Urbana
)
,
Shinsei Ryu
(
- Illinois U., Urbana
)
,
Andreas W.W. Ludwig
(
- UC, Santa Barbara
)

- Phys.Rev.B 93 (2016) 23, 235119
•
e-Print:
- 1604.01085
•
DOI:
- 10.1103/PhysRevB.93.235119

[12]

Reduced density matrices and entanglement entropy in free lattice models J. Phys. A: Math. Theor. 42 504003

Peschel I
,
Eisler V

•
DOI:
- 10.1088/1751-8121/42/50/504003

[13]

Entanglement, combinatorics and finite-size effects in spin-chains J. Stat Mech. P02063

Nienhuis B
,
Campostrini M
,
Calabrese P

•
DOI:
- 10.1088/1742-5468/2009/02/P02063

[14]

Prolate spheroidal wave functions, Fourier analysis, and uncertainty V: the discrete case Bell Labs Tech. J 57 1371, Crossref:

Slepian D

•
DOI:
- 10.1002/j.1538-7305.1978.tb02104.x

[15]

Free-fermion entanglement and spheroidal functions J. Stat Mech. P04028

Eisler V
,
Peschel I

•
DOI:
- 10.1088/1742-5468/2013/04/P04028

[16]

Local temperatures and local terms in modular Hamiltonians

Raul Arias
(
- La Plata U. and
- Centro Atomico Bariloche
)
,
David Blanco
(
- Buenos Aires, CONICET
)
,
Horacio Casini
(
- Centro Atomico Bariloche
)
,
Marina Huerta
(
- Centro Atomico Bariloche
)

- Phys.Rev.D 95 (2017) 6, 065005
•
e-Print:
- 1611.08517
•
DOI:
- 10.1103/PhysRevD.95.065005

[17]

Calculation of reduced density matrices from correlation functions

Ingo Peschel

- J.Phys.A 36 (2003) 14, L205,
- Journal of Physics A: Mathematical and General 36 (2003) 14, L205-L208
•
e-Print:
- cond-mat/0212631
•
DOI:
- 10.1088/0305-4470/36/14/101