Built on

J. L. F. Barbon and C. A. Fuertes, “Holographic entanglement entropy probes (non)locality,” JHEP 0804
Original
1928
Earlier work this paper cites.
E. M. Lifshitz, “On the Theory of Second-Order Phase Transitions I & II,” Zh. Eksp. Teor. Fiz 11 (1941) 255 & 269
1941
Earlier work this paper cites.
H. Casini, M. Huerta and L. Leitao, “Entanglement entropy for a Dirac fermion in three dimensions: Vertex contribution,” Nucl. Phys. B 814
Original
1968
Earlier work this paper cites.
J. A. Hertz, “Quantum critical phenomena,” Phys. Rev. B 14
1976
Earlier work this paper cites.
G. Vidal, “Entanglement monotones,” J. Mod. Opt. 47 (2000) 355. doi:10.1080/09500340008244048 [quant-ph/9807077]
2000
Earlier work this paper cites.
I. Peschel, “Calculation of reduced density matrices from correlation functions,” J. Phys. A: Math. Gen. 36, L205 (2003) [arXiv:cond-mat/0212631]
2003
Earlier work this paper cites.
H. Casini and M. Huerta, “Entanglement and alpha entropies for a massive scalar field in two dimensions,” J. Stat. Mech. 0512
2005
Earlier work this paper cites.
E. Fradkin and J. E. Moore, “Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum,” Phys. Rev. Lett. 97
2006
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
H. Casini and M. Huerta, “Universal terms for the entanglement entropy in 2+1 dimensions,” Nucl. Phys. B 764
2006
Earlier work this paper cites.
T. Hirata and T. Takayanagi, “AdS/CFT and strong subadditivity of entanglement entropy,” JHEP 0702
2007
Earlier work this paper cites.
S. Kachru, X. Liu and M. Mulligan, “Gravity duals of Lifshitz-like fixed points,” Phys. Rev. D 78
Original
2008
Earlier work this paper cites.
H. Casini and M. Huerta, “Entanglement entropy in free quantum field theory,” J. Phys. A 42
Original
2009
Earlier work this paper cites.
P. Calabrese and J. Cardy, “Entanglement entropy and conformal field theory,” J. Phys. A 42
Original
2009
Earlier work this paper cites.
H. Casini and M. Huerta, “Remarks on the entanglement entropy for disconnected regions,” JHEP 0903
Original
2009
Earlier work this paper cites.
I. Peschel, V. Eisler, “Reduced density matrices and entanglement entropy in free lattice models,” J. Phys. A: Math. Gen. 42, 504003 (2009) [arXiv:0906.1663]
Original
2009
Earlier work this paper cites.
L Amico, R Fazio, A Osterloh, and V Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80, 517 (2008); J Eisert, M Cramer, and M B Plenio, Area laws for the entanglement entropy - a review, Rev. Mod. Phys. 82, 277 (2010);
2010
Earlier work this paper cites.
S. N. Solodukhin, “Entanglement Entropy in Non-Relativistic Field Theories,” JHEP 1004
Original
2010
Earlier work this paper cites.

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2017

Entanglement in Lifshitz-type Quantum Field Theories

Mozaffar, M. Reza Mohammadi, Mollabashi, Ali

Understand

We study different aspects of quantum entanglement and its measures, including entanglement entropy in the vacuum state of a certain Lifshitz scalar theory.

We present simple intuitive arguments based on "non-local" effects of this theory that the scaling of entanglement entropy depends on the dynamical exponent as a characteristic parameter of the theory.
The scaling is such that in the massless theory for small entangling regions it leads to area law in the Lorentzian limit and volume law in the $z\to\infty$ limit.
We present strong numerical evidences in (1+1) and (2+1)-dimensions in support of this behavior.

Built on

J. L. F. Barbon and C. A. Fuertes, “Holographic entanglement entropy probes (non)locality,” JHEP 0804
Original
1928
Earlier work this paper cites.
E. M. Lifshitz, “On the Theory of Second-Order Phase Transitions I & II,” Zh. Eksp. Teor. Fiz 11 (1941) 255 & 269
1941
Earlier work this paper cites.
H. Casini, M. Huerta and L. Leitao, “Entanglement entropy for a Dirac fermion in three dimensions: Vertex contribution,” Nucl. Phys. B 814
Original
1968
Earlier work this paper cites.
J. A. Hertz, “Quantum critical phenomena,” Phys. Rev. B 14
1976
Earlier work this paper cites.
G. Vidal, “Entanglement monotones,” J. Mod. Opt. 47 (2000) 355. doi:10.1080/09500340008244048 [quant-ph/9807077]
2000
Earlier work this paper cites.
I. Peschel, “Calculation of reduced density matrices from correlation functions,” J. Phys. A: Math. Gen. 36, L205 (2003) [arXiv:cond-mat/0212631]
2003
Earlier work this paper cites.
H. Casini and M. Huerta, “Entanglement and alpha entropies for a massive scalar field in two dimensions,” J. Stat. Mech. 0512
2005
Earlier work this paper cites.
E. Fradkin and J. E. Moore, “Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum,” Phys. Rev. Lett. 97
2006
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
H. Casini and M. Huerta, “Universal terms for the entanglement entropy in 2+1 dimensions,” Nucl. Phys. B 764
2006
Earlier work this paper cites.
T. Hirata and T. Takayanagi, “AdS/CFT and strong subadditivity of entanglement entropy,” JHEP 0702
2007
Earlier work this paper cites.
S. Kachru, X. Liu and M. Mulligan, “Gravity duals of Lifshitz-like fixed points,” Phys. Rev. D 78
Original
2008
Earlier work this paper cites.
H. Casini and M. Huerta, “Entanglement entropy in free quantum field theory,” J. Phys. A 42
Original
2009
Earlier work this paper cites.
P. Calabrese and J. Cardy, “Entanglement entropy and conformal field theory,” J. Phys. A 42
Original
2009
Earlier work this paper cites.
H. Casini and M. Huerta, “Remarks on the entanglement entropy for disconnected regions,” JHEP 0903
Original
2009
Earlier work this paper cites.
I. Peschel, V. Eisler, “Reduced density matrices and entanglement entropy in free lattice models,” J. Phys. A: Math. Gen. 42, 504003 (2009) [arXiv:0906.1663]
Original
2009
Earlier work this paper cites.
L Amico, R Fazio, A Osterloh, and V Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80, 517 (2008); J Eisert, M Cramer, and M B Plenio, Area laws for the entanglement entropy - a review, Rev. Mod. Phys. 82, 277 (2010);
2010
Earlier work this paper cites.
S. N. Solodukhin, “Entanglement Entropy in Non-Relativistic Field Theories,” JHEP 1004
Original
2010
Earlier work this paper cites.