Geometric or Entanglement Entropy  

In General > s.a. entanglement; quantum entropy; Density Matrix [reduced].
* Idea: A quantity which characterizes the correlations between subsystems A and B in a larger quantum-mechanical system; It is calculated as the von Neumann entropy of the reduced density matrix ρA for subsystem A, obtained by ignoring the correlations between A and B in a (pure) state of the whole system,

SA = –k tr ρA ln ρA ;

If the subsystem is defined by a domain A in space, then the entanglement entropy is called geometric entropy.
* Result: In many cases, the leading term of the entanglement entropy of A for the vacuum state is proportional to the area of the boundary ∂A.
@ Intros and reviews: Calabrese & Cardy IJQI(06)qp/05-conf [intro]; Casini & Huerta JPA(09)-a0905; Solodukhin LRR(11)-a1106.
@ General references: Sorkin in(83)-a1402; Callan & Wilczek PLB(94) [flat space]; Benedict & Pi AP(96)ht/95; Popescu & Rohrlich PRA(97)qp/96; Mukohyama PRD(98)gq, et al gq/98-conf; Hammer in(04)ht/98; Giraldi & Grigolini PRA(01); Brustein & Yarom PRD(04)ht/03 [subsets of Minkowski space]; Casini CQG(04)ht/03; Calabrese & Cardy JSM(04)ht [in quantum field theory, see oct(08) revision]; Solodukhin PLB(08)-a0802 [and extrinsic geometry]; Calabrese et al JPA(09)#50 [and issue articles]; Koksma et al AP(10)-a1002 [entropy and correlators]; Padmanabhan PRD(10)-a1007 [and quantum of area]; Hertzberg & Wilczek PRL(11)-a1007 [calculable contributions]; Ercolessi et al PRB(12)-a1201 [correlation length and corrections]; Balachandran et al PRA(13)-a1301 [algebraic approach]; Bianchi & Myers a1212 [as a probe of the architecture of spacetime]; Neiman PRL(13)-a1310 [and non-additive imaginary term in the action]; Rosenhaus & Smolkin JHEP(14)-a1403 [perturbative calculation]; Astaneh et al PRD(14)-a1407 [maximizing surface]; Asplund & Berenstein AP(16)-a1503 [and classical entropy].
@ Area law: Buniy & Hsu PLB(07)ht/05 [faster-than-A scaling, correlations, holography]; Riera & Latorre PRA(06)qp; Pakman & Parnachev JHEP(08) [and holography]; Eisert et al RMP(10)-a0808 [rev]; Brandão & Horodecki CMP(15)-a1206 [and exponential decay of correlations]; Collins et al JPA(13) [for random graph states]; Mariën et al a1411 [stability]; Chandran et al Ent(16)-a1511 [intuitive explanation, and logarithmic prefactor]; Leichenauer et al JHEP(16)-a1604 [evolution of the universal area law]; > s.a. entanglement phenomenology [rate of production]; statistical-mechanical systems [lattice systems].

Related Topics > s.a. Subsystems.
@ Infrared divergences: Mallayya et al PRD(14)-a1404; Yazdi a1608 [and zero modes].
@ And holography: Ryu & Takayanagi PRL(06)ht, Solodukhin PRL(06) [and AdS-cft]; Hubeny et al JHEP(07)-a0705 [covariant]; Nishioka et al JPA(09)-a0905; Casini et al JHEP(11)-a1102 [derivation for spherical entangling surfaces]; Takayanagi CQG(12), GRG(14); Headrick et al JHEP(14)-a1408 [and causality]; Bueno & Myers JHEP(15)-a1505 [corner contributions]; Rangamani & Takayanagi a1609 [rev]; > s.a. holography.
@ Dynamics: Calabrese & Cardy JSM(05)cm [1D]; Avery & Paulos PRL(14)-a1407 [bounds on time rate of change]; Zhang et al PRE(15)-a1501 [near equilibrium, and relaxation]; Casini et al JHEP(16)-a1509 [time evolution and causality constraints].
@ Measures of entanglement: Vedral et al PRL(97)qp; Henderson & Vedral PRL(00)qp/99 [entropy]; Wu & Zhang PRA(01)qp/00; Brandão & Vianna PRL(04)qp; Miranowicz & Ishizaka PRA(08)-a0805.
@ Surfaces, shape dependence: Balachandran et al IJMPA(97)ht/95 [and edge states]; Bhattacharyya & Sinha IJMPD(13)-a1305-GRF [from surface terms in general relativity]; Carmi JHEP(15)-a1506 [shape dependence]; Dorn a1608 [regions with conical singularities]; Kusuki et al a1703 [Lorentz-boosted subsystems].
@ Other topics: Wódkiewicz PRA(95)qp [EPR]; Piani PRL(09), Friedland & Gour JMP(11)-a1007 [relative entropy of entanglement]; Jacobson IJMPD(12)-a1204-GRF [finiteness, and existence of gravity]; Klebanov et al JHEP(12), JHEP(12)-a1207 [and the renormalization group]; Kalogeropoulos EPJB(14)-a1403 [extensivity]; Nishioka & Yarom JHEP(16)-a1509 [with gauge and gravitational anomalies]; > s.a. temperature.

Variations and Related Topics > s.a. entanglement entropy for various types of systems.
@ Rényi entanglement entropy: Drut & Porter PRB(15)-a1506 [interacting fermions].
@ Topological entanglement entropy: Kitaev & Preskill PRL(06); Brown et al PRL(13)-a1303.
@ Other variations and special cases: Das & Shankaranarayanan PRD(06)gq/05 [field not in the ground state]; Fursaev PRD(06)ht [critical phenomena and analog quantum gravity]; Casini & Huerta JHEP(09)-a0812 [for disconnected regions]; Solodukhin JHEP(10)-a0909 [non-relativistic field theory]; Solodukhin JPA(12)-a1112 [with fluctuating entangling surfaces]; Liu & Mezei JHEP(13)-a1202 [refinement,"renormalized"]; Kumar et al PRD(14)-a1401 [area scaling in genus-1 geometries]; Ibnouhsein et al PRD(14)-a1407 [renormalized]; Maxfield JHEP(15)-a1412 [3D gravity]; Taylor JHEP(16)-a1507 [generalized].


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