We study the logarithmic negativity and the moments of the partial transpose in the ground state of a two dimensional massless harmonic square lattice with nearest neighbour interactions for various configurations of adjacent domains. At leading order for large domains, the logarithmic negativity and the logarithm of the ratio between the generic moment of the partial transpose and the moment of the reduced density matrix at the same order satisfy an area law in terms of the length of the curve shared by the adjacent regions. We give numerical evidence that the coefficient of the area law term in these quantities is related to the coefficient of the area law term in the Rényi entropies. Whenever the curve shared by the adjacent domains contains vertices, a subleading logarithmic term occurs in these quantities and the numerical values of the corner function for some pairs of angles are obtained. In the special case of vertices corresponding to explementary angles, we provide numerical evidence that the corner function of the logarithmic negativity is given by the corner function of the Rényi entropy of order 1/2.

Entanglement negativity in a two dimensional harmonic lattice: Area law and corner contributions / De Nobili, Cristiano; Coser, Andrea; Tonni, Erik. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2016:8(2016), pp. 1-27. [10.1088/1742-5468/2016/08/083102]

Entanglement negativity in a two dimensional harmonic lattice: Area law and corner contributions

De Nobili, Cristiano;Coser, Andrea;Tonni, Erik
2016-01-01

Abstract

We study the logarithmic negativity and the moments of the partial transpose in the ground state of a two dimensional massless harmonic square lattice with nearest neighbour interactions for various configurations of adjacent domains. At leading order for large domains, the logarithmic negativity and the logarithm of the ratio between the generic moment of the partial transpose and the moment of the reduced density matrix at the same order satisfy an area law in terms of the length of the curve shared by the adjacent regions. We give numerical evidence that the coefficient of the area law term in these quantities is related to the coefficient of the area law term in the Rényi entropies. Whenever the curve shared by the adjacent domains contains vertices, a subleading logarithmic term occurs in these quantities and the numerical values of the corner function for some pairs of angles are obtained. In the special case of vertices corresponding to explementary angles, we provide numerical evidence that the corner function of the logarithmic negativity is given by the corner function of the Rényi entropy of order 1/2.
2016
2016
8
1
27
083102
https://arxiv.org/abs/1604.02609
http://cdsads.u-strasbg.fr/abs/2016JSMTE..08.3102D
De Nobili, Cristiano; Coser, Andrea; Tonni, Erik
File in questo prodotto:
File Dimensione Formato  
De_Nobili_2016_J._Stat._Mech._2016_083102.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 2.06 MB
Formato Adobe PDF
2.06 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
postprint.pdf

Open Access dal 10/08/2017

Descrizione: Postprint
Tipologia: Documento in Post-print
Licenza: Non specificato
Dimensione 3.11 MB
Formato Adobe PDF
3.11 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/32847
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 44
  • ???jsp.display-item.citation.isi??? 36
social impact