Entanglement negativity in two-dimensional free lattice models

Viktor Eisler, Zoltán Zimborás

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We study the scaling properties of the ground-state entanglement between finite subsystems of infinite two-dimensional free lattice models, as measured by the logarithmic negativity. For adjacent regions with a common boundary, we observe that the negativity follows a strict area law for a lattice of harmonic oscillators, whereas for fermionic hopping models the numerical results indicate a multiplicative logarithmic correction. In this latter case we conjecture a formula for the prefactor of the area-law violating term, which is entirely determined by the geometries of the Fermi surface and the boundary between the subsystems. The conjecture is tested against numerical results and a good agreement is found.

Original languageEnglish
Article number115148
JournalPhysical Review / B
Volume93
Issue number11
DOIs
Publication statusPublished - 31 Mar 2016

Fingerprint

Fermi surface
harmonic oscillators
Ground state
Fermi surfaces
scaling
ground state
Geometry
geometry

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electronic, Optical and Magnetic Materials

Cite this

Entanglement negativity in two-dimensional free lattice models. / Eisler, Viktor; Zimborás, Zoltán.

In: Physical Review / B, Vol. 93, No. 11, 115148, 31.03.2016.

Research output: Contribution to journalArticleResearchpeer-review

@article{024363b0c390412bb7825cb6d807680b,
title = "Entanglement negativity in two-dimensional free lattice models",
abstract = "We study the scaling properties of the ground-state entanglement between finite subsystems of infinite two-dimensional free lattice models, as measured by the logarithmic negativity. For adjacent regions with a common boundary, we observe that the negativity follows a strict area law for a lattice of harmonic oscillators, whereas for fermionic hopping models the numerical results indicate a multiplicative logarithmic correction. In this latter case we conjecture a formula for the prefactor of the area-law violating term, which is entirely determined by the geometries of the Fermi surface and the boundary between the subsystems. The conjecture is tested against numerical results and a good agreement is found.",
author = "Viktor Eisler and Zolt{\'a}n Zimbor{\'a}s",
year = "2016",
month = "3",
day = "31",
doi = "10.1103/PhysRevB.93.115148",
language = "English",
volume = "93",
journal = "Physical Review / B",
issn = "1098-0121",
publisher = "American Physical Society",
number = "11",

}

TY - JOUR

T1 - Entanglement negativity in two-dimensional free lattice models

AU - Eisler, Viktor

AU - Zimborás, Zoltán

PY - 2016/3/31

Y1 - 2016/3/31

N2 - We study the scaling properties of the ground-state entanglement between finite subsystems of infinite two-dimensional free lattice models, as measured by the logarithmic negativity. For adjacent regions with a common boundary, we observe that the negativity follows a strict area law for a lattice of harmonic oscillators, whereas for fermionic hopping models the numerical results indicate a multiplicative logarithmic correction. In this latter case we conjecture a formula for the prefactor of the area-law violating term, which is entirely determined by the geometries of the Fermi surface and the boundary between the subsystems. The conjecture is tested against numerical results and a good agreement is found.

AB - We study the scaling properties of the ground-state entanglement between finite subsystems of infinite two-dimensional free lattice models, as measured by the logarithmic negativity. For adjacent regions with a common boundary, we observe that the negativity follows a strict area law for a lattice of harmonic oscillators, whereas for fermionic hopping models the numerical results indicate a multiplicative logarithmic correction. In this latter case we conjecture a formula for the prefactor of the area-law violating term, which is entirely determined by the geometries of the Fermi surface and the boundary between the subsystems. The conjecture is tested against numerical results and a good agreement is found.

UR - http://www.scopus.com/inward/record.url?scp=84963611939&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.93.115148

DO - 10.1103/PhysRevB.93.115148

M3 - Article

VL - 93

JO - Physical Review / B

JF - Physical Review / B

SN - 1098-0121

IS - 11

M1 - 115148

ER -