Modular operators and entanglement in supersymmetric quantum mechanics

Rupak Chatterjee, Ting Yu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The modular operator approach of Tomita-Takesaki to von Neumann algebras is elucidated in the algebraic structure of certain supersymmetric (SUSY) quantum mechanical systems. A von Neumann algebra is constructed from the operators of the system. An explicit operator characterizing the dual infinite degeneracy structure of a SUSY two dimensional system is given by the modular conjugation operator. Furthermore, the entanglement of formation for these SUSY systems using concurrence is shown to be related to the expectation value of the modular conjugation operator in an entangled bi-partite supermultiplet state thus providing a direct physical meaning to this anti-unitary, anti-linear operator as a quantitative measure of entanglement. Finally, the theory is applied to the case of two-dimensional Dirac fermions, as is found in graphene, and a SUSY Jaynes Cummings model.

Original languageEnglish
Article numberabf585
JournalJournal of Physics A: Mathematical and Theoretical
Volume54
Issue number20
DOIs
StatePublished - May 2021

Keywords

  • Concurrence
  • Entanglement
  • SUSY quantum mechanics
  • Tomita-Takesaki modular theory
  • Von Neumann algebras

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