TY - JOUR
T1 - Modular operators and entanglement in supersymmetric quantum mechanics
AU - Chatterjee, Rupak
AU - Yu, Ting
N1 - Publisher Copyright:
© 2021 Institute of Physics Publishing. All rights reserved.
PY - 2021/5
Y1 - 2021/5
N2 - 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.
AB - 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.
KW - Concurrence
KW - Entanglement
KW - SUSY quantum mechanics
KW - Tomita-Takesaki modular theory
KW - Von Neumann algebras
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U2 - 10.1088/1751-8121/abf585
DO - 10.1088/1751-8121/abf585
M3 - Article
AN - SCOPUS:85105026801
SN - 1751-8113
VL - 54
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 20
M1 - abf585
ER -