(3+1) -Dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions

Mauro Cirio, Giandomenico Palumbo, Jiannis K. Pachos

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Currently, there is much interest in discovering analytically tractable (3+1)-dimensional models that describe interacting fermions with emerging topological properties. Towards that end we present a three-dimensional tight-binding model of spinless interacting fermions that reproduces, in the low-energy limit, a (3+1)-dimensional Abelian topological quantum field theory called the BF model. By employing a mechanism equivalent to Haldane's Chern insulator, we can turn the noninteracting model into a three-dimensional chiral topological insulator. We then isolate energetically one of the two Fermi points of the lattice model. In the presence of suitable fermionic interactions, the system, in the continuum limit, is equivalent to a generalized (3+1)-dimensional Thirring model. The low-energy limit of this model is faithfully described by the BF theory. Our approach directly establishes the presence of (2+1)-dimensional BF theory at the boundary of the lattice and it provides a way to detect the topological order of the model through fermionic density measurements.

LanguageEnglish
Article number085114
Pages1-15
Number of pages15
JournalPhysical Review B: Condensed Matter and Materials Physics
Volume90
Issue number8
DOIs
Publication statusPublished - 13 Aug 2014

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abstract = "Currently, there is much interest in discovering analytically tractable (3+1)-dimensional models that describe interacting fermions with emerging topological properties. Towards that end we present a three-dimensional tight-binding model of spinless interacting fermions that reproduces, in the low-energy limit, a (3+1)-dimensional Abelian topological quantum field theory called the BF model. By employing a mechanism equivalent to Haldane's Chern insulator, we can turn the noninteracting model into a three-dimensional chiral topological insulator. We then isolate energetically one of the two Fermi points of the lattice model. In the presence of suitable fermionic interactions, the system, in the continuum limit, is equivalent to a generalized (3+1)-dimensional Thirring model. The low-energy limit of this model is faithfully described by the BF theory. Our approach directly establishes the presence of (2+1)-dimensional BF theory at the boundary of the lattice and it provides a way to detect the topological order of the model through fermionic density measurements.",
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(3+1) -Dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions. / Cirio, Mauro; Palumbo, Giandomenico; Pachos, Jiannis K.

In: Physical Review B: Condensed Matter and Materials Physics, Vol. 90, No. 8, 085114, 13.08.2014, p. 1-15.

Research output: Contribution to journalArticleResearchpeer-review

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