### 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.

Language | English |
---|---|

Article number | 085114 |

Pages | 1-15 |

Number of pages | 15 |

Journal | Physical Review B: Condensed Matter and Materials Physics |

Volume | 90 |

Issue number | 8 |

DOIs | |

Publication status | Published - 13 Aug 2014 |

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### Cite this

*Physical Review B: Condensed Matter and Materials Physics*,

*90*(8), 1-15. [085114]. https://doi.org/10.1103/PhysRevB.90.085114

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*Physical Review B: Condensed Matter and Materials Physics*, vol. 90, no. 8, 085114, pp. 1-15. https://doi.org/10.1103/PhysRevB.90.085114

**(3+1) -Dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions.** / Cirio, Mauro; Palumbo, Giandomenico; Pachos, Jiannis K.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - (3+1) -Dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions

AU - Cirio, Mauro

AU - Palumbo, Giandomenico

AU - Pachos, Jiannis K.

PY - 2014/8/13

Y1 - 2014/8/13

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84927534608&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.90.085114

DO - 10.1103/PhysRevB.90.085114

M3 - Article

VL - 90

SP - 1

EP - 15

JO - Physical Review B: Condensed Matter and Materials Physics

T2 - Physical Review B: Condensed Matter and Materials Physics

JF - Physical Review B: Condensed Matter and Materials Physics

SN - 2469-9950

IS - 8

M1 - 085114

ER -