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

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 BF model. By employing a mechanism equivalent to the Haldane's Chern insulator, we can turn the non-interacting 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 generalised (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.

16 pages, 4 figures

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• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Mott Insulators
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• Classification of interacting electronic topological insulators in three dimensions
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Cited by in corpus (16)

• Revealing tensor monopoles through quantum-metric measurements
• Bulk-boundary correspondence in (3+1)-dimensional topological phases
• Tensor Berry connections and their topological invariants
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• Covariant fracton gauge theory with boundary
• Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases
• Fermion-fermion duality in 3+1 dimensions
• Fermionic dualities with axial gauge fields
• 't Hooft surface in lattice gauge theory
• Hamiltonian Formalism of Topologically Massive Electrodynamics
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• On valley asymmetry in a topological interaction for quasi-particles
• Emergence of charge density wave and superconducting phase transitions through Lorentz-invariant interactions in the Haldane-Hubbard model
• Emergent Dynamics of Spacetime and Matter from a Topological Phase
• A note on higher rank descriptions of massless and massive spin-1 particles
• Emergent fracton strings from covariant bi-form gauge field theory