Abstract
We study an improved holographic model for the strongly coupled nodal line semimetal which satisfies the duality relation between the rank two tensor operators overline{psi}{gamma}^{mu v}psi and overline{psi}{gamma}^{mu v}{gamma}^5psi . We introduce a Chern-Simons term and a mass term in the bulk for a complex two form field which is dual to the above tensor operators and the duality relation is automatically satisfied from holography. We find that there exists a quantum phase transition from a topological nodal line semimetal phase to a trivial phase. In the topological phase, there exist multiple nodal lines in the fermionic spectrum which are topologically nontrivial. The bulk geometries are different from the previous model without the duality constraint, while the resulting properties are qualitatively similar to those in that model. This improved model provides a more natural ground to analyze transports or other properties of strongly coupled nodal line semimetals.
Highlights
Topological semimetals exhibit lots of robust and exotic quantum properties and have attracted enormous research interests during the past few years [2, 3]
We introduce a Chern-Simons term and a mass term in the bulk for a complex two form field which is dual to the above tensor operators and the duality relation is automatically satisfied from holography
We have considered an improved holographic nodal line semimetal model in which the duality relation between the rank two operators ψγμνψ and ψγμνγ5ψ in the dual field theory is satisfied
Summary
Topological nodal line semimetal is realized in a Lorentz violating field theoretical model [3, 8, 9, 28] with the following Lagrangian. The band structure and the eigenstates of this Dirac system can be determined and reveal a quantum phase transition from the nodal line semimetal phase to gapped system by tuning the ratio between bxy and m. The external source b5μν is set to be pure imaginary to make the Hamiltonian real. With this choice of Lagrangian in (2.5), the band structure, i.e. E± = ± (4bxy ± m2 + kx2 + ky2)2 + kz is the same as that described with the Lagrangian of (2.1) up to a prefactor of bxy [8, 9]. The model (2.5) with the duality relation of the rank two operators (2.4) is called the improved nodal line semimetal. There still exists a quantum phase transition from a nodal line semimetal to a gapped phase, as shown in figure 1
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