Fold bifurcation entangled surfaces for one-dimensional Kitaev lattice model

In this paper, we investigate a feasible holography with the Kitaev model using dilatonic gravity in AdS(2). We propose a generic dual theory of gravity in the AdS(2) and suggest that this bulk action is a suitable toy model in studying quantum mechanics in Kitaev model using gauge/gravity duality. This gives a possible equivalent description for the Kitaev model in the dual gravity bulk. Scalar and tensor perturbations are investigated in details. In the case of near AdS perturbation, we show that the geometry still freezes as is AdS, while the dilation perturbation decays at the AdS boundary safely. The time-dependent part of the perturbation is an oscillatory model. We discover that the dual gravity induces an effective and renormalizable quantum action. The entanglement entropy for bulk theory is computed using extremal surfaces. We prove that these surfaces have a fold bifurcation regime of criticality.

Automated summary

This paper investigates the feasibility of holography with the Kitaev model using dilatonic gravity in AdS(2). A generic dual theory of gravity in AdS(2) is proposed, providing a suitable toy model for studying quantum mechanics in the Kitaev model using gauge/gravity duality. Scalar and tensor perturbations are analyzed, and it is shown that near AdS perturbations freeze as AdS, while dilation perturbations decay safely at the AdS boundary. The time-dependent part of the perturbation exhibits an oscillatory model, and the dual gravity induces an effective and renormalizable quantum action, with entanglement entropy computed for the bulk theory using extremal surfaces showing a fold bifurcation regime of criticality.