Pinch point is a singularity of magnetic structure factor discovered first in spin ice. In this talk, we address two topics concerning this notion.

In the first part, we introduce an itinerant electric model which we name as spin ice metal. This model was originally introduced to address the trimerized charge ordering of CsW2O6 [1,2].

Despite the absence of macroscopic degeneracy in the ground state, the quasiparticle spectrum as observed by angle-resolved inverse photoemission spectroscopy exhibits pinch points.

Moreover, this system ``disguises" itself as spin ice in the sense that the entire spectrum turns out to be identical to the analytical form of magnetic structure factor of spin ice [3].

We start with the microscopic formulation of this model and reveal the secret of this trick.

In the second part, we report our recent findings on the property of wavefunctions composing the pinch point singularity in the flat band description [4]. 

We focus on the two topologically distinct classes of flat band wavefunction: the compact localized state (CLS), and the non-contractible loop state (NLS). 

We establish their simple mathematical relationship, showing that different Bloch NLSs can be derived as momentum derivatives of a Bloch CLS, depending on the approaching direction toward the singular point. 

This CLS-NLS correspondence helps visualize the pinch point as an interference pattern among NLSs. 

On the basis of this relation, we also address the loop state fractionalization associated with the transition into the higher-order topological phase.

 

[1] H. Nakai and C. Hotta, Nat. Commun. 13, 579 (2022).

[2] H. Nakai, M. Kawano, and C. Hotta, Phys. Rev. B 108, L081106 (2023).

[3] H. Nakai, M. Udagawa, C. Hotta, in preparation.

[4] M. Udagawa, H. Nakai, C. Hotta, arXiv:2404.13533.