Vison crystal in quantum spin ice on the breathing pyrochlore lattice

TL;DR

This paper explores how the breathing pyrochlore lattice and specific spin couplings induce a novel $U(1)_{rac{ ext{pi}}{2}}$ phase with dense vison packing, revealing new emergent phenomena and excitations in quantum spin ice.

Contribution

It introduces the imaginary ring flip term resulting from $J_{z ext{-} ext{pm}}$ coupling and breathing lattice effects, leading to a new quantum spin ice phase with unique excitations.

Findings

Discovery of the $U(1)_{rac{ ext{pi}}{2}}$ phase with dense vison packing.

Identification of the imaginary ring flip as a chemical potential and three-photon vertex.

Emergence of a structured high-energy continuum interpreted as three photon up-conversion.

Abstract

Recent excitement in the quantum spin ice community has come from the experimental discovery of pseudospin-$1/2$ breathing pyrochlores, including Ba$_3$Yb$_2$Zn$_5$O$_{11}$, in which inversion symmetry is broken by the `up' and `down' tetrahedra taking different physical sizes. We show here that the often-neglected $J_{z\pm}$ coupling between Kramers ions, in combination with the breathing nature of the lattice, can produce an imaginary ring flip term. This can lead to an unconventional '$U(1)_{\pi/2}$ phase', corresponding to a maximally dense packing of visons on the lattice. Coherent dynamics persists in all phases, together with its emergent QED description, in a manner reminiscent of fragmentation in spinon crystals. We characterize the enlarged QSI phase diagram and its excitations, showing that the imaginary ring flip acts both as a chemical potential for visons and as an effective three-photon vertex akin to strong light-matter coupling. The novel coupling causes a structured high-energy continuum to emerge above the photon dispersion, which is naturally interpreted as three photon up-conversion in a nonlinear optical crystal.