Quantum Spin Ice Thin Films

Quantum spin liquids (QSL) host a range of fascinating phenomena, including a lack of long-range order down to zero temperature, emergent gauge fields and fractionalized excitations. A well-studied example is "quantum spin ice" (QSI), which realizes a three-dimensional U(1) QSL with a well-defined photon excitation and deconfined magnetic and electric charges. In this work, we study the effect of confined geometry on quantum spin ice in experimentally relevant thin film geometries. Classical spin ice (CSI) thin films have been shown to display much of the same physics as bulk CSI, but can realize U(1) or Z2 classical spin liquid phases depending on the boundary conditions. To explore this physics in QSI films, we consider the effect of orphan bonds at the boundaries on the effective Hamiltonian in the QSI phase. Starting from the classical U(1) phase, we find that quantum fluctuations at the boundary renormalize the bulk Ising interactions and modify the photon dispersion. As the strength of these boundary effects increases, the photon mode softens, and the boundary spins partially order into a sub-extensive set of one-dimensional chain states. In contrast, for a system corresponding to the classical Z2 phase, the boundary geometry permits additional string-like operators which induce a photon gap in the semi-classical theory.