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Quantum spin ice (QSI) is an emblematic three-dimensional $U(1)$ quantum spinliquid (QSL) on the pyrochlore lattice that hosts gapless photon-like modes andspinon excitations. Despite its notable status and the current rise of strongmaterial candidates Ce$_2$(Zr, Sn, Hf)$_2$O$_7$, there are still only a fewanalytical approaches to model the low-energy behavior of QSI. These analyticalmethods are essential to gain insight into the physical interpretation ofmeasurements. We here introduce the self-consistent exclusive bosonrepresentation (SCEBR) to model emergent spinon excitations in QSI. By treatingthe presence of other emergent charges in an average way, the SCEBR extends therange of validity of the exclusive boson representation previously introducedby Hao, Day, and Gingras [Hao, Day, and Gingras, Physical Review B, 90, 214430(2014)] to numerous cases of physical relevance. We extensively benchmark theapproach and provide detailed analytical expressions for the spinon dispersion,the Bogoliubov transformation that diagonalizes the system, and the dynamicalspin structure factor for 0- and $\pi$-flux QSI. Finite temperature propertiesare further investigated to highlight essential differences between thethermodynamic behavior of the 0- and $\pi$-flux phases. We notably show thatthe SCEBR predicts a reduction of the spinon bandwidth with increasingtemperature, consistent with previous quantum Monte-Carlo results, throughsuppression of spinon hopping by thermal occupation. The SCEBR thus provides apowerful analytical tool to interpret experiments on current and futurecandidate material that has several advantages over other widely used methods.

Finite Temperature Dynamics in 0-Flux and $\pi$-Flux Quantum Spin Ice: Self-Consistent Exclusive Boson Approach