Searching for Two-Neutrino and Neutrinoless Double Beta Decay of ${}^{134}$Xe with the PandaX-4T Experiment

${}^{134}$Xe is a candidate isotope for neutrinoless double beta decay~($0\nu \beta \beta$) search. In addition, the two-neutrino case ($2\nu \beta \beta$) allowed by the Standard Model of particle physics has not yet been observed. Utilizing the 10.4% of ${}^{134}$Xe in the natural xenon in the PandaX-4T detector and its first 94.9-day exposure, we have established the most stringent constraints on $2\nu \beta \beta$ and $0\nu \beta \beta$ of ${}^{134}$Xe half-lives, with limits of $2.8\times {10}^{22}$ yr and $3.0\times {10}^{23}$ yr at 90% confidence level, respectively. The $2\nu \beta \beta$ ($0\nu \beta \beta$) limit surpasses the previously reported best result by a factor of 32 (2.7), highlighting the potential of large monolithic natural xenon detectors.