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Effective gauge theories based on slave particle construction are widely usedto describe quantum number fractionalization in strongly correlated electronsystems. However, even setting aside the intense debates on the confinementissue of the slave particles, there are still significant conflicts betweentheory and experiment. In particular, a $T^{2/3}$ specific heat anomaly hasbeen predicted as the key signature of low-lying gauge fluctuation in a $U(1)$spin liquid with a large spinon Fermi surface, which is however never observed.Here we show that such an anomaly is actually an artifact of a Gaussianapproximation and is absent when the no double occupancy constraint on theslave particles is strictly enforced. We also show that projective constructionbased on slave particle representation provides a unified understanding on themechanism of spin fractionalization and the nonlocal nature of a physicalspinon in one and two dimensional spin liquids.

physical review. b./physical review. b

Absence of the $T^{2/3}$ specific heat anomaly in a $U(1)$ spin liquid  with a large spinon Fermi surface: confinement of slave particles and  non-locality of spinons