A note on path integral formulism of $Z_{2}$ slave-spin representation of Hubbard model

TL;DR

This paper derives a path integral formulation for the $Z_{2}$ slave-spin representation of the Hubbard model, providing a foundation for future theoretical investigations in strongly correlated electron systems.

Contribution

It introduces a derivation of the path integral formalism specific to the $Z_{2}$ slave-spin approach, which was not previously detailed.

Findings

Provides a systematic derivation of the path integral for $Z_{2}$ slave-spin Hubbard model

Facilitates further theoretical and computational studies in strongly correlated systems

Offers a basis for exploring quantum phase transitions in the model

Abstract

This is a note on the derivation of path integral formulism for $Z_{2}$ slave-spin representation of Hubbard model and may be helpful for further study in related works. We are rather happy to receive any comments and other discussions are welcome.