Systematic Mapping of the Hubbard Model to the Generalized t-J Model

TL;DR

This paper presents a systematic method to derive the generalized t-J model from the Hubbard model near half-filling using continuous unitary transformations, clarifying the conditions for its validity and parameter determination.

Contribution

It introduces a self-similar continuous unitary transformation approach to map the Hubbard model to the generalized t-J model, including a truncation scheme and parameter analysis.

Findings

The t-J model can be derived from the Hubbard model at strong coupling.

The effective model parameters are explicitly determined.

The validity of the t-J model depends on sufficiently large interaction strength.

Abstract

The generalized t-J model conserving the number of double occupancies is constructed from the Hubbard model at and in the vicinity of half-filling at strong coupling. The construction is realized by a self-similar continuous unitary transformation. The flow equation is closed by a truncation scheme based on the spatial range of processes. We analyze the conditions under which the t-J model can be set up and we find that it can only be defined for sufficiently large interaction. There, the parameters of the effective model are determined.