randomquestion
- 6
- 2
- Homework Statement
- Why Does the t-J Model Include a Density-Density Term?
- Relevant Equations
- $$H_{t-J} = -t \sum_{\langle i,j \rangle, \sigma} \mathcal{P} (c_{i\sigma}^\dagger c_{j\sigma} + \text{h.c.}) \mathcal{P} + J \sum_{\langle i,j \rangle} \left( \mathbf{S}_i \cdot \mathbf{S}_j - \frac{1}{4} n_i n_j \right)$$
$$H_{\text{AF}} = J \sum_{\langle i,j \rangle} \mathbf{S}_i \cdot \mathbf{S}_j$$
I'm reading "Lecture Notes on Electron Correlation and Magnetism" by P. Fazekas, and I came across a question regarding the form of the Heisenberg term in the t-J model.
In Chapter 5.1.4, the t-J model is written where there is an additional density-density term in the exchange interaction.
However, in Chapter 5.1.5, the antiferromagnetic Heisenberg model is written without this extra term.
I understand that the density-density term arises naturally when deriving the t-J model from the Hubbard model in the large-U limit. However, I’m trying to get an intuitive explanation of why this term is included in the t-J model but not in the standard Heisenberg model.
Does it relate to the presence of hole doping in the t-J model, or is it more of a reference energy shift? How should I think about its physical meaning?
Would appreciate any insights!
In Chapter 5.1.4, the t-J model is written where there is an additional density-density term in the exchange interaction.
However, in Chapter 5.1.5, the antiferromagnetic Heisenberg model is written without this extra term.
I understand that the density-density term arises naturally when deriving the t-J model from the Hubbard model in the large-U limit. However, I’m trying to get an intuitive explanation of why this term is included in the t-J model but not in the standard Heisenberg model.
Does it relate to the presence of hole doping in the t-J model, or is it more of a reference energy shift? How should I think about its physical meaning?
Would appreciate any insights!