I am trying to understand Wen and Zee's article on topological quantum numbers of Hall fluid on curved space: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.69.953
They passingly mentiond the fact that a spinning particle with orbital angular momentum $s$ moving on a manifold with...
I am reading the fifth chapter on perturbation theory of Condensed Matter Field Theory by Altland and Simons. This question is about the section starting on page 223.
To discuss self energy, they introduced a vector field ##\phi = \{ \phi^a \}, a = 1, \cdots , N##. The action of the field is...
I am new to path integral and struggling with the computation involving Gaussian functional integrals. Could anyone show me the steps of computing the following integral?
\int D \phi e^{-S},
where
S = \int dx~d \tau [(\frac{\partial \phi}{\partial x})^2+2 i \frac{\partial \theta}{\partial...
Thanks again and sorry about the unclear question in my last post.
My actual question is: just looking at the hopping term in the Hubbard Model on an extended lattice (say a square lattice)
\hat H_t = \displaystyle\sum_{\langle i j \rangle} a^{\dagger}_{i \sigma} a_{j \sigma},
since the...
Thank you for your answer. I am having trouble to see why the hopping term only involves two sites. Vaguely I have a feeling that this has to do with the fact that we are only considering the perturbation to second order, but I don't know how to draw the connections.
This is a question from Altland and Simons book "Condensed Matter Field Theory".
In the second exercise on page 64, the book claims that if we define \hat P_s, \hat P_d to be the operators that project onto the singly and doubly occupied subspaces respectively, then at half-filling the...