Reference for open XX spin chain with external magnetic field

I would like a reference on the diagonalization of an open XX spin 1/2 chain with homogenous external magnetic field. I am new to the subject and I haven't been able to find a reference for it.

Edit:

$$H = h \sum\limits_{j=1}^{N} \sigma_j^z - J \sum\limits_{j=1}^{N-1} (\sigma_j^x \sigma_{j+1}^x + \sigma_j^y \sigma_{j+1}^y)$$ I would like the transformation that allows me to express the Hamiltonian in the form $$H = \sum_k \Lambda_k \eta^{\dagger} _k \eta_k + constants$$ I know the procedure. Just want a reference to double check my results.

• Please add some more details. (E.g., write a Hamiltonian.) It is not even clear in which direction the field is pointing. Also, what exactly do you mean (or: need) when you say "diagonalize"? – Norbert Schuch Dec 23 '15 at 23:00
• In this case, it looks like this can be done by mappipng it to non-interacting fermions. But then you should modify your question: It's not that you want to know how to diagonalize this Hamiltian, but you want a reference. (Or would you be happy with an answer explaining that it can be mapped to free fermions?) You might also consider using the "reference-request" (edit: sorry, "specific-reference") tag in that case. – Norbert Schuch Dec 23 '15 at 23:25
• If you just want to check your results, you could also just do numerical tests on small system sizes. – Norbert Schuch Dec 23 '15 at 23:35
• Some references seem to be linked here physics.stackexchange.com/q/2014 – Norbert Schuch Dec 23 '15 at 23:40