# Random XX spin chain in 1D

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1. Oct 11, 2015

### mimpim

Hi,
Consider model of one dimensional spin chain with a random couplings J. The Hamiltonian is the following:

$$H = \sum_i J_i (S_i^x S_{i+1}^x+ S_i^y S_{i+1}^y)$$,
Which by Jordan-Wigner transformation we can transform it to the fermionic representations.

$$H = \sum_i J_j/2 (c_i c_{i+1}^{\dagger}+h.c)$$.

My question is can we solve this model exactly? (I know when the couplings J are constant we can solve this model exactly and have analytic solution. But how about when we have a random couplings)
I appreciate any help and comment.

2. Oct 16, 2015