I am looking for the definition of integrable and the definition of chaotic in the context of spin chains. In particular, consider the NN Ising model with both transverse and longitudinal fields:
H=∑jZjZj+1+h∑jX+g∑jZ
It is said that for g=0, the spin chain is integrable for all h. Whereas for general values of h and g the system is chaotic. What makes the system integrable at g=0, besides being exactly solvable via Jordan-Wigner transformation? Are all chaotic spin chains nonintegrable?
Thanks