Mixed Field Ising Chain. The Mixed Field Ising model (MFI) is a simple generalization of the Transverse Field Ising model with dynamics is governed by the following Hamiltonian: N N N HMFI = −J Σ ZˆiZˆi+1 − hx Σ Xˆi − hz Σ Zˆi. (1.54) i=1 i=1 − − This model has a few different manifestations, dependent on the point in the parameter space (hx, hz), which make it a rich playground for the theoretical testing of new hypotheses. For hz = 0 this model reduces to the TI model (1.4.2), and for hx = 0 reduces to the regular Ising model. We used the latter in Chapter 3 as a representative case of classical systems. The prominence of this model is that it is an archetype of quantum-chaotic behavior. At a particular point in the parameter space hx = 1.05 and hz = 0.5 it has the RMT-like spectral statistics [61]. Even though this point is not an isolated instance of chaotic behavior, sometimes it is referred to as ”strong-chaoticity” [52], since, by varying (hx, hz), the spectral statistics of the model continuously transform between Wigner-Dyson distribution at hx = 1.05 and hz = 0.5 and Poisson distribution at an integrable point hx = 0 or hz = 0 in the parameter space. This smooth interpolation between chaotic and integrable regimes is what makes this model particularly convenient as a theoretical toy model.
