I was modelling the 1D transverse quantum Ising model and made a Kronecker product loop to find the Hamiltonian of the system, for a given magnetic field configuration. Now, my question is that when I outputted the eigenvectors of the Hamiltonian, they were always real. This highly contrasted with say a Linear Vibrational Coupling/ Linear+Quadratic Coupling model, as their Hamiltonians had complex eigenvectors.
I might be missing something here, why should the Eigenvectors of the 1D Transverse Quantum Ising be real, please help me out. I am a beginner in condensed matter physics and linear algebra so would appreciate it if someone explained from the basics.