Exactly Solvable 1D Quantum Models with Gamma Matrices
In this paper, we write exactly solvable generalizations of 1-dimensional quantum XY and Ising-like models by using 2^d-dimensional Gamma matrices as the degrees of freedom on each site. We show that these models result in quadratic Fermionic Hamiltonians with Jordan-Wigner like transformations. We illustrate the techniques using a specific case of 4-dimensional Gamma matrices and explore the quantum phase transitions present in the model.