Exactly Solvable 1D Quantum Models with Gamma Matrices

Abstract

In this paper, we write exactly solvable generalizations of 1-dimensional quantum XY and Ising-like models by using $2^d$-dimensional Gamma ($\Gamma$) 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.

25 Pages, 4 Figures

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Cited by in corpus (1)

• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains