A Class of Asymmetric Gapped Hamiltonians on Quantum Spin Chains and its Characterization I

We introduce a class of gapped Hamiltonians on quantum spin chains, which allows asymmetric edge ground states. This class is an asymmetric generalization of the class of Hamiltonians (Fannes et al. Commun Math Phys 144:443–490, 1992). It can be characterized by five qualitative physical properties of ground state structures. In this Part I, we introduce the models and investigate their properties.