No abstract

We study properties of localized effective spins induced in gapped quantum spin chains by local inhomogeneities of the lattice. As a prototype, we study effective spins induced in impunity sites doped AKLT model by constructing the exact ground state in a matrix product state (MPS) form. We characterize their responses to external fields by studying an extended Zeeman interaction. We also study the antiferromagnetic bond-alternating Heisenberg chain with defect structures. For this model, an MPS representation similar to that for the AKLT model, "a uniform MPS with windows", is constructed, and it gives a good approximation of the ground state. We discuss the trade-off relation between the window length and the precision of the MPS ansatz. The effective exchange interaction between the induced spins is also investigated by using this representation.

We investigate the relaxation dynamics of open non-integrable quantum many-body systems in the thermodynamic limit by using a tensor-network formalism. We simulate the Lindblad quantum master equation (LQME) of infinite systems by making use of the uniform matrix product operators (MPO) as the ansatz of their density matrices. Furthermore, we establish a method to measure the thermodynamic equivalence between two states described by the uniform MPOs. We numerically show that when an initial state of the LQME is a thermal Gibbs state, a time evolved state is always indistinguishable from a Gibbs state with a time-dependent effective temperature in the weak-dissipation and thermodynamic limit.