# Characterization of localized effective spins in gapped quantum spin chains

## TL;DR

This paper investigates localized effective spins in gapped quantum spin chains caused by lattice inhomogeneities, using matrix product states to analyze their properties, responses to external fields, and interactions.

## Contribution

It introduces exact MPS representations for induced spins in AKLT and bond-alternating Heisenberg models, enabling detailed analysis of their responses and interactions.

## Key findings

- Effective spins can be characterized using MPS representations.
- The response of induced spins to external magnetic fields is analyzed.
- The effective exchange interaction between spins is quantified.

## 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.