# Bloch oscillations of multi-magnon excitations in a Heisenberg XXZ chain

## TL;DR

This paper investigates Bloch oscillations of multi-magnon excitations in a Heisenberg XXZ chain, revealing new fractional oscillations and proposing methods to measure magnetic field gradients using ultracold atoms.

## Contribution

It introduces a universal relation between ferromagnetic and anti-ferromagnetic systems and uncovers fractional bounded-magnon Bloch oscillations under strong interactions.

## Key findings

- Discovery of fractional bounded-magnon Bloch oscillations.
- Universal relation between ferromagnetic and anti-ferromagnetic systems.
- Method to determine magnetic field gradient using ultracold atoms.

## Abstract

The studies of multi-magnon excitations will extend our understandings of quantum magnetism and strongly correlated matters. Here, by using the time-evolving block decimation algorithm, we investigate the Bloch oscillations of two-magnon excitations under a gradient magnetic field. Through analyzing the symmetry of the Hamiltonian, we derive a rigorous and universal relation between ferromagnetic and anti-ferromagnetic systems. Under strong interactions, in addition to free-magnon Bloch oscillations, there appear fractional bounded-magnon Bloch oscillations which can be understood by an effective single-particle model. To extract the frequencies of Bloch oscillations and determine the gradient of magnetic field, we respectively calculate the fidelity in the time domain and the sub-standard deviation in the frequency domain. Our study not only explore the interaction-induced Bloch oscillations of multi-magnon excitations, but also provides an alternative approach to determine the gradient of magnetic field via ultracold atoms in optical lattices.