Single magnon excited states of a Heisenberg spin-chain using a quantum computer

TL;DR

This paper introduces a quantum computing method to efficiently calculate single magnon excited states in Heisenberg spin-chains, demonstrating implementation on small chains with insights into circuit complexity.

Contribution

The paper presents a novel quantum algorithm for finding magnon excited states in Heisenberg chains, including practical implementation and analysis of circuit complexity.

Findings

Successful implementation on 4-site and 8-site chains

Insights into quantum circuit complexity and scaling

Demonstration of method on IBM quantum processor

Abstract

Excited states of spin-chains play an important role in condensed matter physics. We present a method of calculating the single magnon excited states of the Heisenberg spin-chain that can be efficiently implemented on a quantum processor for small spin chains. Our method involves finding the stationary points of the energy vs wavenumber curve. We implement our method for 4-site and 8-site Heisenberg Hamiltonians using numerical techniques as well as using an IBM quantum processor. Finally, we give an insight into the circuit complexity and scaling of our proposed method.