An introduction to the spectrum, symmetries, and dynamics of spin-1/2 Heisenberg chains

TL;DR

This paper introduces the fundamental concepts of quantum spin-1/2 Heisenberg chains, focusing on their spectral properties, symmetries, and dynamics, with computational tools provided for further exploration.

Contribution

It offers an accessible introduction to the spectral and dynamical analysis of Heisenberg spin chains, including online code resources for reproducing results.

Findings

Analysis of eigenvalues and eigenstates reveals symmetry properties.

Time evolution demonstrates characteristic quantum dynamics.

Computational tools facilitate further research and education.

Abstract

Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. The goal of this paper is to provide an introduction to the subject by focusing on the time evolution of a Heisenberg spin-1/2 chain and interpreting the results based on the analysis of the eigenvalues, eigenstates, and symmetries of the system. We make available online all computer codes used to obtain our data.