# Density waves in strongly correlated quantum chains

## TL;DR

This paper reviews exact numerical results for one-dimensional quantum systems with half-filled bands, focusing on various models including Peierls transitions, competing interactions, and topological states in fermion and anyon systems.

## Contribution

It provides a comprehensive review of numerical results across multiple models of strongly correlated quantum chains, highlighting recent advances and diverse phenomena.

## Key findings

- Detailed characterization of Peierls transitions in various models
- Insights into symmetry-protected topological states in fermion and anyon systems
- Comparison of competing interactions in one-dimensional quantum chains

## Abstract

We review exact numerical results for one-dimensional quantum systems with half-filled bands. The topics covered include Peierls transitions in Holstein, Fr\"ohlich, Su-Schrieffer-Heeger, and Heisenberg models with quantum phonons, competing fermion-boson and fermion-fermion interactions, as well as symmetry-protected topological states in fermion and anyon models.