Exploring ideas in topological quantum phenomena: A journey through the SSH model

TL;DR

This paper provides an educational overview of one-dimensional topological phases focusing on the SSH model, covering concepts like entanglement, geometric phase, and electron interactions, supported by numerical experiments and shared code.

Contribution

It offers a pedagogical introduction to topological quantum phenomena with practical numerical tools, emphasizing the SSH model's role in understanding complex physics.

Findings

Demonstrates topological properties using the SSH model

Illustrates entanglement and geometric phase concepts

Provides numerical codes for simulation

Abstract

Geared as an invitation for undergraduates, beginning graduate students, we present a pedagogical introduction to one-dimensional topological phases -- in particular the Su-Schrieffer-Heeger model. In the process, we delve upon ideas of entanglement using the correlator method and the von-Neumann density-matrix method, geometric phase, polarization, transport signatures and the role of electron-electron interactions. Through hands-on numerical experiments, whose $\href{https://github.com/hnoend/SSH_codes}{codes}$ are shared, we try to drive home the message why a program of simulating quantum electronics with topological toy models is the store house for discovering fantastic physics ideas.