Quantum spin liquids

TL;DR

This paper introduces key theoretical concepts in quantum spin liquids, including zero modes, topological theorems, valence-bond models, large-N approaches, and gauge theories, providing foundational insights into their complex quantum behavior.

Contribution

It synthesizes various theoretical frameworks and ideas essential for understanding quantum spin liquids, highlighting their interconnections and significance.

Findings

Zero modes indicate classical degeneracies.

Topological theorems constrain quantum states.

Gauge theories describe emergent phenomena.

Abstract

These notes are an introduction to a few selected theoretical ideas in the field of quantum spin liquids: classical zero modes and breakdown of the 1/S expansion, the Lieb-Schultz-Mattis-Hastings theorem and Oshikawa's argument, the short-ranged resonating valence-bond picture, large-N limit (Schwinger bosons) and Z_2 gauge theory.