Quantum spin liquids and valence bond solids

Quantum Condensed Matter Physics: Lecture 10

Theoretical physicist Dr Andrew Mitchell presents an advanced undergraduate / introductory Master's level lecture course on Quantum Condensed Matter Physics at University College Dublin. This is a complete and self-contained set of lectures, in which the theory is built up from scratch, and requires only a knowledge of basic quantum mechanics.

In this lecture I discuss quantum spin systems with antiferromagnetic interactions. The classical Neel state is not an eigenstate of the Heisenberg exchange Hamiltonian, but the ground state can be understood in terms of so-called resonating valence bonds. We discuss how magnetic frustration leads to macroscopic ground state degeneracy and the suppression of magnetic ordering, to produce a quantum spin liquid state. We also explore a class of exactly solvable spin models with valence bond solid ground states, such as the AKLT chains. This gives insight into topological defects and fractionalization in quantum condensed matter systems.

Navigate through the lectures of this course in order using the playlist:
   • Quantum condensed matter physics lect...  

Recommended course textbook: "Many-body quantum theory in condensed matter physics" by Bruss and Flensberg