Quantum phase transitions, spontaneous symmetry breaking, mean field theory

Quantum Condensed Matter Physics: Lecture 9 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 phase transitions in quantum many body systems, and focus in particular on the phenomenon of spontaneous symmetry breaking in spin systems. We will take as a concrete example the onset of ferromagnetism in the Heisenberg model on cooling through the Curie temperature, and see how the system spontaneously develops magnetization and becomes polarized. The low-temperature phase is ordered and of a lower symmetry than that of the high-temperature disordered phase. We solve the model and analyze the phase transition using a simple but powerful approximation: mean field theory. Navigate through the lectures of this course in order using the playlist:    • Quantum condensed matter physics lecture p...   Recommended course textbook: "Many-body quantum theory in condensed matter physics" by Bruss and Flensberg