Quantum phase transitions: a variational mean-field perspective

Abstract

To illustrate a simple mean-field-like approach for examining quantum phase transitions we consider the J − J ′ quantum Heisenberg antiferromagnet on a square lattice. The exchange couplings J and J ′ are competing with each other. The ratio J ′ /J is the control parameter and its change drives the transition. We adopt a variational ansatz, calculate the ground-state energy as well as the order parameter and describe the quantum phase transition inherent in the model. This description corresponds completely to the standard Landau theory of phase transitions. We also discuss how to generalize such an approach for more complicated quantum spin models.

Contributions to theory of quantum spin models: 60th anniversary of Oleg Derzhko

“…All of us read with great pleasure new research papers by Oleg, some of which have already become cornerstones of the modern quantum theory of magnetism. The pedagogical mastery of Oleg can be corroborated by a few excellent review articles [28,38] and book chapters [39][40][41][42] available due to their unique style of writing even to nonexperts, as well as the pedagogical article about quantum phase transitions from a variational mean-field perspective made in collaboration with Professor Johannes Richter [43] already included in the Master and PhD study programmes at several universities from Ukraine and abroad.…”