Field-induced phase transitions of tetramer-singlet states in synthetic SU(4) magnets

Abstract

Phase transitions of quantum dimer magnets can be explained in terms of Bose-Einstein condensation of magnons. Here we consider a natural extension of the dimer magnets to SU(4)-symmetric tetramer systems, which could be created with four nuclear-spin components (named “u,” “d,” “c,” and “s”) of 173Yb atoms in optical superlattices. We apply the cluster mean-field approximation to the SU(4) Heisenberg model on a tetramerized square lattice, and study the phase transition phenomena in the presence of the field that creates a population imbalance between the two components u,d and the other two c,s. When the population of the four components is balanced, the ground state is approximately given by the direct product of local SU(4)-singlet states. When the field is applied, the population ratio of the components u and d is increased and the system eventually reaches a “saturated” state, which is a SU(2) system with only u and d. We show that in the saturation process, the system exhibits two successive step-like transitions, in contrast to the standard dimer magnets with continuous transition process associated with Bose-Einstein condensation of magnons. The intermediate phase in between the two step-like transitions is a nontrivial solid phase with alternating arrangement of the SU(4)-singlet and four-site resonating-valence-bond states.