Nematic and Spin Singlet Mott states of Spin-One Bosons

Fei Zhou, Michiel Snoek

Fei Zhou

Jean-Sébastien Bernier, K. Sengupta, Yong Baek Kim

Michiel Snoek, Fei Zhou

We present microscopic wave functions of spin-singlet Mott insulating states and nematic Mott insulating states. We also investigate quantum phase transitions between the spin-singlet Mott phase and the nematic Mott phase in both large-$N$ limit and small-$N$ limit $(N$ being the number of particles per site) in high-dimensional bipartite lattices. In the mean-field approximation employed in this article we find that phase transitions are generally weakly first order.

Fei Zhou, Michiel Snoek, Jeroen Wiemer +1 more

We study magnetically stabilized nematic order for spin-one bosons in optical lattices. We show that the Zeeman field-driven quantum phase transitions between non-nematic Mott states and quantum spin nematic Mott states in the weak hopping limit are in the universality class of the ferromagnetic $XXZ$ $(S=1∕2)$ spin model. We further discuss these transitions as condensation of interacting magnons. The development of O(2) nematic order when external fields are applied corresponds to condensation of magnons, which breaks a U(1) symmetry. Microscopically, this results from a coherent superposition of two non-nematic states at each individual site. Nematic order and spin-wave excitations around critical points are studied and critical behaviors are obtained in a dilute gas approximation. We also find that spin-singlet states are unstable with respect to quadratic Zeeman effects and Ising nematic order appears in the presence of any finite quadratic Zeeman coupling. All discussions are carried out for states in three-dimensional bipartite lattices.

Laurent de Forges de Parny, F. Hébert, V. G. Rousseau +1 more

We study, using quantum Monte Carlo (QMC) simulations, the ground state properties of spin-1 bosons trapped in a square optical lattice. The phase diagram is characterized by the mobility of the particles (Mott insulating or superfluid phase) and by their magnetic properties. For ferromagnetic on-site interactions, the whole phase diagram is ferromagnetic and the Mott insulators-superfluid phase transitions are second order. For antiferromagnetic on-site interactions, spin nematic order is found in the odd Mott lobes and in the superfluid phase. Furthermore, the superfluid-insulator phase transition is first or second order depending on whether the density in the Mott is even or odd. Inside the even Mott lobes we observe a singlet-to-nematic transition for certain values of the interactions. This transition appears to be first order.