Spin-one bosons in low dimensional Mott insulating states

TL;DR

This paper investigates the ground states and excitations of spin-one bosons in low-dimensional Mott insulators, revealing dimerized valence bond crystal states with specific degeneracies depending on lattice geometry and boson number.

Contribution

It provides a detailed analysis of the ground states and excitations of spin-one bosons in low-dimensional Mott insulators, highlighting the role of boson number and lattice geometry.

Findings

Odd boson number per site leads to dimerized valence bond crystal states.

Even boson number per site results in a nondegenerate spin singlet state.

In square lattices, odd boson number favors dimerized valence bond crystals.

Abstract

We analyze the strong coupling limit of spin-one bosons in low dimensional Mott insulating states. In 1D lattices, for an odd number of bosons per site ($N_0$), the ground state is a dimerized valence bond crystal state with a two-fold degeneracy; the low lying elementary spin excitations carry spin one. For an even number of bosons per site, the ground state is a nondegenerate spin singlet Mott state. We also argue that in a square lattice in a quantum disordered limit the ground states should be dimerized valence bond crystals for an odd integer $N_0$. Finally, we briefly report results for non-integer numbers of bosons per site in one-dimensional lattices.