Spin Singlet Mott States and Evidence For Spin Singlet Quantum Condensates of Spin-One Bosons in Lattices

TL;DR

This paper explores spin singlet Mott states of spin-one bosons, revealing their unique properties, dynamics, and potential quantum condensates, with implications for understanding spin-charge separation and superfluid states in lattice systems.

Contribution

It introduces a comprehensive analysis of spin singlet Mott states, their characterization via quantum dimer models, and evidence for novel spin singlet quantum condensates in spin-one boson systems.

Findings

Spin singlet Mott states do not break rotational symmetry.

Low energy physics described by a Bose-Hubbard model with Ising gauge fields.

Evidence for charge-e and charge-2e spin singlet superfluids in 1D lattices.

Abstract

We have investigated spin singlet Mott states of spin-one bosons with antiferromagnetic interactions. These spin singlet states do not break rotational symmetry and exhibit remarkably different macroscopic properties compared with nematic Mott states of spin-one bosons. We demonstrate that the dynamics of spin singlet Mott states is fully characterized by even- and odd-class quantum dimer models. The difference between spin singlet Mott states for even and odd numbers of atoms per site can be attributed to a selection rule in the low energy sectors of on-site Hilbert spaces; alternatively, it can also be attributed to an effect of Berry's phases on bosonic Mott states. We also discuss evidence for spin singlet quantum condensate of spin-one atoms. Our main finding is that in a projected spin singlet Hilbert space, the low energy physics of spin-one bosons is fully characterized by a Bose-Hubbard model of interacting spinless bosons carrying charges of Ising gauge fields; the other major finding is spin-charge separation in some one-dimensional Mott states. We propose charge-e spin singlet superfluid for an odd number of atoms per lattice site and charge-2e spin singlet superfluid for an even number of atoms per lattice site in one-dimensional lattices. All discussions in this article are limited to integer numbers of bosons per site.