We analyze the behavior of cold spin-1 particles with antiferromagnetic interactions in a one-dimensional optical lattice using density matrix renormalization group calculations. Correlation functions and the dimerization are shown and we also present results for the energy gap between ground state and the spin excited states. We confirm the anticipated phase diagram, with Mott-insulating regions of alternating dimerized $S=1$ chains for odd particle density versus on-site singlets for even density. We find no evidence for any additional ordered phases in the physically accessible region, however for sufficiently large spin interaction, on-site singlet pairs dominate leading, for odd density, to a breakdown of the Mott insulator or, for even density, a real-space singlet superfluid.We analyze the behavior of cold spin-1 particles with antiferromagnetic interactions in a one-dimensional optical lattice using density matrix renormalization group calculations. Correlation functions and the dimerization are shown and we also present results for the energy gap between ground state and the spin excited states. We confirm the anticipated phase diagram, with Mott-insulating regions of alternating dimerized $S=1$ chains for odd particle density versus on-site singlets for even density. We find no evidence for any additional ordered phases in the physically accessible region, however for sufficiently large spin interaction, on-site singlet pairs dominate leading, for odd density, to a breakdown of the Mott insulator or, for even density, a real-space singlet superfluid.

arXiv:cond-mat/0606265Physical Review ANov 28, 200625 citations

Microscopic wave functions of spin-singlet and nematic Mott states of spin-one bosons in high-dimensional bipartite lattices

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.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.

arXiv:cond-mat/0306198Physical Review BMar 16, 200467 citations

The condensation of spin-1/2 lattice bosons

P. Fazekas, P. Entel

The European Physical Journal BSep 1, 19833 citations

Singlet Mott state simulating the bosonic Laughlin wave function

Biao Lian, Shoucheng Zhang

We study properties of a class of spin-singlet Mott states for arbitrary spin $S$ bosons on a lattice, with particle number per cite $n=S/l+1$ , where $l$ is a positive integer. We show that such a singlet Mott state can be mapped to a bosonic Laughlin wave function on a sphere with a finite number of particles at filling $\ensuremath{\nu}=1/2l$. Spin, particle, and hole excitations in the Mott state are discussed, among which the hole excitation can be mapped to the quasihole of the bosonic Laughlin wave function. We show that this singlet Mott state can be realized in a cold-atom system on an optical lattice and can be identified using Bragg spectroscopy and Stern-Gerlach techniques. This class of singlet Mott states may be generalized to map to bosonic Laughlin states with filling $\ensuremath{\nu}=q/2l$.We study properties of a class of spin-singlet Mott states for arbitrary spin $S$ bosons on a lattice, with particle number per cite $n=S/l+1$, where $l$ is a positive integer. We show that such a singlet Mott state can be mapped to a bosonic Laughlin wave function on a sphere with a finite number of particles at filling $\ensuremath{\nu}=1/2l$. Spin, particle, and hole excitations in the Mott state are discussed, among which the hole excitation can be mapped to the quasihole of the bosonic Laughlin wave function. We show that this singlet Mott state can be realized in a cold-atom system on an optical lattice and can be identified using Bragg spectroscopy and Stern-Gerlach techniques. This class of singlet Mott states may be generalized to map to bosonic Laughlin states with filling $\ensuremath{\nu}=q/2l$.

arXiv:1310.6105Physical Review BJan 31, 20147 citations

S=1

chains for odd particle density versus on-site singlets for even density. We find no evidence for any additional ordered phases in the physically accessible region, however for sufficiently large spin interaction, on-site singlet pairs dominate leading, for odd density, to a breakdown of the Mott insulator or, for even density, a real-space singlet superfluid.

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.

We study properties of a class of spin-singlet Mott states for arbitrary spin

S

bosons on a lattice, with particle number per cite

n=S/l+1

, where

l

is a positive integer. We show that such a singlet Mott state can be mapped to a bosonic Laughlin wave function on a sphere with a finite number of particles at filling $\ensuremath{\nu}=1/2l$. Spin, particle, and hole excitations in the Mott state are discussed, among which the hole excitation can be mapped to the quasihole of the bosonic Laughlin wave function. We show that this singlet Mott state can be realized in a cold-atom system on an optical lattice and can be identified using Bragg spectroscopy and Stern-Gerlach techniques. This class of singlet Mott states may be generalized to map to bosonic Laughlin states with filling $\ensuremath{\nu}=q/2l$.