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arXiv:cond-mat/0207041 · Europhysics Letters (EPL)

Spin-one bosons in low-dimensional Mott insulating states

Fei Zhou

Published Aug 1, 2003• 17 citations
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Abstract

We analyze the strong-coupling limit of spin-one bosons in low-dimensional lattices. In one-dimensional lattices, for an odd number of bosons per site ( N 0 = 2 k + 1), the ground state is a dimerized-valence-bond crystal with a twofold degeneracy; the low-lying elementary spin excitations carry spin-one. For an even number of bosons per site ( N 0 = 2 k ), the ground state is a nondegenerate spin singlet Mott state. We also argue that for square lattices in a quantum spin disordered limit, ground states should be dimerized-valence-bond crystals for an odd integer N 0 . Finally, we briefly report results on exotic states for non-integer numbers of bosons per site in one-dimensional lattices.

DOI
10.1209/epl/i2003-00555-0

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We analyze the strong-coupling limit of spin-one bosons in low-dimensional lattices. In one-dimensional lattices, for an odd number of bosons per site ( N 0 = 2 k + 1), the ground state is a dimerized-valence-bond crystal with a twofold degeneracy; the low-lying elementary spin excitations carry spin-one. For an even number of bosons per site ( N 0 = 2 k ), the ground state is a nondegenerate spin singlet Mott state. We also argue that for square lattices in a quantum spin disordered limit, ground states should be dimerized-valence-bond crystals for an odd integer N 0 . Finally, we briefly report results on exotic states for non-integer numbers of bosons per site in one-dimensional lattices.
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=1S=1S=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.
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We propose that a valence-bond-solid (VBS) order can be stabilized in certain two-dimensional antiferromagnets due to spin-lattice coupling. In contrast to the VBS state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) type, the spin-lattice coupling-induced VBS state can occur when 2S2S2S is not an integer multiple of the coordination number zzz. S=2S=2S=2 spins on the triangular lattice with z=6z=6z=6 is discussed as an example. Within the Schwinger boson mean-field theory the ground state is derived as the direct product of states, one of which represents the conventional long-range ordered spins, and the other given by the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ modulation of the valence bond amplitudes. Excitation spectrum for the modulated valence bond state is worked out within the single-mode approximation. The spectrum offers a new collective mode, distinct from the spin wave excitations of the magnetically ordered ground state, and observable in neutron scattering.
We consider insulating phases of cold spin-1 bosonic particles with antiferromagnetic interactions, such as 23Na,{}^{23}\mathrm{Na},23Na, in optical lattices. We show that spin-exchange interactions give rise to several distinct phases, which differ in their spin correlations. In two- and three-dimensional lattices, insulating phases with an odd number of particles per site are always nematic. For insulating states with an even number of particles per site, there is always a spin-singlet phase, and there may also be a first-order transition into the nematic phase. The nematic phase breaks spin rotational symmetry but preserves time reversal symmetry, and has gapless spin-wave excitations. The spin-singlet phase does not break spin symmetry and has a gap to all excitations. In one-dimensional lattices, insulating phases with an odd number of particles per site always have a regime where translational symmetry is broken and the ground state is dimerized. We discuss signatures of various phases in Bragg scattering and time-of-flight measurements.
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Spinor Bose condensates loaded in optical lattices have a rich phase diagram characterized by different magnetic order. Here we apply the density matrix renormalization group to accurately determine the phase diagram for spin-1 bosons loaded on a one-dimensional lattice. The Mott lobes present an even or odd asymmetry associated to the boson filling. We show that for odd fillings the insulating phase is always in a dimerized state. The results obtained in this work are also relevant for the determination of the ground state phase diagram of the S = 1 Heisenberg model with biquadratic interaction.