Quantum phase transitions around the staggered valence bond solid

Valence Bond Solid (VBS) phases are non-magnetic states in which spin singlets spontaneously form and localize on specific bonds of a lattice. They have been studied extensively in large-N spin models, in dimer Hamiltonians. The phase transitions from such VBS states can be interesting, and sometimes of non-Landau type. A natural method to study these transitions is using the Z₂ lattice gauge theory, which describes all the symmetries of the system as well as the topological constraints implied by having microscopically a spin-1/2 spin per site. In this description one obtains the VBS states by condensing Z₂ vortices, or visons, coming from the Z₂ spin liquid state.

The way in which this happens depends upon the momentum of the visons that condense. The simplest case leads to the so-called "columnar" VBS state.

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Our work:

Here we allowed for other momenta for the visons, which is what is needed to reach the "staggered" VBS state. This staggered VBS state is seen in some models and is often simpler-looking.

However, what we find is that the order parameter for the staggered VBS is naturally embedded in a continuous order parameter manifold in a more interesting way than the columnar VBS is. By the vison analysis, we obtain O(3), O(4), CP(2) and CP(3) order parameters for various cases.

Read the paper.