Chung-Hou Chung:

Sergei Isakov et al., Supersolid phase of hard-core bosons on anisotropic triangular lattice, arXiv:0708.3084.

Ying-Jer Kao:

I will briefly review the supersolid phase and address some of the issues of the supersolid phases in lattice models, with the focus on the square lattice.

Stefan Wessel:

Supersolid phases (i.e. density-modulated superfluids) may emerge from quantum fluctuations via an order-by-disorder effect.
I will give a short summary of our previous works on bosons on the
triangular and Kagome lattice, and present some preliminary findings on the XXZ model on the Shastry-Sutherland lattice of SrCu2(BO3)2. A recent work by Hassan et al. (arxiv0707.0866) addresses the triangular lattice case within a self-consistent cluster mean field theory.

Oleg Tchernyshyov:

A pedagogical example of a supersolid in 1 dimension has been worked out by Cristian Batista et al. at Los Alamos. They look at an antiferromagnetic S=1 chain with XXZ couplings and easy-axis anisotropy. The model has a "half-integer" magnetization plateau with two simple Ising ground states (+–+–... and –+–+...). Ordinarily, such plateaus end via a condensation of domain walls. A finite concentration of domain walls kills the Ising order restoring the translational symmetry. Since the walls are mobile, they form a Luttinger liquid, which is the analogue of a superfluid in 1+1 dimensions.

In the model of Batista et al. domain walls condense in pairs. A pair of domain walls is a nontopological soliton that does not disrupt long-range Ising order. At the same time, the solitons are mobile, so the ground state is a superfluid (or whatever remains of it in 1+1 dimensions) with a broken translational symmetry. Hence a supersolid.

P. Sengupta and C. D. Batista, Spin supersolid in anisotropic spin-one Heisenberg chain,