Supersolidity in the triangular lattice spin-1/2 XXZ model: A variational perspective

We study the spin-1/2 XXZ model on the triangular lattice with a nearest neighbor antiferromagnetic Ising coupling $J_z>0$ and unfrustrated ($J_\perp0$) kinetic terms in zero magnetic field. Incorporating long-range Jastrow correlations over a mean field spin state, we obtain the variational phase diagram of this model on large lattices for arbitrary $J_z$ and either sign of $J_\perp$. For $J_\perp<0$, we find a $\sqrt{3}\times\sqrt{3}$ supersolid for $J_z/|J_\perp| \gtrsim 4.7$, in excellent agreement with quantum Monte Carlo data. For $J_\perp >0$, a distinct $\sqrt{3}\times\sqrt{3}$ supersolid is found to emerge for $J_z/J_\perp \geq 1$. Both supersolids exhibit a spontaneous density deviation from half-filling. At $J_z/J_\perp=\infty$, the crystalline order parameters of these two supersolids are nearly identical, consistent with exact results.Comment: 4 pages, 4 figures, 1 table, published versio

Excitations in correlated superfluids near a continuous transition into a supersolid

We study a superfluid on a lattice close to a transition into a supersolid phase and show that a uniform superflow in the homogeneous superfluid can drive the roton gap to zero. This leads to supersolid order around the vortex core in the superfluid, with the size of the modulated pattern around the core being related to the bulk superfluid density and roton gap. We also study the electronic tunneling density of states for a uniform superconductor near a phase transition into a supersolid phase. Implications are considered for strongly correlated superconductors.Comment: 4 pages, 2 figures, published versio

Extending Luttinger's theorem to Z(2) fractionalized phases of matter

Luttinger's theorem for Fermi liquids equates the volume enclosed by the Fermi surface in momentum space to the electron filling, independent of the strength and nature of interactions. Motivated by recent momentum balance arguments that establish this result in a non-perturbative fashion [M. Oshikawa, Phys. Rev. Lett. {\bf 84}, 3370 (2000)], we present extensions of this momentum balance argument to exotic systems which exhibit quantum number fractionalization focussing on $Z_2$ fractionalized insulators, superfluids and Fermi liquids. These lead to nontrivial relations between the particle filling and some intrinsic property of these quantum phases, and hence may be regarded as natural extensions of Luttinger's theorem. We find that there is an important distinction between fractionalized states arising naturally from half filling versus those arising from integer filling. We also note how these results can be useful for identifying fractionalized states in numerical experiments.Comment: 24 pages, 5 eps figure