We study a novel state of matter: algebraic Bose liquid (ABL). An ABL is a quantum bosonic system on a 2d or 3d lattice that does not break any symmetry in its ground state, but still able to stabilize a gapless spectrum. At high energy these boson systems only have the simplest U(1) global symmetry associated with the conservation of boson number, but at low energy the system is described by self-dual gauge fields. In this talk we will present two new ABL phases emerged from a quantum Boson model on the cubic lattice. At low energy these two ABL phases are described by the linearized z=2 and z=3 Lifshitz gravity respectively. We will show that the self-duality of the field theory is crucial to guarantee the stability of the ABL.
Cenke Xu, arXiv:cond-mat/0602443, Phys. Rev. B. 74, 224433
Cenke Xu and Petr Horava, arXiv:1003.0009