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Bond algebraic liquid phase in strongly correlated multiflavor cold atom systems

When cold atoms are trapped in a square or cubic optical lattice, it should be possible to pump the atoms into excited $p-$level orbitals within each well. Following earlier work, we explore the metastable equilibrium that can be established before the atoms decay into the $s-$wave orbital ground state. We will discuss the situation with integer number of bosons on every site, and consider the strong correlation "insulating" regime. By employing a spin-wave analysis together with a new duality transformation, we establish the existence and stability of a novel gapless "critical phase", which we refer to as a "bond algebraic liquid". The gapless nature of this phase is stabilized due to the emergence of symmetries which lead to a quasi-one dimensional behavior. Within the algebraic liquid phase, both bond operators and particle flavor occupation number operators have correlations which decay algebraically in space and time. Upon varying parameters, the algebraic bond liquid can be unstable to either a Mott insulator phase which spontaneously breaks lattice symmetries, or a $\mathbb{Z}_2$ phase. The possibility of detecting the algebraic liquid phase in cold atom experiments is addressed. Although the momentum distribution function is insufficient to distinguish the algebraic bond liquid from other phases, the density correlation function can in principle be used to detect this new phase of matter.