Low Energy Effective Action of Lightly Doped Two-Leg t-J Ladders

We derive the low energy effective action of lightly doped two-leg t-J ladders with the help of slave fermion technique. Because of the underlying spin liquid state, we can assume the existence of a short-ranged antiferromagnetic order for some range of parameters in the lightly doped case. This leads to the usual t ′ − J model. The continum limit of this model consists of two kinds of Dirac fermions which are coupled to the O(3) non-linear sigma model in terms of the gauge coupling with opposite sign of ”charges”. There is another kind of attractive force between these Dirac fermions. We show that the latter is essential to determine the low energy properties of lightly doped two-leg t-J ladders. The effective Hamiltonian we derive is a bosonic Gaussian model and the boson field basically describes the particle density fluctuation. We also find two types of spin excitations. One is the magnon as in the undoped case and the other is the bound state of spinons and holons. All have energy gaps. Finally, we discuss the possible instabilities charge density wave (CDW) and ∗Email address: [email protected] †Email address: [email protected]