Dualities in Spin Ladders

الأصل · EN

We introduce a set of discrete modular transformations Tℓ,Uℓ and Sℓ in order to study the relationships between the different phases of the Heisenberg ladders obtained with all possible exchange coupling constants. For the 2 legged ladder we show that the RVB phase is invariant under the Sℓ transformation, while the Haldane phase is invariant under Uℓ. These two phases are related by Tℓ. Moreover there is a "mixed" phase, that is invariant under Tℓ, and which under Uℓ becomes the RVB phase, while under Sℓ becomes the Haldane phase. For odd ladders there exists only the Tℓ transformation which, for strong coupling, maps the effective antiferromagnetic spin 1/2 chain into the spin 3/2 chain.