Dualities in Spin Ladders

Abstract

We introduce a set of discrete modular transformations $T_{\ell },U_{\ell }$ and $S_{\ell }$ 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 $S_{\ell }$ transformation, while the Haldane phase is invariant under $U_{\ell }$. These two phases are related by $T_{\ell }$. Moreover there is a "mixed" phase, that is invariant under $T_{\ell }$, and which under $U_{\ell }$ becomes the RVB phase, while under $S_{\ell }$ becomes the Haldane phase. For odd ladders there exists only the $T_{\ell }$ transformation which, for strong coupling, maps the effective antiferromagnetic spin 1/2 chain into the spin 3/2 chain.

REVTEX file, 5 pages, 2 EPS figures

Cited by in corpus (1)

• The Matrix Product Approach to Quantum Spin Ladders