Dualities in Spin Ladders

Details Dualities in Spin Ladders Dualities in Spin Ladders

1997-06-11

arxiv.org/abs/cond-mat/9706104v1

Physics

Condensed Matter

REVTEX file, 5 pages, 2 EPS figures

Scientific paper

10.1088/0305-4470/31/6/013

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.

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