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{\small Abstract, 378$^{th}$ WE-Heraeus Seminar,
        Bad Honnef, 22-26 October 2006}\\
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{\large\bf Groundstate properties of disordered and dimerized spin chains} \\

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{\underline{Ulrich Eckern}} and Cosima Schuster\\

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{\small{\em
Institut f\"ur Physik, Universit\"at Augsburg, 86135 Augsburg, Germany}} \\

{\tt cosima@physik.uni-augsburg.de}
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Recent experiments on  CuGeO$_3$ and NaV$_2$O$_5$,
which show at low temperature a transition to a non-magnetic
ground state accompanied by a
structural transition, led to renewed interest in spin-Peierls systems.
In this context, we have investigated the ground state properties of the
$XXZ$ model, defined by ...

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... lattice energy.

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{\em (ii) Antiferromagnetic coupling}, $\Delta<0$ ($V>0$):  A Peierls-type
energy gap opens for small $\Delta$, which is strongly enhanced when $\Delta$
decreases to $-1$. For $\Delta \ll -1$, the gap is given by
$2J|\Delta |$, a result which is apparent in the fermionic model (for 
half-filling and large $V$, a ``hop" of a fermion costs the energy $V$).

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The magnetization (filling) dependence of our results will be discussed.

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[1] C.\ Schuster and U.\ Eckern, 
    Eur.\ Phys.\ J.\ B {\bf 5}, 395-402 (1998);
    C.\ Schuster,
    Ph.\ D.\ thesis, University of Augsburg, 1999.

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[2] P.\ Schmitteckert, T.\ Schulze, C.\ Schuster, P.\ Schwab, and U.\ Eckern,
    Phys.\ Rev.\ Lett.\ {\bf 80}, 560 (1998). 

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