 97511 Tohru Koma, Bruno Nachtergaele
 The complete set of ground states of the ferromagnetic XXZ chains
(68K, LaTeX)
Sep 18, 97

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We show that the wellknown translation invariant ground states and the
recently discovered kink and antikink ground states are the complete set of
pure infinitevolume ground states (in the sense of local stability) of the
spinS ferromagnetic XXZ chains with Hamiltonian
H=sum_x [ S^1_x S^1_{x+1} + S^2_x S^2_{x+1} + Delta S^3_x S^3_{x+1} ],
for all Delta >1, and all S=1/2,1,3/2,.... For the isotropic model (Delta =1)
we show that all ground states are translation invariant.
For the proof of these statements we propose a strategy for demonstrating
completeness of the list of the pure infinitevolume ground states of a
quantum manybody system, of which the present results for the XXX and XXZ
chains can be seen as an example. The result for Delta>1 can also be proved
by an easy extension to general $S$ of the method used in [T. Matsui, Lett.
Math. Phys. 37 (1996) 397] for the spin1/2 ferromagnetic XXZ chain with
$\Delta>1$. However, our proof is different and does not rely on the existence
of a spectral gap. In particular, it also works to prove absence of
nontranslationally invariant ground states for the isotropic chains (Delta=1),
which have a gapless excitation spectrum.
Our results show that, while any small amount of the anisotropy is enough
to stabilize the domain walls against the quantum fluctuations, no boundary
condition exists that would stabilize a domain wall in the isotropic model
(Delta=1).
 Files:
97511.tex