Wolodymyr SKRYPNIK
Institute of Mathematics of NAS of Ukraine,
3 Tereshchenkivs'ka Str.,
01601 Kyiv,
UKRAINE
E-mail: skrypnik@imath.kiev.ua

On quantum systems with exact ground states and their order parameters

Abstract:
Different many-body quantum systems with exact ground states are discussed. Special emphasis is made on lattice systems with Gibbsian ground states. For generalized XXZ models it is shown that there exist two order parameters (magnetizations in the first and third  directions) in the Gibbsian ground state and conditions are found which guarantee its uniqueness.