Application de la méthode de renormalisation par la matrice densité à une chaine de spins dans le cadre du modèle d'Heisenberg

Abstract

The densitymatrixrenormalizationgroupmethodhasbecomeinthepastthirtyyearsa stronger numericaltoolforthestudyofstaticanddynamicphysicalpropertiesoffundamental physicssystems.Theapplicationofthismethodtoanantiferromagneticspinchainwithin the Heisenbergmodelformagneticsystemsspinsallowsustoreproducesomewellknown theoretical resultsaboutrelativelylongspinchainscomaparedtothosediagonalzableusing standard routines.Also,thenumericalstudyallowsustocon rmtheexistenceofanenergy gap fora s = 1-spin chain(haldaneconjecture),butthenonexistenceofaanenergygapfora s = 1 21-spin chain.Thee ectofbothperiopdicandopenboundaryconditionsonthebehavior of theenergyspectraofthespinsystemisstudied.Also,thee ectofrandomcouplingonthe behaviorosenergylevelofaspinsystemisstudied.Intheotherhand,alinear tallowsusto write anexpressionofthegroundstateenergyasafunctionofthelengthofthespinchain.