Spectral and Entanglement Properties of the Random Exchange Heisenberg Chain

We study the many-body localization problem in the non-abelian SU(2)-invariant random antiferromagnetic exchange model in 1D. Exact and sparse matrix diagonalization methods are used to calculate eigenvalues and eigenvectors of the Hamiltonian matrix. We investigate the behaviour of the energy level gap-ratio statistic, participation ratio, entanglement entropy and the entanglement spectral parameter as a function of disorder strength. Different distributions of random couplings are considered. We find, up to $L=24$, a clear distinction between our non-abelian model and the more often studied random field Heisenberg model: the regime of seemingly localized behaviour is much less pronounced in the random exchange model than in the field model case.