Seminarium Fizyki Materii Skondensowanej

The motion of a single hole in the t-J_z model on a square lattice is one of the oldest and (naively) best understood problems in the field of strongly correlated electrons. This is because such a problem can approximately be mapped onto the case of a single particle moving in the linear potential. The latter yields a series of eigenstates whose energies scale as (J_z/t)^2/3, leading to the onset of a so-called ladder spectral function. Here we show that such a spectrum is indeed realized on a Bethe lattice. However, on the square lattice the situation is far richer: besides the ladder spectrum, the spectral function of a t-J_z model contains also a substantial incoherent part as well as eigenstates whose energies scale linearly with J_z/t.