Numerical Studies of the two-leg Hubbard ladder

The Hubbard model on a two-leg ladder structure has been studied by a combination of series expansions at T=0 and the density-matrix renormalization group. We report results for the ground state energy $E_0$ and spin-gap $\Delta_s$ at half-filling, as well as dispersion curves for one and two-hole excitations. For small $U$ both $E_0$ and $\Delta_s$ show a dramatic drop near $t/t_{\perp}\sim 0.5$, which becomes more gradual for larger $U$. This represents a crossover from a "band insulator" phase to a strongly correlated spin liquid. The lowest-lying two-hole state rapidly becomes strongly bound as $t/t_{\perp}$ increases, indicating the possibility that phase separation may occur. The various features are collected in a "phase diagram" for the model.Comment: 10 figures, revte

The J1-J2 model: First order phase transition versus deconfinement of spinons

We revisit the phase transition from the N\'eel ordered to a valence bond solid (VBS) state in the two-dimensional $J_1-J_2$ antiferromagnetic Heisenberg model. In the first part we address the question whether or not this transition could be an example of a second order phase transition due to a deconfinement of spinons. We give arguments based on series expansion and spin-wave theory that this is not the case and the transition is most likely first order. The method proposed here to detect first order phase transitions seems to be very sensitive and might be useful in other models as well. In the second part we analyze possible VBS patterns in the magnetically disordered phase based on numerical data for different susceptibilities, obtained in the ordered phase, which test the breaking of lattice symmetries. We conclude that a columnar dimerization pattern is the most likely candidate.Comment: 7 pages, 7 figures, small changes, references adde