J1-J2 Heisenberg model at and close to its z=4 quantum critical point

We study the frustrated J(1) - J(2) Heisenberg model with ferromagnetic nearest-neighbor coupling J(1) < 0 and antiferromagnetic next-nearest-neighbor coupling J(2) > 0 at and close to the z = 4 quantum critical point (QCP) at J(1)/J(2) = -4. The J(1) - J(2) model plays an important role for recently synthesized chain cuprates as well as in supersymmetric Yang-Mills theories. We study the thermodynamic properties using field theory, a modified spin-wave theory, as well as numerical density-matrix renormalization group calculations. Furthermore, we compare with results for the classical model obtained by analytical methods and Monte Carlo simulations. As one of our main results, we present numerical evidence that the susceptibility at the QCP seems to diverge with temperature T as chi similar to T-1.2 in the quantum case, in contrast to the classical model where chi similar to T-4/3.