Accurate determination of the Gaussian transition in spin-1 chains with single-ion anisotropy

Abstract

The Gaussian transition in the spin-1 Heisenberg chain with single-ion anisotropy is extremely difficult to treat, both analytically and numerically. We introduce an improved density-matrix renormalization group procedure with strict error control, which we use to access very large systems. By considering the bulk entropy, we determine the Gaussian transition point to four-digit accuracy, D-c/J = 0.968 45(8), resolving a long-standing debate in quantum magnetism. With this value, we obtain high-precision data for the critical behavior of quantities, including the ground-state energy, gap, and transverse string-order parameter, and for the critical exponent nu = 1.472(2). Applying our improved technique at J(z) = 0.5 highlights essential differences in critical behavior along the Gaussian transition line.