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

TL;DR

This paper introduces an improved DMRG method with strict error control to precisely determine the Gaussian transition point in spin-1 chains with single-ion anisotropy, resolving previous uncertainties.

Contribution

The authors develop a high-precision DMRG approach that accurately locates the Gaussian transition point and analyzes critical behavior in spin-1 chains, addressing longstanding debates.

Findings

Transition point D_c/J = 0.96845(8) determined with high accuracy

Critical exponent ν = 1.472(2) obtained from data

Differences in critical behavior along the transition line highlighted

Abstract

The Gaussian transition in the spin-one Heisenberg chain with single-ion anisotropy is extremely difficult to treat, both analytically and numerically. We introduce an improved DMRG 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 4-digit accuracy, $D_{c}/J = 0.96845(8)$, 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.