Logarithmic corrections and antiferromagnetic chains (abstract)

Abstract

There has recently been considerable interest in the numerical calculation of critical exponents for quantum spin chains with general spin s, stimulated by a remarkable prediction by Haldane and conformally invariant field theoretic calculations. In several instances numerical calculations have differed considerably from theoretical predictions, with misleading results. These discrepancies have generally been attributed to the presence of marginal operators resulting in logarithmic corrections which slow numerical convergence. Such phenomena seem to be ubiquitous in the area of quantum spin chains. However, until recently, no calculation was available for estimating quantitatively the expected shifts in exponent values obtained by numerical means. The purpose of this work is to call attention to such a calculation1 for the integrable Takhtajan–Babujian family of quantum spin chains, and make specific comparisons with a variety of spin chain exponents obtained numerically.2,3 Agreement with the analytic formulas is extremely good in all cases. This is an indication that finite-size scaling is a powerful tool for extracting critical exponents even in models with logarithmic corrections, provided that these corrections are taken into account in lowest order using the method of Ref. 1.