Phase diagrams and correlation exponents for quantum spin chains of arbitrary spin quantum number

Abstract

The low-temperature properties of the spin-S quantum spin chain are studied representing a spin-S operator as the sum of 2S spin-1/2 operators. The resulting system of 2S-coupled spin-1/2 systems is studied in the weak-coupling limit, using a continuum representation. It is shown that under scaling, the coupling becomes strong. Under the additional hypothesis (which is shown to be true for S=1) that strong coupling represents correctly the properties of the spin-S system, the following results are obtained: (i) there are, in general, two types of planar (massless) phases XY1 and XY2, separated by an Ising-like transition; (ii) for half-odd-integer S the exponent \ensuremath{\eta} governing the asymptotic power-law decay of transverse spin correlations takes the universal value \ensuremath{\eta}=1 at the boundary between XY1 and the adjacent uniaxial antiferromagnetic phase; (iii) for integer S there is an additional singlet phase between XY1 and the antiferromagnetic state, with \ensuremath{\eta}=(1/4) at the limit of XY1; (iv) a spin-Peierls instability only exists for half-odd-integer S; (v) a magnetic field along the z direction may lead to a transition from the singlet or antiferromagnetic state to a planar phase. Universal scaling relations between exponents for transverse and longitudinal correlations in the phases XY1 and XY2 and an explicit asymptotic expression for correlation functions are derived. Finally, implications of the present results for some generalizations of the spin chain problem are briefly discussed. The above points (ii) and (iii) confirm predictions by Haldane, which were derived using quite different methods.