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APS

Spin-1 Heisenberg chain in a Magnetic Field

Fabian H. L. Eßler, Ian K. Affleck

Published Mar 1, 2004• 0 citations
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A nonlinear susceptibilities (the third derivative of a magnetization mSm_SmS​ by a magnetic field hhh ) of the SSS=1/2 ferromagnetic Heisenberg chain and the classical Heisenberg chain are calculated at low temperatures T.T.T. In both chains the nonlinear susceptibilities diverge as T−6T^{-6}T−6 and a linear susceptibilities diverge as T−2.T^{-2}.T−2. The arbitrary spin SSS Heisenberg ferromagnet [[[ H=∑i=1N{−JSiSi+1−(h/S)Siz}{\cal H} = \sum_{i=1}^{N} \{ - J{\bf S}_{i} {\bf S}_{i+1} - (h/S) S_{i}^{z} \}H=∑i=1N​{−JSi​Si+1​−(h/S)Siz​} (J>0),(J>0),(J>0), ]]] has a scaling relation between mS,m_S,mS​, hhh and T:T:T: mS(T,h)=F(S2Jh/T2).m_S(T,h) = F( S^2 Jh/T^2).mS​(T,h)=F(S2Jh/T2). The scaling function F(x)F(x)F(x)=(2xxx/3)-(44x3x^{3}x3/135) + O(x5x^{5}x5) is common to all values of spin S.S.S.
We discuss some properties of an integrable and conformally invariant Heisenberg chain with alternating spins S and S' (S'>S) in the presence of a magnetic field. The zero-field magnetic susceptibility is computed and turns out to be only dependent on the spin S. For small enough magnetic field, the low-lying excitations are related to the deformed SU(2) parafermionic field theory at levels 2S and 2(S'-S). Generalizations to these results for other mixed systems are commented on.