Anomalous low-temperature specific heat of the antiferromagnetic SU(N) Heisenberg model in a field

We discuss the low-temperature specific heat of the integrable SU(N)invariant Heisenberg model in one dimension with degrees of freedom in the symmetric rankm tensor representation, especially for the antiferromagnetic coupling. It is known that the linear specific heat coefficient γ[N,m] is a function of a field which breaks the SU(N) invariance of the internal degrees of freedom. We calculate the γ[N,m] in a zero field and in a small field. The in-field γ[N,m] is less than the zero-field γ[N,m] as expected since the entropy is reduced in the ordered system. The zero-field γ [N,m] is the same as the one obtained by the prediction of the critical behavior of 1D quantum spin systems via conformal field theory. This extends the previous results for N=2 to an arbitrary N. The Bethe-ansatz method yields singular behavior in numerous other models with SU(N) symmetry, for instance, the N-component 1D fermion gas interacting via a δfunctional repulsion [1]-[4], the Gross-Neveu model [5], the N-component supersymmetric 1D t-j model [6], and the N-degenerate 1D Hubbard chain [7, 8]. In particular, the logarithmic singularities in zero-temperature susceptibility to a field are common to these models. For a small Zeeman splitting H and for arbitrary N and m [9], χ(H) χ(0) = ( 1 + m N |lnH| − mln|NlnH| N2ln2H + · · · ) . (1) The nonanalytic field dependence of the susceptibility suggests a singular behavior in the low-temperature specific heat, C = γT , as H and T tend to zero [9]-[11], i.e., lim H→0 lim T→0 γ 6= lim T→0 lim H→0 γ. (2) In this letter we calculate the linear specific heat coefficient γ in the limit of T → 0 with and without the SU(N)-invariance breaking field. Our main result is that for a small magnetic field H , lim H→0 lim T→0 γ = N(N − 1) 12J  1 + ∑N−1 j=1 G (N,m,j) + (i 2π N ) N − 1 