Boundary Susceptibility in the Spin-$1/2$ Chain: Curie-Like Behavior without Magnetic Impurities

We investigate the low-temperature thermodynamics of the spin-$1/2$ Heisenberg chain with open ends. On the basis of boundary conformal field theory arguments and numerical density matrix renormalization group calculations, it is established that in the isotropic case the impurity susceptibility exhibits a Curie-like divergent behavior as the temperature decreases, even in the absence of magnetic impurities. A similar singular temperature dependence is also found in the boundary contributions of the specific heat coefficient. In the anisotropic case, for $1/2<\Delta <1$, these boundary quantities still show a singular temperature dependence obeying a power law with an anomalous dimension. Experimental consequences will be discussed.

Figure 1

The boundary susceptibility ${\chi }_{\mathrm{B}}$ as a function of $T$ according to the DMRG calculations (black points), compared to the result of the field theory in Eq. (18). Inset: approximate temperature dependence of the average Curie constant per impurity for an impurity density of $\rho =0.1\%$