Scaling exponents in spin-1/2 Heisenberg chains with dimerization and frustration studied with the density-matrix renormalization group

In conformal field theory, key properties of spin-1/2 chains, such as the ground state energy per site and the excitation gap, scale with dimerization delta as delta(alpha) with known exponents alpha and logarithmic corrections. The logarithmic corrections vanish in a spin chain with nearest (J=1) and next-nearest-neighbor interactions (J(2)), for J(2c)=0.2411. Density-matrix renormalization group analysis of a frustrated spin chain with no logarithmic corrections yields the field theoretic values of alpha, and the scaling relation is valid up to the physically realized range, delta similar to 0.1. However, chains with logarithmic corrections (J(2)< 0.2411 J) are more accurately fit by simple power laws with different exponents for physically realized dimerizations. We show the exponents decreasing from approximately 3/4 to 2/3 for the spin gap and from approximately 3/2 to 4/3 for the energy per site, and error bars in the exponent also decrease as J(2) approaches to J(2c).