DMRG study of scaling exponents in spin-½ Heisenberg chains with dimerization and frustration

Abstract

In conformal field theory, key properties of spin-½ chains, such as the ground state energy per site and the excitation gap, scale with dimerization δ as δ^α with known exponents α and logarithmic corrections. The logarithmic corrections vanish in a spin chain with nearest (J=1) and next-nearest-neighbor interactions (J₂), 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 α, and the scaling relation is valid up to the physically realized range, δ~0.1. However, chains with logarithmic corrections (J₂<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 ¾ to ⅔ 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 J₂ approaches to J_2c.