Critical properties of the spin-1/2 Heisenberg chain with frustration and bond alternation

We study the S = 1/2 Heisenberg chain with frustration and alternation which is expressed by H = ∑_j{[1 + (-1)^jδ]S_j · S_j+1 + J₂S_j · S_j+2}, both analytically and numerically. We focus on the J₂ = 0.2411 case, where there is no marginal operator which brings about the logarithmic corrections in various quantities. By using the bosonization method, we calculate the energy gap, the change in the ground-state energy due to the alternation (so-called energy gain), the spin correlation and the string correlation (not only their exponents but also their amplitudes), and compare them with the results of the numerical diagonalization for finite systems. We point out the existence of the logarithmic correction in the energy gain despite the absence of the marginal operator. Taking into account this logarithmic correction, we can obtain a reasonable hyperscaling relation between the critical exponents of the energy gap and an energy gain from the numerical data.