delta-function Bose-gas picture of S=1 antiferromagnetic quantum spin chains near critical fields

We study the zero-temperature magnetization curve (M-H curve) of the one-di mensional quantum anti-ferromagnet of spin one. The Hamiltonian H we consid er is of the bilinear-biquadratic form: H = Sigma(i)f((s) over right arrow( i).s(i+1)) (+Zeeman term) where (s) over right arrow(i) is the spin operato r at site i and f(X) = X + beta X-2 with 0 less than or equal to beta < 1. We focus on validity of the delta-function Bose-gas picture near the two cr itical fields: upper-critical field H-s above which the magnetization satur ates and the lower-critical field H-c associated with the Haldane gap. As f or the behavior near H-s, we take ''low-energy effective S matrix" approach , where the correct effective Bose-gas coupling constant c is extracted fro m the two down-spin S matrix in its low-energy limit. We find that the resu lting value of c differs from the spin-wave value. We draw the M-H curve by using the resultant Bose gas, and compare it with numerical calculation wh ere the product-wave-function renormalization-group (PWFRG) method, a varia nt of White's density-matrix renormalization group method, is employed. Exc ellent agreement is seen between the PWFRG calculation and the correctly ma pped Bose-gas calculation. We also test the validity of the Bose-gas pictur e near the lower-critical field H-c. Comparing the PWFRG-calculated M simil ar to H curves with the Bose-gas prediction, we find that there are two dis tinct regions, I and II, of beta separated by a critical value beta(c)(appr oximate to 0.41). In region I, 0 < beta < beta(c), the effective Bose coupl ing c is positive but rather small. The small value of c makes the "critica l region" of the square-root behavior M similar to root H-H-c very narrow. Further, we find that in the beta --> beta(c) - 0, the square-root behavior transmutes to a different one, M similar to (H - H-c)(theta) with theta ap proximate to 1/4. In region II, beta(c) < beta < 1, the square-root behavio r is more pronounced as compared with region I, but the effective coupling c becomes negative. [S0163-1829(99)09009-8].