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- W2022894603 abstract "We study the zero-temperature magnetization curve $(Mensuremath{-}H$ curve) of the one-dimensional quantum antiferromagnet of spin one. The Hamiltonian H we consider is of the bilinear-biquadratic form: $H={ensuremath{sum}}_{i}f({s}_{i}ensuremath{cdot}{s}_{i+1})$ (+Zeeman term) where ${s}_{i}$ is the spin operator at site i and $f(X)=X+ensuremath{beta}{X}^{2}$ with $0<~ensuremath{beta}<1.$ We focus on validity of the $ensuremath{delta}$-function Bose-gas picture near the two critical fields: upper-critical field ${H}_{s}$ above which the magnetization saturates and the lower-critical field ${H}_{c}$ associated with the Haldane gap. As for the behavior near ${H}_{s},$ we take ``low-energy effective S matrix'' approach, where the correct effective Bose-gas coupling constant c is extracted from the two down-spin S matrix in its low-energy limit. We find that the resulting value of c differs from the spin-wave value. We draw the $Mensuremath{-}H$ curve by using the resultant Bose gas, and compare it with numerical calculation where the product-wave-function renormalization-group (PWFRG) method, a variant of White's density-matrix renormalization group method, is employed. Excellent agreement is seen between the PWFRG calculation and the correctly mapped Bose-gas calculation. We also test the validity of the Bose-gas picture near the lower-critical field ${H}_{c}.$ Comparing the PWFRG-calculated $Mensuremath{-}H$ curves with the Bose-gas prediction, we find that there are two distinct regions, I and II, of $ensuremath{beta}$ separated by a critical value ${ensuremath{beta}}_{c}(ensuremath{approx}0.41).$ In region I, $0<ensuremath{beta}<{ensuremath{beta}}_{c},$ the effective Bose coupling c is positive but rather small. The small value of c makes the ``critical region'' of the square-root behavior $Mensuremath{sim}sqrt{Hensuremath{-}{H}_{c}}$ very narrow. Further, we find that in the $stackrel{ensuremath{rightarrow}}{ensuremath{beta}}{ensuremath{beta}}_{c}ensuremath{-}0,$ the square-root behavior transmutes to a different one, $Mensuremath{sim}(Hensuremath{-}{H}_{c}{)}^{ensuremath{theta}}$ with $ensuremath{theta}ensuremath{approx}1/4.$ In region II, ${ensuremath{beta}}_{c}<ensuremath{beta}<1,$ the square-root behavior is more pronounced as compared with region I, but the effective coupling c becomes negative." @default.
- W2022894603 created "2016-06-24" @default.
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- W2022894603 date "1999-03-01" @default.
- W2022894603 modified "2023-09-27" @default.
- W2022894603 title "δ-function Bose-gas picture ofS=1antiferromagnetic quantum spin chains near critical fields" @default.
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- W2022894603 doi "https://doi.org/10.1103/physrevb.59.6806" @default.
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