Effect of the single-ion-type anisotropy energy for the S = 1 spins to the ground-state properties of the spin-1/2-1/2-1-1 chain

Abstract

The spin-1/2-1 chain, in which a S = 1/2 spin and a S = 1 spin are arranged alternatively and coupled by the nearest neighbor antiferromagnetic exchange interaction, has been extensively studied numerically, analytically, and experimentally. The characteristic feature of this mixed spin chain is that its ground state is ferrimagnetic. More generally the spin-1/2-1/2-1-1 chain in which two S = 1/2 and two S = 1 spins are arranged alternatively was recently proposed by the present authors. The nearest neighbor exchange interaction between a S = 1/2 spin and the neighboring S = 1 spin is denoted by J(sub 2), between the next two neighboring S = 1 spins by J(sub 3), between the next neighboring S = 1 spin and S = 1/2 spin by J(sub 4), and the next two neighboring S = 1/2 spins by J(sub 1). Using mainly the density matrix renormalization group method proposed by White, the ground state phase diagram on the upper half (J(sub 1) greater than 0.0) of the J(sub 1) versus J(sub 2) plane with J(sub 3) fixed at 1.0 was numerically determined. Three kinds of nearest neighbor two spin correlation functions in the ground state and the string order parameter O(sub string) in the thermodynamic limit were calculated. Considering the J(sub 1) or J(sub 2) dependencies of these quantity, how each ground state phase can be presented by Valence Bond Solid (VBS) picture was clarified. It should be noted that the obtained ground state phase can be classified into two groups depending upon whether the O(sub string) is finite or vanishes. In this report, the effect of the single ion type anisotropy energy term H(sub D) where D is the self coupling constant of a spin in H(sub D) for the S = 1 spins on the ground state phase diagram in the case of D = 0 was discussed. By the method similar to that used in the D = 0 case, the phase transition for a variety values of J(sub 1) and J(sub 2) with J(sub 3) fixed at 1.0 was explored, and the ground state phase diagram on the D versus J(sub 2) (or J(sub 1)) plane was obtained.

S=1/2スピンとS=1スピンが交互に並び、最近接スピン同士が反強磁性的に結合しているスピン-1/2-1鎖が数値的、解析的および実験的に多く研究されてきた。この混合スピン鎖の特徴はその基底状態がフェリ磁性を示すということである。より一般的に、2つのS=1/2スピンと2つのS=1スピンが交互に並ぶスピン-1/2-1/2-1-1鎖を、著者らは最近提唱した。S=1/2と隣のS=1スピン間の最近接交換相互作用をJ(sub 2)、次の隣合うS=1スピン間についてはJ(sub 3)、次のS=1と隣のS=1/2スピン間についてはJ(sub 4)、次の隣合うS=1/2スピン間についてはJ(sub 1)とする。Whiteにより提唱された密度行列くりこみ群法を主に用いることにより、J(sub 3)を1.0に固定したときの、J(sub 1)とJ(sub 2)のなす平面の上半面(J(sub 1)>0.0)における基底状態の相図を数値により求めた。基底状態における3種の最近接2スピン相関関数、および熱力学的極限における弦秩序パラメータO(sub string)を計算した。これらの量のJ(sub 1)またはJ(sub 2)依存性を考えて、各基底状態相が原子価結合固体(VBS)像によりどのように表すことができるかを明らかにした。得られた基底状態相は、O(sub string)が有限であるか消滅するかに依存して2つのグループに分類できることは、特筆すべきことである。本報告において、S=1スピンの単一イオン型異方性エネルギー項H(sub D)(DはH(sub D)項におけるスピン自己結合定数)がD=0の基底状態相図に与える効果を論じた。D=0のときに用いたのと同様な方法により、J(sub 3)を1.0に固定して、J(sub 1)およびJ(sub 2)の多くの値について相転移を調べ、DとJ(sub 2)(またはJ(sub 1))のなす平面上での基底状態相図を得た。