【摘要】：通過(guò)解析和數(shù)值計(jì)算的方法研究了橫場(chǎng)中具有周期性各向異性的一維XY自旋模型的量子相變和量子糾纏.主要討論了周期為二的情況,即各向異性參數(shù)交替地取比值為α的兩個(gè)值.結(jié)果表明,與橫場(chǎng)中均勻XY模型相比,α=-1所對(duì)應(yīng)的模型在參數(shù)空間的相圖存在著明顯的不同.原來(lái)的Ising相變?nèi)匀淮嬖?沒有了沿x和y方向的各向異性鐵磁(FM_x,FM_y)相,即各向異性相變消失,出現(xiàn)了一個(gè)新的相,并且該相內(nèi)沿x和y方向的長(zhǎng)程關(guān)聯(lián)函數(shù)相等且大于零,我們稱新相為各向同性鐵磁(FM_(xx))相.這是由于系統(tǒng)新的對(duì)稱性所導(dǎo)致的.解析結(jié)果還說(shuō)明系統(tǒng)在FM_(xx)相中的單粒子能譜有兩個(gè)零點(diǎn),是一個(gè)無(wú)能隙的相.最后,利用馮·諾依曼熵?cái)?shù)值地研究了系統(tǒng)在新相內(nèi)各點(diǎn)的量子糾纏,發(fā)現(xiàn)該相內(nèi)每一點(diǎn)的馮·諾依曼熵的標(biāo)度行為與均勻XY模型在各向異性相變處的相似,即S_L～1/33襙2L+Const.
[Abstract]:The quantum phase transition and quantum entanglement of one-dimensional XY spin model with periodic anisotropy in transverse field are studied by analytical and numerical methods. In this paper, we mainly discuss the case where the period is two, that is, the anisotropy parameter alternately takes two values of the ratio 偽. The results show that the phase diagram of the model corresponding to 偽 =-1 is obviously different from that of the uniform XY model in the transverse field. The original Ising phase transition still exists, without the anisotropy ferromagnetic (FM_x,FM_y) phase along the x and y directions, that is, the anisotropy phase transition disappears and a new phase appears, and the long-range correlation function along the x and y directions in the phase is equal and greater than zero. We call the new phase isotropic ferromagnetic (FM_ (xx) phase). This is caused by the new symmetry of the system. The analytical results also show that the single particle energy spectrum of the system in FM_ (xx) phase has two zeros, which is a phase with incompetent gap. Finally, the quantum entanglement of the system at each point in the new phase is studied by using von Neiman entropy. It is found that the scaling behavior of the von Neiman entropy of each point in the phase is similar to that of the uniform XY model at the anisotropy phase transition, that is, S_L~1/33 鈮，

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